United StatesEnvironmental ProtectionAgency

Office of Water(WH 585)

EPA-823-R-92-004August 1992

TechnicalGuidanceManualforPerformingWasteLoadAllocationsBook III:Estuaries

Part 3Use Of Mixing Zone ModelsIn Estuarine Waste LoadAllocations

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TITLE: Technical Guidance Manual for Performing Wasteload Allocations,

Book III: Estuaries – Part 3: Use of Mixing Zone Models in Estuarine Waste Load Allocations

EPA DOCUMENT NUMBER: EPA-823-R92-004 DATE: August 1992 POINT OF CONTACT: TBD ABSTRACT As part of ongoing efforts to keep EPA’s technical guidance readily accessible to water quality practitioners, selected publications on Water Quality Modeling and TMDL Guidance available at http://www.epa.gov/waterscience/pc/watqual.html have been enhanced for easier access. This document is part of a series of manuals that provides technical information related to the preparation of technically sound wasteload allocations (WLAs) that ensure that acceptable water quality conditions are achieved to support designated beneficial uses. The document provides information on the legal requirements for mixing zones and describes the background and application of predictive models for mixing zone analysis. Book III Part 3 describes how the detailed prediction of conditions in the initial mixing phase of a wastewater discharge relates to legal definitions of mixing zones. It also gives an overview of the major physical processes that govern hydrodynamic mixing of aqueous discharges, and introduces (1) jet integral models that are applicable to a limited subset of near-field processes and (2) the CORMIX expert system for mixing zones, that addresses both near-field and far-field processes under a variety of conditions. Four case studies are included to illustrate the application of the jet integral models and of CORMIX. KEYWORDS: Wasteload Allocations, Estuaries, Modeling, Water Quality

Criteria, Mixing Zones

TECHNICAL GUIDANCE MANUAL

FOR PERFORMING WASTE LOAD ALLOCATIONS

BOOK III: ESTUARIES

PART 3: Use of Mixing Zone Models in Estuarine Waste Load

Allocations

Project OfficerHiranmay Biswas, Ph.D.

Edited ByRobert B. Ambrose, Jr., P.E.1James L. Martin, Ph.D., P.E.2

Prepared byGerhard H. Jirka, Ph.D., P.E.3

1. Center for Exposure Assessment Modeling,

Environmental Research Laboratory, U.S. EPA, Athens, GA

2. ASCI Corporation, U.S. EPA, Athens, Georgia

3. DeFrees Hydraulics Laboratory, School of Civil and Environmental Engineering,

Cornell University, Ithaca, NY

Prepared for

U.S. ENVIRONMENTAL PROTECTION AGENCY401 M. Street, S.W.

Washington, D.C. 20460

Table of Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..xiii

7. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1

7.1 Initial Mixing in Estuaries and Coastal Waters . . . . . . . . . . . . . . . . . 7-17.2 Mixing Zone Requirements: Legal Background . . . . . . . . . . . . . . . . 7-17.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-37.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3

8. Physical Processes and Modeling Methodologies . . . . . . . . . . . . . . . . . . 8-1

8.1 Ambient and Discharge Conditions . . . . . . . . . . . . . . . . . . . . . . 8-18.2 Hydrodynamic Mixing Processes . . . . . . . . . . . . . . . . . . . . . . . 8-18.3 Mathematical Predictive Models . . . . . . . . . . . . . . . . . . . . . . . . 8-58.4 Buoyant Jet Integral Models . . . . . . . . . . . . . . . . . . . . . . . . . . 8-78.5 CORMIX: Expert System Methodology for Mixing Zone Analysis . . . . . . 8-118.6 Mixing Zone Predictions Under Unsteady Reversing Tidal Currents . . . . 8-238.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-25

9. Case Studies of Mixing Zone Prediction . . . . . . . . . . . . . . . . . . . . . . . 9-1

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-19.2 Case AA - Single Port Discharge: Industrial Outfall in Tidal Fjord . . . . . . . 9-29.3 Case BB - Multiport Diffuser: Municipal Sewage Discharge

into Coastal Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-59.4 Case CC - Single Port Discharge: Brine Discharge From

an Oil Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-89.5 Case DD Multiport Diffusers: Cooling Water Discharge

into Shallow Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-109.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-12

GlossaryAcute Toxicity1 - Any toxic effect that is producedwithin a short period of time, usually 24-96 hours.Although the effect most frequently considered ismortality, the end result of acute toxicity is not neces-sarily death. Any harmful biological effect may be theresult.

Aerobic1 - Refers to life or processes occurring onlyin the presence of free oxygen; refers to a conditioncharacterized by an excess of free oxygen in theaquatic environment.

Algae (Alga)1 - Simple plants, many microscopic,containing chlorophyll. Algae form the base of thefood chain in aquatic environments. Some speciesmay create a nuisance when environmental condi-tions are suitable for prolific growth.

Allochthonous1- Pertaining to those substances, ma-terials or organisms in a waterway which originateoutside and are brought into the waterway.

Anaerobic2 - Refers to life or processes occurring inthe absence of free oxygen; refers to conditions char-acterized by the absence of free oxygen.

Autochthonous1 - Pertaining to those substances,materials, or organisms originating within a particularwaterway and remaining in that waterway.

Autotrophic1 - Self nourishing; denoting those organ-isms that do not require an external source of organicmaterial but can utilize light energy and manufacturetheir own food from inorganic materials; e.g., greenplants, pigmented flagellates.

Bacteria1- Microscopic, single-celled or noncellularplants, usually saprophytic or parasitic.

Benthal Deposit2 - Accumulation on the bed of awatercourse of deposits containing organic matterarising from natural erosion or discharges of waste-waters.

Benthic Region1 - The bottom of a waterway; thesubstratum that supports the benthos.

Benthal Demand2 - The demand on dissolved oxygenof water overlying benthal deposits that results fromthe upward diffusion of decomposition products of thedeposits.

Benthos1 - Organisms growing on or associated prin-cipally with the bottom of waterways. These include:(1) sessile animals such as sponges, barnacles, mus-

sels, oysters, worms, and attached algae; (2) creep-ing forms such as snails, worms, and insects; (3)burrowing forms, which include clams, worms, andsome insects; and (4) fish whose habits are moreclosely associated with the benthic region than otherzones; e.g., flounders.

Biochemical Oxygen Demand2 - A measure of thequantity of oxygen utilized in the biochemical oxida-tion of organic matter in a specified time and at aspecific temperature. It is not related to the oxygenrequirements in chemical combustion, being deter-mined entirely by the availability of the material as abiological food and by the amount of oxygen utilizedby the microorganisms during oxidation. AbbreviatedBOD.

Biological Magnification1 - The ability of certain or-ganisms to remove from the environment and store intheir tissues substances present at nontoxic levels inthe surrounding water. The concentration of thesesubstances becomes greater each higher step in thefood chain.

Bloom1 - A readily visible concentrated growth oraggregation of minute organisms, usually algae, inbodies of water.

Brackish Waters1 - Those areas where there is amixture of fresh and salt water; or, the salt content isgreater than fresh water but less than sea water; or,the salt content is greater than in sea water.

Channel Roughness2 - That roughness of a channel,including the extra roughness due to local expansionor contraction and obstacles, as well as the roughnessof the stream bed proper; that is, friction offered to theflow by the surface of the bed of the channel in contactwith the water. It is expressed as roughness coeffi-cient in the velocity formulas.

Chlorophyll1 - Green photosynthetic pigment presentin many plant and some bacterial cells. There areseven known types of chlorophyll; their presence andabundance vary from one group of photosyntheticorganisms to another.

Chronic Toxicity1 - Toxicity, marked by a long dura-tion, that produces an adverse effect on organisms.The end result of chronic toxicity can be death al-though the usual effects are sublethal; e.g., inhibitsreproduction, reduces growth, etc. These effects arereflected by changes in the productivity and popula-tion structure of the community.

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Coastal Waters1 - Those waters surrounding the con-tinent which exert a measurable influence on uses ofthe land and on its ecology. The Great Lakes and thewaters to the edge of the continental shelf.

Component Tide2 - Each of the simple tides intowhich the tide of nature is resolved. There are fiveprincipal components; principal lunar, principal solar,N2, K, and O. There are between 20 and 30 compo-nents which are used in accurate predictions of tides.

Coriolis Effect2- The deflection force of the earth’srotation. Moving bodies are deflected to the right inthe northern hemisphere and to the left in the southernhemisphere.

Datum2 - An agreed standard point or plane of stateelevation, noted by permanent bench marks on somesolid immovable structure, from which elevations aremeasured or to which they are referred.

Density Current2 - A flow of water through a largerbody of water, retaining its unmixed identity becauseof a difference in density.

Deoxygenation2 - The depletion of the dissolved oxy-gen in a liquid either under natural conditions associ-ated with the biochemical oxidation of organic matterpresent or by addition of chemical reducing agents.

Diagenetic Reaction - Chemical and physicalchanges that alter the characteristics of bottom sedi-ments. Examples of chemical reactions include oxi-dation of organic materials while compaction is anexample of a physical change.

Dispersion2 - (1) Scattering and mixing. (2) The mix-ing of polluted fluids with a large volume of water in astream or other body of water.

Dissolved Oxygen2 - The oxygen dissolved in water,wastewater, or other liquid, usually expressed in mil-ligrams per liter, or percent of saturation. AbbreviatedDO.

Diurnal2 - (1) Occurring during a 24-hr period; diurnalvariation. (2) Occurring during the day time (as op-posed to night time). (3) In tidal hydraulics, having aperiod or cycle of approximately one tidal day.

Drought2 - In general, an extended period of dryweather, or a period of deficient rainfall that mayextend over an indefinite number of days, without anyquantitative standard by which to determine the de-gree of deficiency needed to constitute a drought.Qualitatively, it may be defined by its effects as a dryperiod sufficient in length and severity to cause at

least partial crop failure or impair the ability to meet anormal water demand.

Ebb Tide1- That period of tide between a high waterand the succeeding low water; falling tide.

Enrichment1 - An increase in the quantity of nutrientsavailable to aquatic organisms for their growth.

Epilimnion1 - The water mass extending from thesurface to the thermocline in a stratified body of water;the epilimnion is less dense that the lower waters andis wind-circulated and essentially homothermous.

Estuary1 - That portion of a coastal stream influencedby the tide of the body of water into which it flows; abay, at the mouth of a river, where the tide meets theriver current; an area where fresh and marine watermix.

Euphotic Zone1 - The lighted region of a body of waterthat extends vertically from the water surface to thedepth at which photosynthesis fails to occur becauseof insufficient light penetration.

Eutrophication1 - The natural process of the maturing(aging) of a lake; the process of enrichment withnutrients, especially nitrogen and phosphorus, lead-ing to increased production of organic matter.

Firth1 - A narrow arm of the sea; also the opening ofa river into the sea.

Fjord (Fiord)1 - A narrow arm of the sea betweenhighlands.

Food Chain1 - Dependence of a series of organisms,one upon the other, for food. The chain begins withplants and ends with the largest carnivores.

Flood Tide2 - A term indiscriminately used for risingtide or landward current. Technically, flood refers tocurrent. The use of the terms “ebb” and “flood” toinclude the vertical movement (tide) leads to uncer-tainty. The terms should be applied only to the hori-zontal movement (current).

Froude’s Number2 - A numerical quantity used as anindex to characterize the type of flow in a hydraulicstructure that has the force of gravity (as the only forceproducing motion) acting in conjunction with the re-sisting force of inertia. It is equal to the square ofcharacteristic velocity (the mean, surface, or maxi-mum velocity) of the system, divided by the productof a characteristic linear dimension, such as diameteror expressed in consistent units so that the combina-tions will be dimensionaless. The number is used in

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open-channel flow studies or in cases in which the freesurface plays an essential role in influencing motion.

Heavy Metals2 - Metals that can be precipitated byhydrogen sulfide in acid solution, for example, lead,silver, gold, mercury, bismuth, copper.

Heterotrophic1 - Pertaining to organisms that aredependent on organic material for food.

Hydraulic Radius2 - The right cross-sectional area ofa stream of water divided by the length of that part ofits periphery in contact with its containing conduit; theratio of area to wetted perimeter. Also called hydraulicmean depth.

Hydrodynamics2 - The study of the motion of, and theforces acting on, fluids.

Hydrographic Survey2 - An instrumental surveymade to measure and record physical characteristicsof streams and other bodies of water within an area,including such things as location, areal extent anddepth, positions and locations of high-water marks,and locations and depths of wells.

Inlet1 - A short, narrow waterway connecting a bay,lagoon, or similar body of water with a large parentbody of water; an arm of the sea, or other body ofwater, that is long compared to its width, and that mayextend a considerable distance inland.

Inorganic Matter2 - Mineral-type compounds that aregenerally non-volatile, not combustible, and not bio-degradable. Most inorganic-type compounds, or reac-tions, are ionic in nature, and therefore, rapidreactions are characteristic.

Lagoon1 - A shallow sound, pond, or channel near orcommunicating with a larger body of water.

Limiting Factor1 - A factor whose absence, or exces-sive concentration, exerts some restraining influenceupon a population through incompatibility with spe-cies requirements or tolerance.

Manning Formula2 - A formula for open-channel flow,published by Manning in 1890, which gives the valueof c in the Chezy formula.

Manning Roughness Coefficient2 - The roughnesscoefficient in the Manning formula for determinationof the discharge coefficient in the Chezy formula.

Marsh1 - Periodically wet or continually flooded areawith the surface not deeply submerged. Covereddominantly with emersed aquatic plants; e.g., sedges,cattails, rushes.

Mean Sea Level2 - The mean plane about which thetide oscillates; the average height of the sea for allstages of the tide.

Michaelis-Menton Equation2 - A mathematical ex-pression to describe an enzyme-catalyzed biologicalreaction in which the products of a reaction are de-scribed as a function of the reactants.

Mineralization2 - The process by which elementscombined in organic form in living or dead organismsare eventually reconverted into inorganic forms to bemade available for a fresh cycle of plant growth. Themineralization of organic compounds occurs throughcombustion and through metabolism by living ani-mals. Microorganisms are ubiquitous, possess ex-tremely high growth rates and have the ability todegrade all naturally occurring organic compounds.

Modeling2 - The simulation of some physical or ab-stract phenomenon or system with another systembelieved to obey the same physical laws or abstractrules of logic, in order to predict the behavior of theformer (main system) by experimenting with latter(analogous system).

Monitoring2 - Routine observation, sampling and test-ing of designated locations or parameters to deter-mine efficiency of treatment or compliance withstandards or requirements.

Mouth2 - The exit or point of discharge of a stream intoanother stream or a lake, or the sea.

Nautical Mile2 - A unit of distance used in oceannavigation. The United States nautical mile is definedas equal to one-sixteenth of a degree of a great circleon a sphere with a surface equal to the surface of theearth. Its value, computed for the Clarke spheroid of1866, is 1,853.248 m (6,080.20ft). The Internationalnautical mile is 1,852 m (6,070.10 ft).

Nanoplankton2 - Very minute plankton not retained ina plankton net equipped with no. 25 silk bolting cloth(mesh, 0.03 to 0.04 mm.).

Neap Tides1 - Exceptionally low tides which occurtwice each month when the earth, sun and moon areat right angles to each other; these usually occurduring the moon’s first and third quarters.

Neuston2 - Organisms associated with, or dependentupon, the surface film (air-water) interface of bodiesof water.

Nitrogenous Oxygen Demand (NOD)2 - A quantita-tive measure of the amount of oxygen required for thebiological oxidation of nitrogenous material, such as

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ammonia nitrogen and organic nitrogen, in wastewa-ter; usually measured after the carbonaceous oxygendemand has been satisfied.

Nutrients1 - Elements, or compounds, essential asraw materials for organism growth and development;e.g., carbon, oxygen, nitrogen, phosphorus, etc.

Organic1 - Refers to volatile, combustible, and some-times biodegradable chemical compounds containingcarbon atoms (carbonaceous) bonded together andwith other elements. The principal groups of organicsubstances found in wastewater are proteins, carbo-hydrates, and fats and oils.

Oxygen Deficit1 - The difference between observedoxygen concentration and the amount that wouldtheoretically be present at 100% saturation for exist-ing conditions of temperature and pressure.

Pathogen1 - An organism or virus that causes a dis-ease.

Periphyton (Aufwuchs)1 - Attached microscopic or-ganisms growing on the bottom, or other submersedsubstrates, in a waterway.

Photosynthesis1 - The metabolic process by whichsimple sugars are manufactured from carbon dioxideand water by plant cells using light as an energysource.

Phytoplankton1 - Plankton consisting of plant life.Unattached microscopic plants subject to movementby wave or current action.

Plankton1 - Suspended microorganisms that haverelatively low powers of locomotion, or that drift in thewater subject to the action of waves and currents.

Quality2 - A term to describe the composite chemical,physical, and biological characteristics of a water withrespect to it’s suitability for a particular use.

Reaeration2 - The absorption of oxygen into waterunder conditions of oxygen deficiency.

Respiration1 - The complex series of chemical andphysical reactions in all living organisms by which theenergy and nutrients in foods is made available foruse. Oxygen is used and carbon dioxide releasedduring this process.

Roughness Coefficient2 - A factor, in the Chezy,Darcy-Weisbach, Hazen-Williams, Kutter, Manning,and other formulas for computing the average velocityof flow of water in a conduit or channel, which repre-

sents the effect of roughness of the confining materialon the energy losses in the flowing water.

Seiche1 - Periodic oscillations in the water level of alake or other landlocked body of water due to unequalatmospheric pressure, wind, or other cause, whichsets the surface in motion. These oscillations takeplace when a temporary local depression or elevationof the water level occurs.

Semidiurnal2 - Having a period or cycle of approxi-mately one half of a tidal day. The predominating typeof tide throughout the world is semidiurnal, with twohigh waters and two low waters each tidal day.

Slack Water2 - In tidal waters, the state of a tidalcurrent when its velocity is at a minimum, especiallythe moment when a reversing current changes direc-tion and its velocity is zero. Also, the entire period oflow velocity near the time of the turning of the currentwhen it is too weak to be of any practical importancein navigation. The relation of the time of slack waterto the tidal phases varies in different localities. Insome cases slack water occurs near the times of highand low water, while in other localities the slack watermay occur midway between high and low water.

Spring Tide1 - Exceptionally high tide which occurstwice per lunar month when there is a new or fullmoon, and the earth, sun, and moon are in a straightline.

Stratification (Density Stratification)1 -Arrange-ment of water masses into separate, distinct, horizon-tal layers as a result of differences in density; may becaused by differences in temperature, dissolved orsuspended solids.

Tidal Flat1 - The sea bottom, usually wide, flat, muddyand nonproductive, which is exposed at low tide. Amarshy or muddy area that is covered and uncoveredby the rise and fall of the tide.

Tidal Prism2 - (1) The volume of water contained in atidal basin between the elevations of high and lowwater. (2) The total amount of water that flows into atidal basin or estuary and out again with movement ofthe tide, excluding any fresh-water flows.

Tidal Range2 - The difference in elevation betweenhigh and low tide at any point or locality.

Tidal Zone (Eulittoral Zone, Intertidal Zone)1 - Thearea of shore between the limits of water level fluctua-tion; the area between the levels of high and low tides.

Tide1 - The alternate rising and falling of water levels,twice in each lunar day, due to gravitational attraction

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of the moon and sun in conjunction with the earth’srotational force.

Tide Gage2 - (1) A staff gage that indicates the heightof the tide. (2) An instrument that automatically regis-ters the rise and fall of the tide. In some instruments,the registration is accomplished by printing the heightsat regular intervals; in others by a continuous graph inwhich the height of the tide is represented by ordinatesof the curve and the corresponding time by the abscis-sae.

Toxicant1 - A substance that through its chemical orphysical action kills, injures, or impairs an organism;any environmental factor which, when altered, pro-duces a harmful biological effect.

Water Pollution1 - Alteration of the aquatic environ-ment in such a way as to interfere with a designatedbeneficial use.

Water Quality Criteria1 - A scientific requirement onwhich a decision or judgement may be based concern-ing the suitability of water quality to support a desig-nated use.

Water Quality Standard1 - A plan that is establishedby governmental authority as a program for waterpollution prevention and abatement.

Zooplankton2 - Plankton consisting of animal life.Unattached microscopic animals having minimal capa-bility for locomotion.

1Rogers, B.G., Ingram, W.T., Pearl, E.H., Welter, L.W.(Editors). 1981, Glossary, Water and WastewaterControl Engineering, Third Edition, American PublicHealth Association, American Society of Civil Engi-neers, American Water Works Association, WaterPollution Control Federation.

2Matthews, J.E., 1972, Glossary of Aquatic EcologicalTerms, Manpower Development Branch, Air andWater Programs Division, EPA, Oklahoma.

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PrefaceThe document is the third of a series of manualsproviding information and guidance for the preparationof waste load allocations. The first documents providedgeneral guidance for performing waste load allocations(Book I), as well as guidance specifically directedtoward streams and rivers (Book II). This documentprovides technical information and guidance for thepreparation of waste load allocations in estuaries. Thedocument is divided into four parts:

Part 1 of this document provides technical informationand policy guidance for the preparation of estuarinewaste load allocations. It summaries the importantwater quality problems, estuarine characterisitics andprocesses affecting those problems, and the simula-tion models available for addressing these problems.Part 2 provides a guide to monitoring and model cali-bration and testing, and a case study tutorial on simu-lation of waste load allocation problems in simplifiedestuarine systems. Part 4 summarizes several histori-cal case studies, with critical review by noted experts.

This part, “Part 3: Use of Mixing Zone Models inEstuarine Wasteload Allocations” describes the initialmixing of wastewater in estuarine and coastal environ-ments and mixing zone requirements. The importantphysical processes that govern the hydrodynamic mix-ing of aqueous discharges are detailed, followed byapplication of available models to four case studysituations.

A draft version of this document received scientificpeer review from the following modeling experts:

Donald R.F. Harleman,Massachusetts Institute of Technology

Gerald T. Orlob,University of California-Davis

Robert V. Thomann,Manhattan College

Steven J. Wright,University of Michigan

Their comments have been incorporated into the finalversion.

Organization: “Technical Guidance Manual for Performing Waste Load Allocations. Book III:Estuaries”

Part Title

1 Estuaries and Waste Load Allocation Models

2 Application of Estuarine Waste Load Allocation Models

3 Use of Mixing Zone Models in Estuarine Waste Load Allocation Modeling

4 Critical Review of Estuarine Waste Load Allocation Modeling

AcknowledgementsThe contents of this section have been removed tocomply with current EPA practice.

xiii

7. Introduction7.1 Initial Mixing in Estuaries and Coastal

WatersThe discharge of waste water into an estuary or coastalwater body can be considered from two vantage pointsregarding its impact on ambient water quality.

On a larger scale, or system wide context, care mustbe taken that water quality conditions that protectdesignated beneficial uses are achieved. This is therealm of the general waste load allocation (WLA) pro-cedures and models as discussed in the first two partsof this manual. As noted, an additional benefit of atechnically sound WLA is that excessive degrees oftreatment which are neither necessary nor productiveof corresponding improvements in water quality for thewhole water body, or at least major sections thereof,can be avoided.

On a local scale, or in the immediate discharge vicinity,additional precautions must be taken to insure thathigh initial pollutant concentrations are minimized andconstrained to small zones, areas or volumes. Thedefinition of these zones, commonly referred to as“mixing zones”, is embodied in United States waterquality regulations, on the Federal and/or State level.The mixing zone is a legally defined spatial quantity -with certain size and shape characteristics - that allowsfor initial mixing of the discharge. More recent regula-tions on discharges of toxic substances define anadditional subregion - labeled herein the “toxic dilutionzone” - within the usual mixing zone. The intent ofthose regulations is to require rapid mixing of toxicreleases to limit the exposure of aqueous flora andfauna to elevated concentrations. The detailed predic-tion of pollutant concentrations and water quality con-stituents in the initial mixing phase of a wastewaterdischarge is the realm of mixing zone models. This isthe subject of this part of the manual. Mixing zonemodels are intended to document for any given com-bination of discharge and environmental conditions thesize and shape of legally defined “mixing zones”, andfor toxic substances, of embedded “toxic dilutionzones”, and the levels of pollutant concentration withinthese zones and at their edge.

There may be a great diversity in the types of initialmixing processes for wastewater discharge. First, thesize and flow characteristics of estuaries or coastalwater can vary widely: the water body may be deep orshallow, stagnant or flowing, and may exhibit ambientdensity stratification of various degrees. Secondly, thedischarge type and configuration can be highly vari-able: the flow may contain various pollutants rangingfrom conventional to toxic substances, vary greatly in

magnitude ranging from low flowrate for a small sewagetreatment plant to the substantial cooling water flow fora large steam-electric power plant, issue with high or lowvelocity, be denser or lighter than the ambient, be lo-cated near shore or far offshore, and exhibit variousgeometric details ranging from single port submergeddischarges to multiport submerged diffusers to surfacedischarges.

Given this diversity of both discharge and ambient envi-ronmental conditions, there are a large number of pos-sible flow patterns which will develop as the dischargewaste stream mixes in the ambient water. These flowpatterns will determine the configuration, size, and in-tensity of the mixing process, and any impact of thedischarge on the water body surface, bottom, shoreline,or other areas. This, in turn, requires that engineeringanalyses, in the form of mixing zone models, be robust,adaptable and reliable under a wide spectrum of flowconditions.

7.2 Mixing Zone Requirements: LegalBackground

7.2.1 Pollutant TypesThe Clean Water Act of 1977 defines five general cate-gories of pollutants: i) conventional, ii) nonconventional,iii) toxics, iv) heat, and v) dredge and fill spoil. The Actdistinguishes between new and existing sources forsetting effluent standards. Table 7-1 lists examples ofthe first three pollutant categories.

Pollutants designated as “conventional” would be “gen-erally those pollutants that are naturally occurring, bio-degradable, oxygen demanding materials and solids. Inaddition, compounds which are not toxic and which aresimilar in characteristics to naturally occurring, biode-gradable substances are to be designated as conven-tional pollutants for the purposes of the provision”.Pollutants designated as “nonconventional” would be“those which are not toxic or conventional” (Congres-sional Research Service, 1978).

7.2.2 Mixing Zone DefinitionsThe mixing zone is defined as an “allocated impactzone” where numeric water quality criteria can be ex-ceeded as long as acutely toxic conditions are pre-vented. A mixing zone can be thought of as a limitedarea or volume where the initial dilution of a dischargeoccurs (USEPA, 1984a). Water quality standards applyat the boundary of the mixing zone, not within the mixingzone itself. USEPA and its predecessor agen-

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cies have published numerous documents giving guid-ance for determining mixing zones. Guidance publish-ed by USEPA in Water Quality Standards Handbook(1984a) supersedes these sources.

In setting requirements for mixing zones, USEPA(1984a) requires that “the area or volume of an individ-ual zone or group of zones be limited to an area orvolume as small as practicable that will not interferewith the designated uses or with the established com-munity of aquatic life in the segment for which the usesare designated,” and the shape be “a simple configu-ration that is easy to locate in the body of water andavoids impingement on biologically important areas,”and “shore hugging plumes should be avoided.”

The USEPA rules for mixing zones recognize the Statehas discretion whether or not to adopt a mixing zoneand to specify its dimensions. USEPA allows the useof a mixing zone in permit applications except whereone is prohibited in State regulations. A review ofindividual State mixing zone policies shows that 48 outof 50 States (the exceptions are Arizona and Pennsyl-vania) make use of a mixing zone in some form(USEPA, 1984a, 1985). State regulations dealing withstreams or rivers generally limit mixing zone widths orcross-sectional areas, and allow lengths to be deter-mined on a case-by-case basis.

In the case of lakes, estuaries and coastal waters,some states specify the surface area that can beaffected by the discharge. (The surface area limitationusually includes the underlying water column and ben-thic area.) If no specific mixing zone dimensions aregiven the actual shape and size can be determined ona case-by-case basis.

Special mixing zone definitions have been developedfor the discharge of municipal wastewater into thecoastal ocean, as regulated under Section 301(h) ofthe Clean Water Act (USEPA, 1982). For those dis-charges the mixing zone was labeled as the “zone of

initial dilution” in which rapid mixing of the waste stream(usually the rising buoyant fresh water plume within theambient saline water) takes place. USEPA (1982) re-quires that the “zone of initial dilution” be a regularlyshaped area (e.g. circular or rectangular) surroundingthe discharge structure (e.g. submerged pipe or diffuserline) that encompasses the regions of high (exceedingstandards) pollutant concentrations under design condi-tions. In practice, limiting boundaries defined by dimen-sions equal to the water depth measured horizontallyfrom any point of the discharge structure are acceptedby the USEPA provided they do not violate other mixingzone restrictions (USEPA, 1982).

7.2.3 Special Mixing Zone Requirements forToxic SubstancesUSEPA maintains two water quality criteria for the allow-able concentration of toxic substances: a criterion maxi-mum concentration (CMC) to protect against acute orlethal effects; and a criterion continuous concentration(CCC) to protect against chronic effects (USEPA, 1985).The less restrictive criterion, the CCC, must be met atthe edge of the same regulatory mixing zone specifiedfor conventional and nonconventional discharges.

In order to prevent lethal concentrations of toxics in theregulatory mixing zone, the restrictive CMC criterionmust be met within a short distance from the outfall orin the pipe itself. If dilution of the toxic discharge in theambient environment is allowed, this requirement, whichwill be defined here as a toxic dilution zone (TDZ), isusually more restrictive than the legal mixing zone forconventional and nonconventional pollutants. USEPA(1991) recommends four alternatives for preventingacute lethality. One alternative is to require that the CMCbe achieved within the pipe itself. The other three alter-natives allow the use of a TDZ.

The first of these involves a high-velocity dischargecombined with a mixing zone spatial limitation. For thisoption, USEPA recommends a minimum exit velocity of3 meters per second (10 feet per second) and a spatiallimitation of 50 times the discharge length scale in anydirection. The discharge length scale is defined as thesquare root of the cross-sectional area of any dischargeoutlet.

The next alternative recommended by USEPA (1991) isnot to use a high-velocity discharge, but rather to ensurethat the most restrictive of the following conditions ismet:

• The CMC must be met within 10% of the distancefrom the edge of the outfall structure to the edge ofthe regulatory mixing zone in any spatial direction.

Conventional Nonconventional Toxicbiochemical oxygendemand (BOD)

chemical oxygendemand (COD)

chloroform/lead

pH fluoride fluorenetotal suspended sol-ids (TSS)

aluminum nickel

fecal coliform bacte-ria

sulfide selenium

oils and grease ammonia benzidine

Table 7-1. Examples of Conventional, Nonconventional, andToxic Pollutants [USEPA 1984 b]

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• The CMC must be met within a distance of 50times the discharge length scale in any spatialdirection. The discharge length scale is defined asthe square-root of the cross-sectional area of anydischarge outlet. This restriction is intended toensure a dilution factor of at least 10 within thisdistance under all possible circumstances, includ-ing situations of severe bottom interaction andsurface interaction.

• The CMC must be met within a distance of 5 timesthe local water depth in any horizontal direction.The local water depth is defined as the naturalwater depth (existing prior to the installation of thedischarge outlet) prevailing under mixing zonedesign condition (e.g. low flow for rivers). Thisrestriction will prevent locating the discharge invery shallow environments or very close to shore,which would result in significant surface and bot-tom concentrations. (USEPA, 1991)

The latter of these geometric restrictions essentiallyeliminates the use of surface (canal-type) dischargesfor the discharge of toxic pollutants.

The final recommended alternative is for the dis-charger to show that a drifting organism would not beexposed to 1-hour average concentrations exceedingthe CMC, or would not receive harmful exposure whenevaluated by other valid toxicological analysis(USEPA, 1991).

7.3 SummaryThe following two chapters in Part 3 of this manual dealwith the background and the application of predictivemodels for mixing zone analysis that address thevarious legal requirements as outlined above.

Chapter 8 first gives an overview of the importantphysical processes that govern the hydrodynamic mix-ing of aqueous discharges. Emphasis is put herein onsubmerged discharges, because of the practical limi-tations on surface discharges, in particular as regardstoxic pollutants. Those processes are divided intonear-field processes (influenced directly by the dis-charge geometry and dynamics and, to some extent,controllable through appropriate design choices) and

into far-field processes (influenced primarily by the ex-isting environmental conditions). It is shown that legalmixing zone requirements can encompass, in general,processes in both near-field and far-field. Then themathematical background and formulations for differentmixing zone models are reviewed. For practical routineapplications, these models fall into two classes: (i) jetintegral models that are applicable only to a sub-set ofnear-field processes including submerged buoyant jetswithout any boundary (surface or bottom) interaction,and (ii) a mixing zone expert system, CORMIX, thataddresses both near-field and far-field processes undera variety of discharge and ambient conditions.

Chapter 9 illustrates the application of jet integral modelsand of the expert system CORMIX. Typical data require-ments for the implementation of these models are dis-cussed. Four case studies are presented in order todemonstrate the capabilities and/or limitations of individ-ual models.

7.4 ReferencesCongressional Research Service, 1978. Legislative His-tory of the Clean Water Act 1977. Congressional Re-search Service, Library of Congress, October 1978, No.95-14 P. 330.

USEPA. 1982. Revised Section 301 (h) Technical Sup-port Document. EPA 430/9-82-011, Washington, DC.

USEPA. 1984a. Water Quality Standards Handbook.Office of Water Regulations and Standards, Washing-ton, DC.

USEPA. 1984b. Technical Guidance Manual for theRegulations Promulgated Pursuant to Section 301 (g)of the Clean Water Act of 1977 (Draft). Washington, DC,August.

USEPA. 1985. Technical Support Document for WaterQuality-based Toxics Control. Office of Water, Washing-ton, DC, September.

USEPA. 1991. Technical Support Document of WaterQuality-based Toxics Control. Office of Water, Washing-ton, DC, March.

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8. Physical Processes and Modeling Methodologies8.1 Ambient and Discharge ConditionsThe mixing behavior of any wastewater discharge isgoverned by the interplay of ambient conditions in thereceiving water body and by the discharge charac-teristics.

The ambient conditions in an estuary or coastal waterbody are described by geometric parameters - such asplan shape of the estuary, vertical cross-sections, andbathymetry, especially in the discharge vicinity and byits dynamic characteristics. The latter are given by thevelocity and density distribution in the estuary, againprimarily in the discharge vicinity.

Many estuaries are highly energetic water bodies andtheir velocity field with its vertical and temporal variabil-ity may be influenced by many factors. Usually themost significant velocity component is controlled bytidal influences, but freshwater inflows, wind-drivencurrents and wave-induced currents may also playimportant roles and, in some cases, may even domi-nate the flow. Furthermore the mean velocity field isoften superposed by secondary currents due to topo-graphic effects or due to baroclinic influences givingrise to complicated three-dimensional flow fields.

The density distribution in estuaries is usually stronglycoupled with the velocity field. Density differences aremostly caused by the freshwater inflow and lighter,less saline, water tends to overflow the more salineocean water. Estuaries are sometimes classified onthe basis of their density structure into well-stratified,partially-stratified and vertically mixed estuaries (Fis-cher et al., 1979). Well stratified estuaries, usuallythose with weak tidal effects, exhibit a two-layer struc-ture with an upper predominantly fresh water layerflowing over a lower saline layer (the so-called saltwedge). The dominant vertical velocity distribution inthat instance is a seaward flow in the upper layer anda reversed landward flow in the lower layer. The otherend of the spectrum is given by vertically well mixedestuaries with strong tidal energetics leading to nearlycomplete vertical mixing although density gradientsmay still exist in the horizontal direction (i.e. along theaxis of the estuary or tidal bay).

Clearly, a major feature of estuarine ambient condi-tions is their time variability. For tidally controlled cur-rents this is given by a time scale equal to the tidalperiod. Other time scales, usually also of the order ofseveral hours, describe wind driven currents andseiche motions. However, the time scale for initial

mixing processes of effluent discharges is usually muchshorter (of the order of minutes to tens of minutes) sothat it usually suffices to analyse certain flow and densityconditions under a steady-state assumption. The con-sideration of tidal reversals and potential pollutant ac-cumulation is discussed further below (Section 8.6).

The discharge conditions relate to the geometric andflux characteristics of the submerged outfall installation.For a single port discharge the port diameter, its eleva-tion above the bottom and its orientation provide thegeometry; for multiport diffuser installations the ar-rangement of the individual ports along the diffuser line,the orientation of the diffuser line and constructiondetails represent additional geometric features. The fluxcharacteristics are given by the discharge flow rate fromthe port, by its momentum flux and by its buoyancy flux.The buoyancy represents the relative density differencebetween discharge and ambient that, upon multiplica-tion with the gravitational acceleration, is a measure ofthe tendency for the effluent flow to rise (for positivebuoyancy) or to fall (for negative buoyancy).

8.2 Hydrodynamic Mixing ProcessesThe hydrodynamics of an effluent continuously dis-charging into a receiving body of water can be concep-tualized as a mixing process occurring in two separateregions. In the first region, the initial jet characteristicsof momentum flux, buoyancy flux, and outfall geometryinfluence the jet trajectory and mixing. This region willbe referred to as the “near-field”, and encompasses thebuoyant jet subsurface flow and any surface or bottominteraction, or in the case of a stratified ambient, termi-nal layer interaction. In this region, designers of theoutfall can usually affect the initial mixing characteristicsthrough appropriate manipulation of design variables.

As the turbulent plume travels further away from thesource, the source characteristics become less impor-tant. Conditions existing in the ambient environment willcontrol trajectory and dilution of the turbulent plumethrough buoyant spreading motions and passive diffu-sion due to ambient turbulence. This region will bereferred to here as the “far-field”.

It is stressed at this point that the distinction betweennear-field and far-field is made purely on hydrodynamicgrounds. It is unrelated to any legal mixing zone defini-tions that address prescribed water quality standards asdiscussed in Section 7.2.2. In many practical cases thelegal mixing zone may, in fact, include near-field hydro-dynamic mixing processes. But that does not

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have to be so: For example, buoyant jet mixing in adeep environment with crossflow may extend far be-yond a legal mixing zone that is defined by a horizontallength equal to the water depth on the basis of section301(h) of the Clean Water Act (USEPA, 1982). As acounter-example, a small source in a strong crossflowmay rapidly enter the passive far-field diffusion region(in form of a bottom attached plume) well before theedge of a legal mixing zone! Thus, in principle, thewhole gamut of mixing processes, ranging from thenear-field to the far-field, must be considered for indi-vidual mixing zone analyses.

8.2.1 Near-Field Processes8.2.1.1 Buoyant Jet MixingThe effluent flow from a submerged discharge portprovides a velocity discontinuity between the dis-charged fluid and the ambient fluid causing an intenseshearing action. The shearing flow breaks rapidlydown into a turbulent motion. The width of the zone ofhigh turbulence intensity increases in the direction ofthe flow by incorporating (“entraining”) more of theoutside, less turbulent fluid into this zone. In this man-ner, any internal concentrations (e.g. of fluid momen-tum or of pollutants) become diluted by theentrainment of ambient water. Inversely, one can

speak of the fact that both fluid momentum and pollut-ants become gradually diffused into the ambient field.

The initial velocity discontinuity may arise in differentfashions. In a “pure jet” (also called “momentum jet” or“non-buoyant jet”), the initial momentum flux in the formof a high-velocity injection causes the turbulent mixing.In a “pure plume,” the initial buoyancy flux leads to localvertical accelerations which then lead to turbulent mix-ing. In the general case of a “buoyant jet” (also called a“forced plume”), a combination of initial momentum fluxand buoyancy flux is responsible.

Thus, buoyant jets are characterized by a narrow turbu-lent fluid zone in which vigorous mixing takes place.Furthermore, depending on discharge orientation andthe direction of buoyant acceleration, generally curvedtrajectories are established in a stagnant uniform-den-sity environment (see Figure 8-1).

Buoyant jet mixing is further affected by ambient cur-rents and density stratification. The role of ambientcurrents is to gradually deflect the buoyant jet into thecurrent direction and to induce additional mixing. Therole of ambient stratification is to counteract the verticalacceleration within the buoyant jet leading ultimately

Figure 8-1. Buoyant jet with round or slot geometry in stagnant uniform-density environment.

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to trapping of the flow at a certain level (trapping levelor terminal level).

8.2.1.2 Boundary Interaction Processes and Near-FieldStabilityAmbient water bodies always have vertical bounda-ries: these are the water surface and the bottom, butin addition “internal boundaries” may exist in the formof layers of rapid density change (pycnoclines). De-pending on the dynamic and geometric characteristicsof the discharge flow, a variety of interaction phenom-ena can occur at such boundaries. Furthermore, in thecase of a continuously (e.g. linearly) stratified ambientwhere flow trapping may occur, other interaction phe-nomena may take place.

In essence, these interaction processes provide atransition between the buoyant jet mixing process inthe near-field, and between buoyant spreading andpassive diffusion in the far-field.

Interaction processes can be (i) gradual and mild or (ii)abrupt leading to vigorous transition and mixing proc-esses. (i) If a buoyant jet is bent-over by the cross-flow

it will gradually approach the surface, bottom or terminallevel and will undergo a smooth transition with littleadditional mixing.

(ii) If a jet is impinging normally, or near-normally, on aboundary, it will rapidly spread in all directions (seeFigure 8-2). Different possibilities exist at that point: (a)If the flow has sufficient buoyancy it will ultimately forma stable layer at the surface (Figure 8-2a,c). In thepresence of weak ambient flow this will lead to anupstream intrusion against the ambient current. (b) If thebuoyancy of the effluent flow is weak or its momentumvery high, unstable recirculation phenomena can occurin the discharge vicinity (see Figure 8-2b,d). This localrecirculation leads to re-entrainment of already mixedwater back into the buoyant jet region. Thus, simplebuoyant jet analyses no longer suffice to predict thesephenomena.

The aspect of near-field stability, i.e. the distinction intostable or unstable conditions, is a key feature of pollu-tion analyses. “Stable discharge” conditions, usuallyoccurring for a combination of strong buoyancy, weakmomentum and deep water, are often referred as “deep

Figure 8-2. Stable or unstable near-field flows produced by submerged buoyant discharges.

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water” conditions. “Unstable discharge” conditions, onthe other had, may be considered synonymous to“shallow water” conditions. Further detail on dischargestability can be found in Jirka (1982 a,b) and Holleyand Jirka (1986).

Yet another type of interaction process concerns sub-merged buoyant jets discharging in the vicinity of thewater bottom into a stagnant or crossflowing ambient.Two types of dynamic interaction processes can occurthat lead to rapid attachment of the effluent plume tothe water bottom (see Figure 8-3). These may be wakeattachment forced by the crossflow or Coanda attach-ment (due to low pressure effects) forced by the en-trainment demand of the effluent jet itself. In eithercase the assumption of free buoyant jets is invalidatedand other analyses have to be pursued for thesebottom-attached flows.

8.2.1.3 Multiport Diffuser Induced Flows in ShallowWater (Intermediate-Field)Some multiport diffuser installations represent largesources of momentum, while their buoyancy effectsmay be relatively weak. Therefore these diffusers willhave an unstable near-field with shallow water condi-tions. This is characteristic, for example, for coolingwater diffusers from thermal power plants. For certaindiffuser geometries (i.e. the unidirectional and thestaged diffuser types; see Section 8.3) strong motionscan be induced in the shallow water environment in theform of vertically mixed currents that laterally entrainambient water and may extend over long distancesbefore they re-stratify or dissipate their momentum. Ina sense, these “diffuser plumes” extend beyond the

strict near-field (of the order of the water depth) and aresometimes referred to as the “intermediate-field” (Jirka,1982b).

8.2.2 Far-Field ProcessesIn the context of this report, far-field mixing processesare characterized by the longitudinal advection of themixed effluent by the ambient current velocity.

8.2.2.1 Buoyant Spreading ProcessesBuoyant spreading processes are defined as the hori-zontally transverse spreading of the mixed effluent flowwhile it is being advected downstream by the ambientcurrent. Such spreading processes arise due to thebuoyant forces caused by the density difference of themixed flow relative to the ambient density. If the dis-charge is nonbuoyant, or weakly buoyant, and the am-bient is unstratified, there is no buoyant spreadingregion in the far-field, only a passive diffusion region.

Depending on the type of near-field flow and ambientstratification several types of buoyant spreading mayoccur: (i) spreading at the water surface, (ii) spreadingat the bottom, (iii) spreading at a sharp internal interface(pycnocline) with a density jump, or (iv) spreading at theterminal level in continuously (e.g. linearly) stratifiedambient fluid.

As an example, the definition diagram and structure ofsurface buoyant spreading processes in unstratifiedcrossflow is shown in Figure 8-4. The laterally spread-

Figure 8-3. Bottom attachment processes for submergeddischarges.

Figure 8-4. Buoyant spreading processes in the far-field(Example: surface spreading).

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ing flow behaves like a density current and entrainssome ambient fluid in the “head region” of the current.The mixing rate is usually relatively small. Further-more, the flow may interact with a nearby bank orshoreline (not shown in the figure). The layer thicknessmay decrease during this phase.

Depending on source and ambient characteristics,buoyant spreading processes can be effective trans-port mechanisms that can quickly spread a mixedeffluent laterally over large distances in the transversedirection. This can be particularly pronounced in casesof strong ambient stratification in which the effluent atthe terminal level that may initially be of considerablevertical thickness collapses into a thin but very widelayer unless this is prevented by lateral boundaries.

8.2.2.2 Passive Ambient Diffusion ProcessesThe existing turbulence in the ambient environmentbecomes the dominating mixing mechanism at suffi-ciently large distances from the discharge point. Theintensity of this passive diffusion process dependsupon the geometry of the ambient shear flow as wellas any existing stratification. In general, the passivelydiffusing flow is growing in width and in thickness (seeFigure 8-5). Furthermore, it may interact with the chan-nel bottom and/or banks.

The strength of the ambient diffusion mechanism de-pends on a number of factors relating mainly to thegeometry of the ambient shear flow and the ambientstratification. In the context of classical diffusion theory(i.e. gradient diffusion, see Fischer et al., 1979) diffu-sion processes in bounded flows (e.g. rivers or narrowestuaries) can be described by constant diffusivities inthe vertical and horizontal direction that depend onturbulent intensity and on channel depth or width asthe length scales. On the other hand, wide “un-bounded” channels or open coastal areas are charac-

terized by plume size dependent diffusivities leading toaccelerating plume growth described, for example, bythe “4/3 law” of diffusion. In the presence of a stableambient stratification the vertical diffusive mixing is gen-erally strongly damped.

8.3 Mathematical Predictive Models

8.3.1 Modeling MethodologyIn principle, one can conceive of two approaches to theprediction of effluent discharges in the water environ-ment: complete models or zone models.

(i) Complete models: These are three-dimensional nu-merical models that directly solve a finite difference orfinite element approximation for the full dynamic andmass conservation equations with various assumptionsfor the turbulent shear and mass transport terms. Inprinciple, with the advent of powerful computing facili-ties, even on the desktop, such a complete modelingapproach that encompasses the entire fluid domain ofinterest with all individual mixing processes appearsfeasible. However, successful applications to date havebeen limited. Apparent reasons for the present short-comings include (1) lack of fully workable turbulenceclosure techniques under the influence of buoyancywhile considering the full range of jet-induced geophysi-cal turbulence; (2) the difficult trade-off of modeling alarge enough domain while providing sufficient resolu-tion in a three-dimensional model (computer capacityand costs); and (3) the unknown nature of the open fluidboundary conditions which need to be specified as partof the elliptic equation system. These boundaries may,in general, contain a combination of stratified inflow andoutflow that is inherently difficult to specify. For thesereasons, complete numerical models are usually notused in routine mixing zone analyses of effluent dis-charges and this is expected to remain so for at leastthe next decade.

(ii) Zone Models: Instead of attempting to integrate thegeneral governing equations over the whole region ofinterest it is frequently useful to divide the region intoseveral zones with distinct behavior (such as individualmixing processes in the near-field and in the far-field).Within these zones it is then possible to simplify thegoverning equations by dropping unimportant terms.This gives a considerable advantage in the mathemati-cal treatment and improved accuracy in the solution.However, a challenge remains because the solutionsare restricted to specific zones. Thus, criteria need tobe established for a meaningful division of the wholeregion into zones, and to provide transition conditionsbetween zones.

Figure 8-5. Passive ambient diffusion processes.

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Current practice in pollution analyses relies on zonemodels. Such models that deal with individual flowprocesses are described in the specialized researchliterature as well as in several monographs (e.g. Fis-cher et al., 1979, Holley and Jirka, 1986). However, aproblem arises because there is limited guidance tothe model user on the limits of applicability of eachmodel, and on how to combine the individual modelsfor an overall prediction of the entire flow process. Theuse of an integrated expert system framework (seebelow) promises to alleviate this problem.

An important group of zone models are the so-calledbuoyant jet integral models that are limited to thebuoyant jet mixing process as described in Section8.2.1.1 without attention to any problems of boundaryinteraction and near-field instability. Several of suchintegral model formulations are available as computerprograms. Whenever their applicability has been as-certained, these models have been found throughnumerous data-model comparisons to be reliable andaccurate. Jet integral models will be reviewed in Sec-tion 8.4.

An integrated framework of zone models for all impor-tant near-field and far-field mixing processes that effecteffluent mixing has recently been developed. Thisframework is in the form of an expert system thatclassifies each discharge/ambient condition as towhich flow processes are important and provides aprediction through a sequence of zone models withappropriate transition conditions. The zone modelingexpert system methodology CORMIX (Doneker andJirka, 1990; Akar and Jirka, 1991) is discussed inSections 8.5 and 8.6.

8.3.2. Zone Model Schematizations ofDischarge and Ambient ConditionsAll zone models require some schematization of thecomplex and arbitrary ambient and discharge condi-tions that may prevail at any discharge site. Thesesimplifications are needed to conform to the require-ments of the individual models.

A schematic definition diagram for a single port dis-charge is given in Figure 8-6. The bottom is assumedto be flat (constant depth) while any banks (if consid-ered in the analysis) are assumed to be vertical.

A corresponding diagram for multiport diffusers is pro-vided in Figure 8-7. Of particular interest for this caseis the alignment angle γ between the crossflow direc-tion and the diffuser axis, the orientation angle β be-tween the individual port axes and the diffuser line, andthe vertical angle θ between port axis and the horizon-tal plane. Three major diffuser types have evolved in

actual design practice and can be characterized bythese angles (see Figure 8-8).

In the unidirectional diffuser, all the ports point in thesame direction perpendicular to the diffuser axis( β=90o). In the staged diffuser, all ports point along thediffuser line ( β = 0o). In the alternating diffuser, theports are arranged in an alternating fashion and point inopposite directions ( β=± 90o). The undirectional andthe staged diffusers possess a net horizontal momen-tum input with a tendency to induce currents within theambient water body. The alternating diffuser has a zeronet horizontal momentum, and a lesser tendency togenerate currents and circulations.

Of course, there are variations on the basic theme foreach of the three diffuser types. Some of these designpossibilities are shown in Figure 8-8. There may bedouble or triple nozzle arrangements (with a small inter-nal angle) for both unidirectional or staged diffusers, andthe port orientation angle β may differ somewhat fromthe nominal value, 90o or 0o, respectively. Or, in caseof the alternating diffuser, there may be multiple portassemblies for each riser with several ports arranged ina circular fashion. Furthermore, alternating diffusers forthermal discharges in shallow water may have a vari-able port orientation along the diffuser axis to controlinstabilities and horizontal circulations (for details, seeJirka, 1982b). Another special case of

Figure 8-6. Schematics of single port discharge geometry inambient channel with rectangular cross-section(width W may be finite or unlimited).

Figure 8-7. Schematics of multiport diffuser geometry inambient channel with rectangular cross-section(width W may be finite or unlimited).

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an alternating diffuser is given by a vertical dischargefrom all ports.

Any diffuser can be deployed with arbitrary alignmentγ. However, the two major arrangements are theperpendicular alignment ( γ ≈ 90 o) and the parallelalignment ( γ ≈ 0o).

8.4 Buoyant Jet Integral Models

8.4.1 Basic Elements: Stagnant UnstratifiedAmbient

The narrow elongated shape of the turbulent zonewithin a buoyant jet (see Figure 8-1) suggests bound-ary-layer type simplifications to the equations of fluidmotion and mass transport. The equations may befurther simplified by integrating across the local jetcross-section thereby yielding a one-dimensionalequation set for the actual three-dimensional problem.This is the essence of jet integral models which solvethe equation set with a simple integration schememarching forward along the trajectory.

The integral method is demonstrated in the followingfor a round buoyant jet issuing into a stagnant unstrati-fied ambient (Figure 8-1). The jet-trajectory is assumedto lie within an x-z coordinate system. Local integrationacross the buoyant jet gives the following flux (integral)quantities:

V

olume flux: Q = 2π∫ u0

∞r d r = 2π I1 uc b2 (1)

Momentum flux (kinematic):

M = 2 π ∫o

∞u2 r d r = 2 π I2 u c

2 b2 (2)

Scalar (pollutant) mass flux:

Q c = 2 π ∫o

∞u c r d r = 2π I3 uc cc b2 (3)

Buoyancy flux:

J = 2π ∫o

∞u g ′ r d r = 2π I3 uc gc

′ b 2 (4)

in which u = mean velocity in the trajectory direction, r= transverse coordinate from local jet centerline, c =mean concentration, and g ′ = mean buoyant accelera-tion relative to the outside fluid where

g′ =ρa − ρ

ρag (5)

ρ = local density, ρa = ambient density, and g = gravita-tional acceleration. In the rightmost integrated quanti-ties, the subscript c indicates centerline values, and thewidth b is a measure of the width of the jet (see below).The profile constants I 1, I 2, I 3, are simple numericalvalues that depend on the chosen profile shape and onthe width definition (see Holley and Jirka, 1986). Fre-quently, a bell-shaped Gaussian profile is

Figure 8-8. Schematic plan views of three major diffuser types: a) Unidirectional diffuser, b) Staged Diffuser, c) Alternatingdiffuser. Any of those diffusers may have a variable alignment γ relative to the ambient current.

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chosen and the width b is conveniently defined by the“1/e width” where the local quantities are 1/e = 37% ofthe centerline value.

When the conservation laws are applied to these fourflux quantities using a control volume of differentiallength ds where s = axial direction along trajectory thefollowing differential equations arise:

Volume flux conservation: dQds = 2π α uc b (6)

i.e. the volume flux (discharge) increases due to en-trainment along the jet periphery.

Axial momentum flux conservation:dMds = 2π I4 gc

′ b 2 sin θ (7)

i.e., only the sin θ component of buoyancy producesacceleration in the axial direction, in which θ = localvertical angle.

Horizontal momentum flux conservation:dds (M cos θ) = 0 (8)

i.e., no acceleration in the horizontal direction.

Scalar flux conservation: dQcds = 0 (9)

Buoyancy flux conservation: dJds = 0 (10)

i.e. in the uniform ambient environment both fluxesstay constant.

In addition, it is necessary to relate the local coordinatesystem ( s, θ ) to the fixed global one ( x, y )

dxds = cos θ (11)

dzds = sin θ (12)

This system of seven ordinary differential equations isfully specified by seven initial conditions at s = 0. Theseare the initial bulk fluxes Mo , Jo , Qo , and Qco (alter-natively,given by Uo , go

′ = g (ρa − ρo) ⁄ ρa , co , and Dand the geometry xo , zo , and θo.

Solution of this ordinary differential equation system byany chosen numerical method yields the seven localbuoyant jet measures. These are M, J, Q, and Qc (oralternatively, the related variables uc , gc

′ , cc , and b)and the trajectory measures x, z, and θ . The local bulk

(flux-averaged) dilution is then given by the ratioQ ⁄ Qo and the local centerline (minimum) dilution by theratio co ⁄ cc.

Two fundamental difficulties exist in the jet integralmethod:

(i) The closure problem: Entrainment and mixing ofambient fluid is a turbulent flow phenomenon. Thevolume flux conservation, Equation 6, presupposes thatthe mean entrainment velocity ve , (see Figure 8-1) islinearly related to the centerline velocity, ve = α uc,where α = entrainment coefficient. Inspection of dataon buoyant jets that undergo a transition from initialjet-like (momentum-dominated) to final plume-like(buoyancy-dominated) behavior shows that α is quitevariable. In some integral models a geometric equationis used instead of Equation 6, namely

Jet spreading: dbds = k (6a)

In which k = spreading coefficient with somewhat lessvariability between the jet-like and plume-like stages.The actual choice of the appropriate equation, Eqs. 6 or6a, and the specification of the coefficient that may bea function of local flow conditions is generally referredto as the “closure problem”. The closure is made differ-ently in the various integral models. A more detaileddiscussion is given by Holley and Jirka (1986).

(ii) The zone of flow establishment: The above equationset is, strictly speaking, not valid in a short initial zoneof flow establishment in which a gradual adjustmentbetween the efflux profile (approximately uniform) to thefinal bell-shaped profile takes place. Since this zone isshort ( ≈ 5D to 10D, where D = diameter of the dischargeport), no major error is introduced if it is simply ne-glected. This is the case in some integral models.Alternately, some models include an adjustment via avirtual origin or others perform a detailed, though ap-proximate, analysis of this zone.

The derivation of integral jet equations for the slotbuoyant jet (see the alternative source conditions indi-cated in Figure 8-1) is quite analogous to the round jet.It is omitted here for brevity (see Holley and Jirka, 1986).The slot buoyant jet is an important element of theanalysis of subsurface multiport diffuser plumes that areformed after merging of the individual round jets.

8.4.2 Extensions to Flowing Stratified AmbientsThe advantage of jet integral models is their readyextension to more complex environmental conditions,such as ambient stratification and crossflow.

8-8

If the receiving water is stratified with a stable densitygradient (dρa ⁄ dz < 0, i .e. the ambient density= ρa ( z ) decreases upward), then the buoyancy flux isnot conserved along an upward jet trajectory but isconstantly decreasing. Eventually the buoyant jet willreach, and may even overshoot, its terminal level zt atwhich the local internal jet density is equal to theambient density ρa ( z t ). The jet will become trappedat this level and spread horizontally in the form of agravitational current. The jet mechanics prior to theterminal level are readily described with the integraltechnique if two extensions are made. First, the buoy-ancy profiles are now defined with respect to the localreference buoyancy

g′ =ρa (z) −ρ

ρa (z)g (13)

instead of Equation 2, leading to modification of Equa-tions 3 and 7, respectively. Second, from mass bal-ance requirements, the buoyancy flux is decreasing atthe same rate at which it is diluted with ambient waterof lesser density. This leads to

d Jd s

= Q gρa

d ρ ad s

(14)

for the round jet, instead of Equation 10. Inherent inthese expressions is the assumption that the average

density of the entrained water is equal to the density atthe level of trajectory (centerline). This excludes casesof very rapid local changes, such as steep pycnoclinesin estuaries.

When a round buoyant jet is discharged into an ambientcrossflow of velocity ua , then it will be deflected in thedirection of the crossflow. This deflection is broughtabout by two force mechanisms, a pressure drag forceFD and a force Fe due to the entrainment of crossflowmomentum. Referring to Figure 8-9, this situation isreadily described in the integral analysis frameworkprovided that several adjustments are made. First, ne-glecting the horseshoe or “kidney” shape (Fischer et al.,1979) which actually exists and assuming that the jetmay be approximated by a circular cross-section, thevelocity profile in the jet cross-section is given by thesum of the ambient velocity component in the directionof the trajectory, ua cos θ, and the bell-shaped jet pro-file. This, then, affects the definition of all jet bulk fluxvariables, M, J, Q and Qc. The definition of the dragforce normal to the jet axis, and per unit length of the jetaxis, is (in kinematic units)

FD = 12 CD ua

2 sin2 θ (2b) (15)

in which CD is a drag coefficient (of order of unity), andthe width of the “jet body” is simply taken as 2b. The

Figure 8-9. Round buoyant jet in ambient crossflow with drag and entrainment forces (Example: vertical discharge).

8-9

entrainment force (entrainment of ambient momen-tum) is

Fe = uadQds (16)

The governing momentum equations, Equations 7 and8 are amplified to

dMds = 2π I4 gc

′ b 2 sin θ + Fe cos θ (17)

dds (M cos θ) = Fe + FD sin θ (18)

Also, it is observed in bent-over jets that the entrain-ment mechanism is considerably more vigorous andthe entrainment velocity not simply proportional to ucas in the previous case. Several analyses have sug-gested that jet entrainment in crossflows has a secondcontribution once the jet is strongly bent-over but stillslowly rising. This second contribution is similar to thatof a horizontal line element of fluid that is rising due toan initial vertical impulse of momentum or due to initialbuoyancy in a stagnant ambient fluid. The rising lineelement experiences turbulent growth and entrain-ment that is proportional to the velocity of rise. Sincethe strongly bent-over jet is similar to this line element,this second entrainment mechanism can be added tothe original entrainment mechanism associated withthe excess of forward jet velocity relative to the sur-rounding fluid. The result is

dQds = 2π α uc b + 2π α2 ua b sin θ cos θ (19)

where α is of the same form as for a buoyant jet instagnant ambient (Equation 6) and α2 is the crossflowinduced entrainment coefficient.

8.4.3 Overview of Jet Integral Models Availablefor Mixing Zone Analysis

A large number of jet integral models for submergedsingle port or multiport discharges are reported in theliterature. However, only a few of these are availablefor practical mixing zone analysis in the form of com-puter programs accessible to the analyst. Several ofthese are discussed below.

The validity and reliability of a jet integral model shouldbe promulgated on at least two considerations: First,is its theoretical formulation sound and does it performaccurately under limiting conditions (e.g. the pure jetor pure plume)? Second, how do the model predic-tions compare with available data, preferably fielddata? No complete evaluation on these grounds ofintegral jet models is attempted here, but some impor-

tant model features will be addressed in Section 3. It isstressed again that none of the following integral jetmodels include any form of boundary interaction proc-esses; in a sense they all assume an unlimited receivingwater body.

The U.S. EPA has published a set of five buoyant jetintegral models (Muellenhoff et al., 1985), all with differ-ent capabilities. These models include computer pro-grams written in FORTRAN for micro or minicomputers.

(1) The computer model UPLUME describes a buoyantjet issuing from a single port into a stagnant environmentwith arbitrary stratification. UPLUME is based on Abra-ham’s (1963) original development using a jet spreadingequation for closure. Empirical adjustment expressionsare included for the zone of flow establishment.

(2) The model UOUTPLM (based on Winiarski andFrick, 1976) uses a somewhat different Lagrangiandescription of buoyant jet mechanics instead of theEulerian system of equations given in Section 8.4.1.Thus, a plume element is tracked in its time-dependentevolution. However, the mechanisms actually includedare similar to the ones discussed above with the excep-tion of the omission of the ambient drag force. Themodel is applicable to a uniform crossflow with co-flow-ing or cross-flowing single port orientation (excludingcounterflows) and with arbitrary density stratification.The model is not applicable for stagnant conditions.

(3) The model UMERGE is an extension of UOUTPLMapplicable to multiport diffusers with perpendicularalignment. Merging is assumed to occur when geomet-ric overlap of the individual equally spaced round jetsoccurs. After merging, the flow is described by thetime-dependent motion of two-dimensional plume ele-ments.

(4) UDKHDEN is a model that computes three-dimen-sional trajectories from either single port or multiportdischarges in crossflows with arbitrary velocity (shearflow) and density distributions. The model is based onthe development by Hirst (1971) and later generaliza-tions by Kannberg and Davis (1976). The initial zone offlow establishment is computed in detail with Hirst’smodel. The three-dimensional equation system is ageneralization of the type discussed in the precedingsection. An entrainment function with dependence on alocal densimetric Froude number is used for closure. Aspecial geometric merging routine describes the grad-ual transition from individual round plumes to the two-dimensional plume. However, the same entrainmentcoefficient is used for round and for plane buoyant jets,making it impossible to verify the model

8-10

for well-known asymptotic conditions. The diffuseralignment relative to the crossflow must be predomi-nantly perpendicular.

(5) The model ULINE is strictly speaking not a jetintegral model but uses an analytical solution for thetwo-dimensional slot plume dilution as a function ofelevation. This solution is modified on the basis ofRoberts’ (1977) experimental results for the effect ofalignment on a diffuser line plume in crossflow. Also astepwise algorithm is included to compute local mixingin an arbitrary crossflow and stratification. The modelomits the merging process, thus assuming an initiallymerged (e.g. closely spaced) diffuser discharge.

Another buoyant jet model is that of Jirka and Fong(1981) to predict general three-dimensional trajecto-ries for a single port discharge in a crossflow witharbitrary stratification. The model uses empirical de-scriptions for the zone of flow establishment as pro-posed by Schatzmann (1978). The model includes anentrainment closure that meets several limiting condi-tions and that has been extensively verified by Wong(1984) in application to ambient stratification. An addi-tional element of the Jirka-Fong model is the descrip-tion of the internal vortex mechanism in crossflow thatcan lead to plume bifurcation when a flow boundary orterminal level is encountered.

8.5 CORMIX: Expert System Methodologyfor Mixing Zone Analysis

8.5.1 IntroductionThe Cornell Mixing Zone Expert System (CORMIX) isa series of software elements for the analysis anddesign of submerged buoyant or nonbuoyant dis-charges containing conventional or toxic pollutants intostratified or unstratified watercourses, with emphasison the geometry and dilution characteristics of theinitial mixing zone. Subsystem CORMIX1 (Donekerand Jirka, 1990) deals with single port discharges andsubsystem CORMIX2 (Akar and Jirka, 1991) ad-dresses multiport diffusers [Another subsystem, COR-MIX3 (Jones and Jirka, 1991), has been developed forsurface discharges, but is not discussed here given thelimitations of surface discharges in meeting toxic dilu-tion criteria; see Chapter 7]. The system is imple-mented on microcomputers with the MS-DOSoperating system.

The user supplies CORMIX with information about thedischarge and ambient environment. CORMIX returnsinformation detailing the hydrodynamic mechanismscontrolling the flow, dilution, geometric informationconcerning the shape of the pollutant plume or flow inthe ambient water body, and design recommendationsallowing the user to improve the dilution characteristics

of the flow. If specified by the user, CORMIX alsopresents information about legal mixing zone dimen-sions and dilution and about toxic mixing zone require-ments.

CORMIX contains two key elements. The first is arigorous flow classification scheme that classifies anygiven discharge/environment situation into one of sev-eral flow classes with distinct hydrodynamic features.The classification scheme places major emphasis onthe near-field behavior of the discharge and uses thelength scale concept as a measure of the influence ofeach potential mixing process. Flow behavior in thefar-field, mostly in the form of boundary interactions, isalso considered.

The second key element is a collection of predictiveelements (modules) that are executed according to aprotocol that pertains to each distinct flow class asdetermined by the classification scheme. These predic-tive elements are all based on simple analytical pertur-bation solutions for each flow process. Furthermore,transition rules are used to describe the spatial extentof each flow process.

The final result is a robust composite flow and mixingzone prediction that is applicable to a diverse variety ofdischarge/ambient conditions. CORMIX1 and 2 havebeen extensively validated with both laboratory and fielddata.

The geometric schematizations assumed in CORMIXhave been summarized in Figures 8-6 to 8-8, respec-tively. In addition, CORMIX assumes a uniform un-sheared ambient velocity profile represented by themean velocity ua. Furthermore, CORMIX requires thatthe ambient density profile be approximated by one offour representative stable profiles as shown in Figure8-10. A dynamically correct approximation of the actualdistribution should keep a balance between over- andunder-estimation of the actual density data. The sim-plest case is a linear density profile shown in Figure8-10a (Stratification Type A). Figure 8-10b describestwo uniform density layers with a density jump (pycno-cline) between layers (Stratification Type B). Figure8-10c illustrates a two layer profile in which the upperlayer is uniform, the lower layer has a linear stratifica-tion, and a density jump occurs between layers (Strati-fication Type C). Finally, Figure 8-10d presents a twolayer system with a uniform upper layer and a linearlystratified bottom layer with no density jump betweenlayers (Stratification Type D). The uniform upper layersin Stratification Types B, C, or D are representative forthe well mixed upper layer that is found in many typesof ambient water bodies and occurs due to wind inducedturbulent mixing.

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8.5.2 Length ScalesLength scales, obtained from dimensional analysis,describe the relative importance of discharge volumeflux, momentum flux, buoyancy flux, ambient cross-flow, and density stratification in controlling flow behav-ior. The length scales will describe the distance overwhich these dynamic quantities control the flow, inparticular within the subsurface buoyant jet regions ofthe mixing process.

8.5.2.1 Single Port DischargesGiven the important flux parameters, Qo , Mo , andJo (see Figure 8-5), the ambient velocity ua, and thebuoyancy gradient ε = − ( g ⁄ ρa ) ( d ρa ⁄ d z ) of a line-arly stratified ambient, the following dynamic lengthscales can be derived for a single port discharge:

LQ = Qo ⁄ Mo1⁄2= discharge (geometric) scale

LM = Mo3⁄4 ⁄ Jo

1⁄2 = jet/plume transition scale

Lm = Mo1⁄2 ⁄ ua = jet/crossflow scale

Lb = Jo ⁄ ua3 = plume/crossflow scale

Lm′ = (Mo ⁄ ε )

1⁄4 = jet/stratification scale

Lb′ = Jo

1⁄4 ⁄ ε3⁄8 = plume/stratification scale

The meaning of these scales is further illustrated inFigure 8-11. For example, the jet/crossflow lengthscale is a measure for the distance over which a purejet will intrude into a crossflow before it gets stronglydeflected (or affected). It should be noted that thelength measures are only “order of magnitude”; pre-

cise coefficients have to be determined from experi-ments or from more detailed flow analysis.

8.5.2.2 Multiport DiffusersThe general diffuser flow field is, of course, three-dimen-sional. However, for near-field mixing analyses the two-dimensional flow parameters are dynamically relevant.For this purpose, the details of individual discharge jetswith port diameter D and spacing S are neglected andreplaced by an equivalent slot width B =(πD2) ⁄ (4 S ) onthe basis of equivalency of momentum flux per unitdiffuser length. This concept has been discussed byJirka (1982b) among others, and has been shown to bea dynamically accurate representation. The main pa-rameters for the two-dimensional slot discharge are thediffuser total flowrate Qc and the discharge buoyancygo

′ . This leads to the following flux parameters (per unitdiffuser length), all expressed in kinematic units:

qo = Qo ⁄ LD = volume flux (flowrate)

mo = qo Uo = Uo2 B = momentum flux

jo = qgo′ = Uogo

′ B = buoyancy flux,

in whichUo = discharge velocity, and

LD = diffuser length.

Through interaction with the ambient parameters, thefollowing length scales describe a multiport diffuserdischarge:

lq = q o2 ⁄ mo = discharge geometric scale

lm = mo ⁄ uα2 = plane jet/crossflow scale

Figure 8-10. Schematic ambient density profiles for use in expert system CORMIX.

8-12

Figure 8-11. Length scales measuring the effects of momentum flux, buoyancy flux, crossflow and stratification of submerged jet behavior.

8-13

lM = mo ⁄ jo2⁄3 = plane jet/plane plume scale

lm′ = (mo ⁄ ε)1⁄3 = plane jet/stratification scale

lb′ = jo1⁄3 ⁄ ε

1⁄2 = plane plume/stratification scale

la = ua ⁄ ε1⁄2 = crossflow/stratification scale

It is interesting to note that no plume/crossflow lengthscale can be defined on dimensional grounds for thetwo-dimensional plume. This is in contrast to the three-dimensional round plume and arises from the fact thatthe vertical velocity of a two-dimensional plume isconstant, ~j o

1⁄3 , leading in the presence of a constantcrossflow to a straight-line trajectory. Thus, no distinc-tion can be made of a plane plume in a weakly de-flected stage followed by a strongly deflected stage.However, it is possible to define a non-dimensionalparameter j o ⁄ U a

3 whose magnitude will be a measureof the slope of the plume trajectory.

8.5.3 Near-Field Flow ClassificationThe classification scheme used in CORMIX puts majoremphasis on the near-field flow configuration. This isbecause a large number of flow configurations canoccur due to the multiplicity of possible interactionprocesses; in contrast the far-field flow is generallymuch simpler with limited shoreline or bottom contactpossibilities.

8.5.3.1 Single Port Discharges (CORMIX1)In the near-f ield the dynamic length scalesLM , Lm , Lb , Lm

′ and Lb′ (LQ has less significance) de-

scribe the interaction with the geometric properties ofthe water body, its depth H or the depth hint to thedensity jump (in general, both of those are indicatedby a layer depth Hs ). Also the orientation angles θoand σo of the discharge are important (Figure 8-6).

Given the possible ambient stratification types a clas-sification procedure (in Doneker and Jirka, 1990) isused to classify the near-field behavior of a givendischarge into one of 35 generic flow classes that aresummarized in Figures 8-12 to 8-15. The four majorflow categories indicated by CORMIX1 are:

i) flows affected by linear stratification leading to inter-nal trapping (S classes, Figure 8-12)

ii) buoyant flows in a uniform ambient layer (V and Hclasses, Figure 8-13)

iii) negatively buoyant flows in a uniform ambient layer(NV and NH classes, Figure 8-14)

iv) bottom attached flows (A classes, Figure 8-15).

Each of the flow classes is indicated on the figures bya sketch that shows its main features in a side view orplan view. All flow criteria shown on the figures are givenas “order of magnitude” relations; somewhat differentforms and numerical constants may be contained inCORMIX1.

A wide spectrum of near-field flow configurations ispossible: these range from flows trapped in linear strati-fication, buoyant jets that are strongly affected by thecrossflow and gradually approach the layer boundary(surface or pycnocline), weakly deflected buoyant jetsthat impinge on the boundary leading to upstreamspreading and/or unstable recirculation, negativelybuoyant jets that form density currents along the bot-tom, and dynamic attachment along the bottom with orwithout eventual buoyant lift-off. It is stressed also that(i) each of these flow classes can occur in combinationwith an upper stratified layer (see stratification types B,C, or D on Figure 8-10) and (ii) the designation “uniformambient layer” in Figures 2-13 and 2-14 can, in fact, alsoapply to a stratified layer if it has been found that thestratification is too weak to trap the flow. Thus, inessence, the actual number of flow configurations thatcan be classified by CORMIX1 is much larger than the35 generic flow classes shown on these figures.

8.5.3.2 Multiport Diffusers (CORMIX2)The classification scheme used by CORMIX2 relies onthe same methodology as for single port discharges.The length scales of the two-dimensional slot jet,IM , Im , Ib , lm′ , and Ia , are compared with the layerdepth Hs and with the diffuser variables, its length LDand its orientation angles, θ, γ, β, σ (see Figure 8-7).The classification procedure (see Akar and Jirka, 1991,for details) yields 31 generic flow classes that fall intothree major categories: (i) flows affected by linear strati-fication leading to internal trapping (MS classes, Figure8-16), ii) buoyant flows in uniform ambient layers (MUclasses, Figure 8-17), and iii) negatively buoyant flowsin uniform ambient layers (MNU classes, Figure 8-18).

While there are some obvious analogies in their appear-ance to the flows produced by single port discharges,the major difference for multiport diffusers lies in thevertically fully mixed (over the layer depth) plumes thatcan be produced by the large momentum sources ofunidirectional or staged diffusers.

8.5.4 Predictive ElementsThe detailed hydrodynamic prediction of the effluentflow and of associated mixing zones in CORMIX iscarried out by appropriate flow modules that are ex-

8-14

Figure 8-11. Length scales measuring the effects of momentum flux, buoyancy flux, crossflow and stratification of submerged jet behavior.

8-15

Figure 8-13. CORMIX1 sub-classification: flow classes for positively buoyant single port discharges in uniform ambient layer.

8-16

Figure 8-14. CORMIX1 sub-classification: flow classes for negatively buoyant single port discharges in uniform ambient layer.

8-17

Figure 8-15. CORMIX1 sub-classification: assessment of dynamic bottom attachment processes and flow classes for bottom-attached flows.

8-18

Figure 8-16. CORMIX2 sub-classification: assessment of density stratification and flow classes for internally trapped multiport discharges.

8-19

Figure 8-17. CORMIX2 sub-classification: flow classes for positively buoyant multiport discharges in uniform ambient layer.

8-20

Figure 8-18. CORMIX2 sub-classification: flow classes for negatively buoyant multiport discharges in uniform ambient layer.

8-21

ecuted according to a protocol that pertains to eachdistinct flow configuration as determined by the classi-fication scheme. These flow protocols have been con-structed on the basis of the same length scalearguments that have been used for the flow classifica-tion. The spatial extent of each flow module is gov-erned by transition rules. These determine transitionsbetween different near-field and far-field mixing re-gions, and distances to boundary interaction.

The flow modules for single port discharge predictions(CORMIX1) are listed in Table 8-1. All modules pre-sent basic analytical solutions for one particular flowprocess with the perturbing influence of one or moreother variables superimposed. For example, the mod-ule for the weakly deflected jet in crossflow (MOD11)is based on a pure jet solution that experiences agradual advection by the crossflow. The group of near-field modules (MOD01 to MOD22) represents, in total,the same predictive ability as buoyant jet integral mod-els (valid in the subsurface region without boundaryinteraction).

The flow modules for multiport diffuser prediction(CORMIX2) are given in Table 8-2. Several groups ofmodules, notably those for the far-field, are similar, oreven identical, to those of CORMIX1.

Extensive comparisons have been conducted for COR-MIX1 and 2 with available laboratory data and a fewlimited field data cases, as well as with buoyant jetintegral models. These comparisons (Doneker andJirka, 1990; Akar and Jirka, 1991) demonstrate that forsubsurface flow the CORMIX predictions were at leastof the same quality as that of jet integral models. Theagreement with data (±20% for trajectories and dilu-tions) is of the same order as the usual scatter amongdifferent data sources.

Modules for Buoyant Jet Near-Field Flowszone of flow establishmentweakly deflected jet in crossflowweakly deflected wall jet in crossflownear-vertical jet in linear stratificationnear-horizontal jet in linear stratificationstrongly deflected jet in crossflowstrongly deflected wall jet in crossflowweakly deflected plume in crossflowstrongly deflected plume in crossflowModules for Boundary Interaction Processesnear-horizontal surface/bottom/pycnocline approachnear-vertical surface/bottom/pycnocline impingement with buoyant upstream spreadingnear-vertical surface/bottom/pycnocline impingement with vertical mixingnear-vertical surface/bottom/pycnocline impingement, upstream spreading, vertical mixing, and buoyant restratificationterminal layer stratified impingement/upstream spreadingterminal layer injection/upstream spreadingModules for Buoyant Spreading Processesbuoyant layer spreading in uniform ambientbuoyant spreading in linearly stratified ambientModules for Attachment/Detachment Processeswake recirculationlift-off/fall-downModules for Ambient Diffusion Processespassive diffusion in uniform ambientpassive diffusion in linearly stratified ambient

Table 8-1. Flow Prediction Modules of CORMIX1 (Single PortDischarges)

Simulation Modules for Buoyant Multiport Diffusers:Subsurface Near-Field Flowsdischarge moduledischarge (staged diffuser)weakly deflected plane jet in crossflowweakly deflected (3-D) wall jet in crossflownear-vertical plane jet in linear stratificationnear-horizontal plane jet in linear stratificationstrongly deflected plane jet in crossflowweakly deflected (2-D) wall jet in crossflowweakly and strongly deflected plane plume in crossflowbuoyant plane plume in stratified stagnant ambientnegatively buoyant line plumeSimulation Modules for Unstable Multiport Diffusers:Mixed Near-Field Flowsunidirectional acceleration zonetee acceleration zonestrongly deflected tee diffuser plumestaged acceleration zonestrongly deflected staged diffuser plumealternating perpendicular diffuser in unstable near-field zonenegatively buoyant staged acceleration zoneSimulation Modules for Boundary Interaction Processes for Stable Multiport Diffusersnear-vertical surface/bottom impingement with buoyant upstream spreadingnear-vertical surface/bottom impingement, upstream spreading, vertical mixing, and buoyant restratificationnear-horizontal surface/bottom/pycnocline approachterminal layer stratified impingement/upstream spreadingterminal layer injection/upstream spreadingSimulation Modules for Unstable Multiport Diffusers:Intermediate Field Flowsdiffuser plume in co-flowdiffuser plume in crossflowSimulation Modules for Buoyant Spreading Processesbuoyant layer spreading in uniform ambientbuoyant spreading in linearly stratified ambientdensity current developing along diffuser lineinternal density current developing along diffuser linediffuser induced bottom density current (2-D)diffuser induced bottom density current (3-D)Simulation Modules for Ambient Diffusion Processespassive diffusion in uniform ambientpassive diffusion in linearly stratified ambient

Table 8-2. Flow Prediction Modules of CORMIX2 (MultiportDiffusers)

8-22

Moreover, CORMIX has been shown to be a robustand accurate predictive methodology for more com-plex flows with various degrees of boundary interac-tion, such as near-field instabilities, buoyant spreadingprocesses, and dynamic bottom interaction. CORMIXappears to correctly diagnose these processesthrough its classification scheme and then providesquantitatively reliable predictions of the sequence ofmixing processes that characterize a given discharge.

However, as all models that are based on some geo-metric schematizations and dynamic simplifications,CORMIX will not be applicable to all possible dischargeconfigurations. To avoid model misuse in such in-stances, specific safeguards, warning labels, and userestrictions have been included in CORMIX. In anycase, recent experience has shown that CORMIX isapplicable and predicts properly for the vast majorityof actual submerged discharge situations (better than95% for CORMIX1 and better than 80% for CORMIX2because of the considerably greater geometric com-plexities of diffuser installations). Furthermore, theuser’s manuals contain special advice sections for theuser dealing with any of the more limiting cases.

8.6 Mixing Zone Predictions UnderUnsteady Reversing Tidal Currents

As has been remarked earlier in Section 8.1, the timescale for initial mixing processes is usually shortenough relative to the tidal period, so that it is accept-able to apply initial mixing models under steady-stateconditions, e.g. corresponding to certain stages withinthe tidal cycle. However, this approach is no longervalid if predictions are desired over a larger areaencompassing distances that, in fact, provide a transi-tion to the far-field.

In the present state-of-the-art no complete models forpollutant predictions in the water environment areavailable (see Section 8.2). This restriction stems fromthe difficulties of representing the variety of transportprocesses that govern the distribution in unconfinedestuarine or coastal water bodies in a single analyticalor numerical technique. Therefore, an integration ofnear-field mixing models and of predictive techniquesfor the far-field effects must be employed. Far-fieldprocesses, that include the transport by the varyingtidal flow, turbulent diffusion, and various biochemicaltransformation phenomena, have been addressed inParts I and II of this estuarine waste load allocationmanual. The following comments provide some guid-ance on estimating, the interaction between near-fieldmixing and far-field accumulation effects. The method-ology is adapted from that suggested by Jirka et al.(1976).

8.6.1 Far-Field Accumulation Effects

The two major methods for estimating the unsteadyfar-field accumulation of discharged material, at vari-able distances from the outfall and in an unsteady tidalflow, are either numerical models or field dispersiontests. In the following it is assumed that a dispersiontest is being employed, but the comments applyequally well to the results of an unsteady numericalmodel.

The schematics of a field dispersion test in a reversingtidal current system are shown in Figure 8-19. Thetracer release line may represent the location of asubmerged multiport diffuser with alternating nozzles.The tidal system is assumed as approximately periodicas indicated by the velocity curve. The figure alsoshows the hypothetical dye concentration trace C(x,y)

measured at some point ( x , y ) as a function of time.(Note that in practice, fewer discrete measurementsover time would be available). If the field dispersiontest consists of a tracer release period, tidal cycleslong, then the continuous monitoring would usuallyindicate a period of concentration build-up, a quasi-steady period and a fall-off period. If an accuratesimulation of the pollutant discharge over a large-scaleand for a long-term is required, then consideration (andmeasurement) for at least two of these periods isnecessary.

Considering the maximum dye concentration duringany tidal cycle at ( x , y ) the following sequence isgenerally observable: During the first cycle C max isfound, in the second cycle the concentration isplus some fraction of dye tracer returning from theprevious cycle, thus C max + rd C max = C max (1+rd ).If these are continuously repeated, then the quasi-steady maximum concentration C

__max is given by the

geometric series

C__

max = C max ( 1 +r d + rd2 + rd

3 + ⟨) (20)

or, in the limit,

C__

max = C max1

1−rd(21)

The quantity rd is labelled the dye return rate of massdischarged in the previous cycle (rd implicitly includesany dye mass decay during the tidal period). Thecomplement quantity (1-rd ) is frequently referred toas flushing rate. The return rate will depend on thecharacteristics of the tidal flow, notably tidal excursion,mean velocity, diffusion, etc. rd is also dependent onthe position ( x , y ) with respect to the release area.Quasi-steady conditions are typically encountered af-ter about 5 to 10 tidal cycles. Build-up curves, similarto Equation 20 correspond also to other quantities of

interest, such as the minimum or average concentra-tions during a tidal cycle, thus

C__

i ( x , y , t ) = Ci ( x , y , t ) 11−rd

(22)

where Ci ( x, y ) is a single cycle concentration quantityof interest (Cmax ,Cmin ,Cavg , etc.).

For the actual pollutant discharge the quasi-steadycondition is usually of primary importance. From Equa-tion 22 it is seen that this depends on two factors: themixing characteristics Ci within a single tidal cycle, andthe return rate from previous cycles. To translate thequasi-steady dye concentration conditions into pollut-ant concentration, therefore, two adjustments areneeded:

(a) Within a tidal cycle, the pollutant concentration c isrelated to the dye concentration C

ci ( x, y, t ) = Ci ( x, y, t ) QcoQdo

e − (kc−kd) ti ( x, y ) (23)

where ti ( x, y ) = time interval between occurence ofevent i (maximum, minimum concentration) at( x , y ) and time of release of that tracer patch, i.e.,travel time. Qco is the pollutant mass release rate andQdo is the dye mass release rate. kc and kd representthe decay constants for pollutant and dye, respec-tively. (for a conservative dye, kd=0). Determination ofti depends on the detailed knowledge of the velocityfield; for average concentrations the average tidalvelocity is representative. It is noted that for points farfrom the release area, especially more than severaltidal excursions away, the exponential correction termin Equation 23 becomes significant. In the dischargevicinity, however, it is frequently negligible, since ti isless than one tidal period. This is, in fact, the usualassumption in most mixing zone predictions.

(b) The return rate for pollutant rc is related to the dyereturn rate rd

rc = rd e −(kc−kd) t ∗(24)

where t ∗ = tidal period (12.4 hours). The quasi-steadypollutant concentration c

_i ( x,y ) is therefore related to

the measured single cycle dye concentrationCi ( x,y )

c_

i ( x , y , t ) = Ci ( x , y , t )QcoQdo

[ e − (kc−kd) ti ] 1−rd1−rc

(25)

Hence, for an accurate prediction of far-field effectsover a large area (larger than the tidal excursionlength) it is necessary to (i) measure the velocity fieldin some detail so ti ( x, y ) can be found for the pointsunder consideration, and (ii) measure not only thequasi-steady period of tracer distribution, but also thebuild-up or fall-off period so the dye return rate rd canbe evaluated as shown in Figure 8-19. In actual tracermonitoring it is not always possible to have continuousrecords. Nevertheless, a few measurements duringthe build-up or fall-off period usually give some indica-tion of rd.

If attention is restricted to a smaller area around thedischarge and if the tracer used is relatively conserva-tive (small kd), then both correction factors in Equation25 are negligible and the measured concentrationscan be used directly to evaluate the pollutant accumu-lation in the far-field.

8.6.2 Linkage to Initial Mixing PredictionsAll initial mixing models discussed in the preceding aresteady-state models and do not consider the far-fieldreturn (accumulation). The following procedure pro-vides an approximate linkage:

(a) Carry out a series of initial mixing predictions usinga steady-state near-field mixing model for differentintervals (e.g. 6 or 12, corresponding to 2 or 1-hourintervals, respectively) within the tidal cycle. The pre-dictions at any point of interest (e.g. at the boundary ofa Legal Mixing Zone) provide approximate time-de-pendent predictions for pollutant concentrationci ( x, y, t ) within a tidal cycle.

(b) Use the far-field pollutant return rate rc, that appliesfor the region of interest (e.g. the Legal Mixing Zone),to calculate the quasi-steady (i.e. long-term) pollutantconcentration

c_

i ( x , y , t ) = ci ( x , y , t ) 11−rc

(26)

The return rate rc that applies to the area of interestcan be estimated using the procedures outlined in thepreceding paragraph, i.e. relying on a dye dispersiontest or numerical model. It should be noted that rc, inturn, is a function of the distance from the outfall: rctends to be very small in the immediate near-field,where the pollutant concentrations are high; rc be-comes larger for increasing distances, where the in-duced concentrations are falling off, however. Thisdependence suggests the following practical guide-lines in the absence of detailed measurements orpredictions for rc :

8-24

Figure 8-19. Schematics of a field tracer dispersion test in a periodically reversing tidal system.

8-25

• For Toxic Dilution Zone (TDZ) predictions, theeffect of far-field return is always negligible (rc ≈ 0)due to the strong spatial restriction of the TDZ.

• For most Legal Mixing Zone predictions, the rcfactor can be expected to vary in the range of ≤0.1to ≈ 0.5 (highly conservative estimate). It is verysmall (≤ 0.1) for deep water discharges in the opencoastal zone that are often associated with internaltrapping or buoyant surface layer formation. Inthose cases, the initial (buoyant jet) mixing is, infact, quite independent of far-field effects. It maybe reasonably high (up to 0.5) for shallow water,vertically mixed, discharges in strongly restrictedestuaries with weak flushing. For additional flush-ing estimates in such tidal channels, see the meth-ods discussed in Fischer et al. (1979).

8.7 ReferencesAbraham, G. 1963. Jet Diffusion in Stagnant AmbientFluid. Publ. No. 29, Delft Hydraulics Laboratory, TheNetherlands.

Akar, P. J., and G. H. Jirka. 1991. CORMIX2: AnExpert System for Hydrodynamic Mixing Zone Analy-sis of Conventional and Toxic Submerged MultiportDiffuser Discharges. Technical Report, U.S. EPA, En-vironmental Research Laboratory, Athens, GA, (inpreparation).

Doneker, R. L., and G. H. Jirka. 1990. CORMIX1: AnExpert System for Hydrodynamic Mixing Zone Analy-sis of Conventional and Toxic Submerged Single PortDischarges. Technical Report EPA 600/3-90/012, U.S.EPA, Environmental Research Laboratory, Athens,GA.

Fischer, H. B. et al. 1979. Mixing in Inland and CoastalWaters. Academic Press, NY. 483 pp.

Hirst, E.A. 1971. Analysis of Buoyant Jets Dischargedto Flowing Stratified Ambients. Rep. ORNL-TM-4685,U.S. Atomic Energy Commission, Oak Ridge NationalLab., Oak Ridge, TN.

Holley, E. R. and G. H. Jirka. 1986. Mixing in Rivers,Technical Report E-86-11, U.S. Army Corps of Engi-neers, Washington, DC.

Jirka, G. H. 1982a. Turbulent Buoyant Jets in ShallowFluid Layers. in Turbulent Jets and Plumes, W. Rodi(Ed.), Pergamon Press.

Jirka, G. H. 1982b. Multiport Diffusers for Heat Dis-posal -A Summary. Journal of the Hydraulics Div.,ASCE, Vol. 108, December.

Jirka, G. H., G. Abraham, and D.R.F. Harleman. 1976.An Assessment of Techniques for Hydrothermal Pre-diction. Technical Report NUREG-0044, U.S. NuclearRegulatory Commission, Washington, DC.

Jirka, G. H. and L.M. Fong. 1981. Vortex Dynamicsand Bifurcation of Buoyant Jets in Crossflow. Journalof the Engineering Mechanics Division, American So-ciety of Civil Engineers, Vol. 107, No. EM3, June.

Jones, G.R. and G.H. Jirka. 1991. CORMIX3: AnExpert System for the Analysis and Prediction of Buoy-ant Surface Discharges, Technical Report, DeFreesHydraulics Laboratory, School of Civil and Environ-mental Engineering, Cornell University. Also to bepublished by U.S. Environmental Protection Agency,Technical Report, Environmental Reasearch Lab, Ath-ens, GA.

Kannberg, L. D., and L.R. Davis. 1976. An Experimen-tal/Analytical Investigation of Deep Submerged Multi-ple Buoyant Jets. EPA-600/3-76-101. U.S.Environmental Protection Agency, Corvallis, OR. 266pp.

Muellenhoff, W. P., et al. 1985. Initial Mixing Charac-teristics of Municipal Ocean Discharges (Vol. 1&2).U.S.EPA. Environmental Research Laboratory, Narra-gansett, R.I.

Roberts, P.J.W. 1977. Dispersion of Buoyant WasteDischarge from Outfall Diffusers of Finite Length. Rep.No. KH-R-35. W. M. Keck Lab. of Hydraulics andWater Resources, California Institute of Technology,Pasadena, CA, 183 pp.

Schatzmann, M. 1978. The Integral Equations forRound Buoyant Jets in Stratified Flows. J. Appl. Mathand Physics 29: 608-20.

USEPA. 1982. Revised Section 301 (h) TechnicalSupport Document. EPA 430/9-82-011, Washington,DC.

Winiarski, L. D., and W.E. Frick. 1976. Cooling towerplume model. EPA-600/3-76-100. U.S. Environ-mental Protection Agency, Corvallis, OR.

Wong, D. R. 1984. Buoyant Jet Entrainment in Strati-fied Fluids. Ph.D. Thesis, Civil Engineering Dept., TheUniversity of Michigan, Ann Arbor, MI.

8-26

9. Case Studies of Mixing Zone Prediction9.1 Introduction

9.1.1 Objectives

This case study section has several objectives: (i) Todemonstrate the typical procedures and data require-ments involved in mixing zone analysis; (ii) To demon-strate that legal mixing zone definitions may requirethe analysis of both near-field and far-field processes;and (iii) To show the relative merits and flexibility ofdifferent methodologies, including jet integral modelsand the expert system CORMIX.

All four case studies deal with hypothetical conditionsthat may, however, exhibit some features of existingdischarges. In the first case study major emphasis isput on various regulatory criteria. None of the casestudies is intended to document model validation. Thiscannot be done since no actual field or laboratory dataexist for these hypothetical situations. For validation ofmodels reference should be made to the original litera-ture on the various models as listed in Chapter 8.However, a few comments on model validity are madein the first case study in order to explain some largedifferences in various model predictions.

9.1.2 Data Needs

As discussed in Section 8.1, the initial mixing of aneffluent depends on the interaction of ambient anddischarge conditions. In estuaries or coastal watersthese conditions may be highly variable. In evaluatingwater quality effects and mixing zone compliance,appropriate design conditions must be chosen. Gen-erally, the critical design conditions relate to thoseenvironmental and discharge factors that lead to thelowest dilution and at times when the environment ismost sensitive. However, it is not always straightfor-ward for the analyst to estimate exactly what combina-tion of factors will lead to this critical condition. For thisreason, an evaluation under a variety of conditionsalways seems necessary to obtain information on mix-ing zone behavior and its sensitivity to design criteria.Data uncertainty is also a factor of concern. The fol-lowing considerations, taken from Muellenhoff et al.(1985), apply here:

“Predicting dilution reliably depends on the availabilityof statistically valid data with which to estimate ambientconditions. The statistical uncertainty in estimates ofabsolute worst case conditions is generally great. Alsothere are inherent biases to some oceanographicmeasurements. For example, current measuring in-struments have finite thresholds. It therefore becomesdifficult to distinguish low values (which may be as high

as 5.0 cm/sec) from zeroes in these data sets. In esti-mating environmental conditions, a more reliable esti-mation can be made at the lowest 10 percentile on acumulative frequency distribution. Data on ambient den-sity structure are not routinely collected. Consequently,there is not usually an existing data set for the site underconsideration. To increase the reliability of ‘worst-case’estimates, data should be evaluated not only for thedischarge site but for nearby coastal areas of similarenvironmental setting.”

“Defining ‘worst-case’ conditions as a combination ofthose conditions affecting initial dilution, each taken atthe worst 10 percentile on cumulative frequency distri-butions, is recommended by USEPA. This approachallows a reliable estimation of these conditions to bemade and prevents the unlikely occurence of moreextreme conditions from biasing the predictions. Theprobability of these conditions occurring simultaneouslyis much less than 10 percent, ensuring that the predicteddilution will be exceeded most of the time. Application ofmultiple ‘worst case’ factors (i.e. flows, stratification andcurrents) to determine a minimum dilution must be donecarefully, however, and in recognition of the criteria forwhich compliance is being determined. For example,although application of an absolute ‘worst case’ dilutionmay be appropriate for determining compliance with anacute toxicity limit, it is more appropriate to identify thelowest 6-month median dilution to determine compli-ance with a 6-month median receiving water limitation.”

Since the discharge conditions can also vary (e.g. itsflowrate or pollutant concentration) it is necessary tocombine the occurences of the varying pollutant loadingwith the varying ambient parameters in order to find thecritical design conditions.

Finally, any set of ambient and discharge conditions willrequire some degree of schematization in order to meetthe predictive model assumptions. This has been dis-cussed in Section 8.3.2 along with Figures 8-6, 8-7 and8-8. The literature or user’s manuals for the variousmodels usually contain some guidance on how to pre-pare the data. As with any model application, it is nec-essary to evaluate the prediction sensitivity to input datathrough repeated model use. The expert system COR-MIX, in fact, has on-screen advice on data preparationavailable to the user.

All available mixing zone models assume a conservativepollutant discharge neglecting any physical, chemical orbiological decay or transformation processes. For mostsubstances this is reasonable due to the

rapidity of the mixing process, especially in the near-field, relative to the reaction time scale of most pollut-ants. If first order reaction processes can be assumedthen the model results on concentration can usually beconverted with an exponential factor to include thedecay process (see Doneker and Jirka, 1990). Theconsideration of pollutant reactions in the context offar-field accumulation involving a larger time scale hasalso been addressed in Section 8.6.1.

9.2 Case AA -Single Port Discharge:Industrial Outfall in Tidal Fjord.

9.2.1 Ambient and Discharge Conditions

A manufacturing plant is located near the upstreamend of a narrow tidal fjord that receives a substantialamount of fresh water inflow. The typical cross-sectionof the fjord is 600 m wide with an average depth of16 m. The preferred discharge location is about 90 mfrom shore where the local water depth is 17.5 m.During typical winter conditions the characteristic am-bient (average tidal) velocity is 0.15 m/s and the verti-cal ambient density distribution is quite uniform with avalue of 1,005.5 kg/m3. During summer design condi-tions, however, the ambient velocity is lower at 0.10m/s and a significant vertical stratification exists asshown in Figure 9-1. The density varies from a bottomvalue of 1,010.0 kg/m3 down to a surface value of1,005.8 kg/m3. The plant operation is also variable. Inwinter the discharge flow rate is 0.15 m3/s and has adischarge temperature of 10°C. In summer the flowrate is lower at 0.10m3/s with a temperature of 15°C.The discharge flow is essentially freshwater but con-tains 1000 ppb of some organic toxic material.

Applicable state regulations limit the mixing zone to 25%of the width of the estuary. Furthermore, the specialmixing zone requirements for toxic substances (seeSection 7.2.3) apply with a CMC value of 100 ppb forthe discharged toxicant.

9.2.2 Case AA1: Initial Design, Winter Conditions

An inital design proposal calls for a single port dischargewith 0.2m port diameter and 0.5 m port height above thebottom. The discharge velocity is 4.8 m/s. The port isoriented in a co-flowing arrangement pointing horizon-tally along the direction of the ambient current.

Figure 9-2 shows a side view of the near-field of thedischarge plume predicted by CORMIX1 (flow class A5).The model shows strong dynamic attachment of theplume to the bottom. After this a gradual buoyant rise tothe surface takes place with a minimum surface dilution

= 164. The extent of the toxic dilution zone (TDZ)is about 10m, essentially comprising the entire bottomattached zone. Thus, benthic organisms will be exposedto toxicant concentrations above CMC values. This in-itial design is considered undesirable and rejected fromfurther consideration.

In view of this bottom attachment, none of the jet integralmodels, included in Section 8.4, i.e. the USEPA models,UOUTPLM and UDKHDEN or the Jirka-Fong model,would be applicable. Therefore, their predictions are notshown on Figure 9-2.

9.2.3 Case AA2: Modified Design, WinterConditions

In order to eliminate plume bottom interference, a modi-fied design is proposed with an increased port height of1.0m and a vertical discharge angle of 10o. This modi-fied design, indeed, does not exhibit any bottom attach-ment as shown in Figure 9-3.

The trajectory predictions of three buoyant jet integralmodels (UOUTPLM, UDKHDEN and JF [Jirka-Fong])and of CORMIX1 (flow class H2) are given in Figure 9-3.Also shown is the width prediction for CORMIX1. All foursubmerged plume trajectories are qualitatively similar;the deviations among trajectories is contained within theplume outline (as indicated by CORMIX1) and wellwithin the usual scatter of experimental data. The TDZis again limited (order of 10 m) as predicted by any ofthe four models. The jet integral models are, of course,limited in their applicability to the submerged jet regionbefore surface interaction. Only CORMIX1 is applicableto the actual interaction process and the subsequentbuoyant spreading along the water surface. This proc-ess is indicated by the width boundary in Figure 9-3.

Figure 9-1. Design case AA: vertical ambient density profilein typical summer conditions.

Considerable differences exist in the predicted surfacedilution at the point of surface interaction. UOUTPLMand UDKHDEN predict a flux-averaged dilution of 212and 495, respectively. On the other hand, JF andCORMIX1 predict minimum (centerline) dilutions of

220 and 146, respectively. Even if the UDKHDEN

model predictions are divided by a factor of 1.7, in orderto account for the typical ratio of flux-averaged andminimum dilutions a considerable difference remainsrelative to the lower dilution value of CORMIX1. To shedfurther light on this disagreement the predictions of the

four models can be compared to what is probably the

Figure 9-3. Case AA2: single port discharge (modified design) in unstratified winter conditions; comparison of jet integralmodels and CORMIX1.

Figure 9-2. Case AA1: single port discharge (initial design) exhibiting bottom attachment as predicted by CORMIX1.

most reliable and comprehensive available field dataset on submerged discharges. Lee and Neville-Jones(1987) report several hundred individual observationsof minimum surface dilution for three single port sub-merged outfalls for municipal discharges in the UnitedKingdom. All of these outfalls are somewhat moredominated by buoyancy than design case AA2. (Thisis indicated, for example, by the fact that CORMIX1predicts a flow class H1 for these outfalls). The predic-tions of all four models are compared with the normal-ized field observations for minimum surface dilution(Figure 9-4). The solid line presents the best-fit regres-sion line for all data points. The average dilution givenby both USEPA models is a factor of 4 (300%) largerthan the observed minimum dilution. When the dilutionpredictions are converted to minimum dilutions (factor1.7) the overprediction is still by about 130%. The JFmodel overprediction is about 50%. CORMIX1, on theother hand, lies within about 15% with the observa-tions. (Note that the model coefficients of CORMIX1have been chosen through extensive comparison withbasic laboratory data, so that this good agreementpresents indeed a model validation and not someforced best-fit). On the basis of this comparison it maybe concluded that the jet integral models (notablyUOUTPLM and UDKHDEN) are quite non-conserva-tive and tend to overestimate actual plume dilutions, atleast for unstratified ambients. The prediction dis-agreement for Case AA2 (Figure 9-3) may be consid-ered in light of this conclusion.

The legal mixing zone LMZ (25% width) is not attainedin the hydrodynamic near-field but rather in the far-fieldas shown by the CORMIX1 predictions of Figure 9-5. Infact, the LMZ is reached at a downstream distance ofabout 600 m when the surface plume is in the buoyantspreading regime. At this point, the average dilution hasincreased to about 250 and the plume half-width is about75 m with a plume thickness of 1.7 m. Actual plumeinteraction with the bank takes place at a further down-stream distance of about 760 m. This result illustratesthe practical fact that legal mixing zone definitions canoften imply sufficiently large distances which then in-clude far-field mixing processes. Simple jet integralmodels do not address this aspect, while CORMIX1 hasbeen implemented to deal with such generalities.

9.2.4 Case AA3: Modified Design, SummerConditions

The drastic effect of ambient stratification on plumenear-field behavior is shown in Figure 9-6. With any ofthe four predictive models the plume is predicted toreach its terminal level of about 3 to 5 m above thebottom at a distance of about 10 m downstream. Thedifferences among the predicted trajectories are small.The TDZ is reached about 8 m downstream as indicatedby CORMIX1 (flow class S3). The predicted dilutionvalues at the terminal level show, again, more variability.If minimum terminal dilutions are compared, thenUOUTPLM, = 16/1.7 = 9, CORMIX1, = 16, andUDKHDEN, = 26/1.7 = 15, provide lower-end (con-servative) predictions, while JF, = 26, is somewhathigher.

The CORMIX1 predictions in Figure 9-6 also show theformation of the internal stratified layer (initial thickness2.4 m) and its gradual collapse and widening with addi-tional mixing. The full development in the far-field isillustrated again in Figure 9-5. The behavior under strati-fied summer conditions is in marked contrast with theunstratified winter conditions (Case AA2). The differ-ence in dilution is notable (related to the much shorterbuoyant jet trajectory in the near-field) as is the muchthinner internal layer. The LMZ is reached at about 680m where the plume half-width is about 75 m and theplume thickness about 0.3 m.

9.3 Case BB -Multiport Diffuser: MunicipalSewage Discharge into Coastal Bay

9.3.1 Ambient and Discharge Conditions

A multiport diffuser is used for the discharge of treatedsewage water from a municipality located on a bay. The

Figure 9-4. Comparison of observed minimum surfacedilution for three submerged single port outfalls(Lee and Neville-Jones, 1987) with predictions ofjet integral models and CORMIX1.

proposed diffuser location is 10 km offshore with anambient water depth of 30 m. In a preliminary evalu-ation two ambient design cases are to be investigated;

1) A weakly stratified ambient with a density variation

from 1,023.2 kg/m3 at the surface to 1,026.4 kg/m3 at thebottom. Figure 9-7 shows the actual density varia-tion, together with the schematizations adopted for dif-

ferent models. 2) A uniform ambient with a density of

Figure 9-6. Case AA3 : single port discharge (modified design) in stratified summer conditions; comparison of jet integralmodels and CORMIX1.

Figure 9-5. Cases AA2 and AA3: predicted (CORMIX1) far-field behavior for single port discharge (modified design) in winterand summer conditions.

1,026.0 kg/m3. In both cases the ambient design ve-locity is 0.156 m/s for the prevailing coastal current.The discharge flow rate is 20 m3/s (460 MGD) with afreshwater density of 998.0 kg/m3.

The preliminary design calls for a total diffuser lengthof 2000 m with a perpendicular alignment relative tothe prevailing current direction. The diffuser employs80 vertical risers with 8 ports attached per riser anddischarging in a circular fashion. The port diameter is0.14 m, the port height is 1.5 m above bottom and the

port angle is 0° (i.e. horizontal).

The legal mixing zone (LMZ) is prescribed by a distanceof 30 m extending in any direction from the diffuser line.No toxic substances are included in this discharge.

9.3.2 Case BB1: Stratified Ambient

When applying any model to a complex diffuser geome-try with riser/port assemblies, some model simplificationis needed. In case of the USEPA multiport models(UDKHDEN,UMERGE and ULINE) the user must, infact, substitute a series of single ports equally spacedalong the diffuser line (thus, in this present case 80 x 8= 640 ports). On the other hand, the input element ofCORMIX2 collects all the pertinent information about theriser/port assemblies, the system then concludes thatthe net horizontal momentum flux for this diffuser is zeroand treats the diffuser as an alternating diffuser with avertical equivalent slot discharge. Thus, in either case,the local details of the eight individual buoyant jetsdischarging from each assembly are neglected.

Figure 9-8 summarizes the predictions of the jet modelsUDKHDEN and ULINE and of the expert system COR-MIX2 (flow class MS5). All three models indicate aterminal layer at about 10 m above the bottom varyingbetween 8 m and 12 m. Also all three models showlimited variability for the predicted average dilution at theterminal level,

_, which is 137 for ULINE, 212 for

UKHDEN, and 166 x 1.4 = 232 for CORMIX2, using anaverage/minimum dilution factor of 1.4 for two-dimen-sional buoyant jets. All these dilution values

may be scrutinized as to whether the mixed effluent flowper unit diffuser length,

_⁄ , exceeds the available

ambient approach flow, , for the layer betweenbottom and terminal level. Denoting the ratio

= (_

⁄ ) ⁄ ( ) one finds =0.7 for ULINE, =1.7

for UDKHDEN, and =1.4 for CORMIX2. In a strictly

Figure 9-7. Design case BB: vertical ambient density profilefor design conditions.

Figure 9-8. Case BB1: multiport diffuser discharge under stratified conditions; comparison of jet integral models and CORMIX2.

two-dimensional flow (i.e. if a diffuser section or theentire diffuser length were bounded by lateral walls)any value > 1 is not possible in steady-state. How-ever, for the actual three-dimensional diffuser the dif-fuser entrainment demand can also be met by lateralflow toward the diffuser line. Futhermore, additionalfreedom to entrain water exists for the internallytrapped plume ( < where is the water depth).Also, note that for low ambient velocity conditions

→0) the above test becomes unreliable for evalu-ating model performance. Thus, for the present caseof an internally trapped plume from a three-dimen-sional diffuser all three model predictions appear rea-sonable.

Note that trajectory information is provided byUDKHDEN and CORMIX2 while ULINE does not pro-vide any spatial data on plume behavior. The LMZ ispredicted by CORMIX2 to have a minimum dilution of116.

At the transition to the far-field CORMIX2 indicates aninitial internal layer thickness of about 16 m. As shownin the far-field plan view of Figure 9-9 this internal layeris gradually spreading, decreasing in thickness, andexperiencing a slight additional mixing in the buoyantspreading phase. Thus, at 10 km downstream from thediffuser line the average dilution is 313, with a half-width of the effluent field of 4.2 km and a thickness of4.7 m.

9.3.3 Case BB2: Uniform Ambient

The corresponding model predictions for the unstratifiedcase are given in Figure 9-10. CORMIX2 indicates a flowclass MU8 which includes a vertically fully mixed near-field with an average dilution,

_= 512. Although its model

printout does not specifically state so, ULINE also pre-dicts a vertically mixed flow with a lower dilution

_= 368.

In contrast, UDKHDEN does not recognize the destabi-lizing effect of the vertically limited environment in cross-flow and predicts a plume with a high surface dilution

_

= 835 and with width dimensions that are of the order ofthe water depth (Figure 9-10). Defining the ratios

= ( ⁄ ) ⁄ ( ) one finds =0.8 for ULINE, =1.0for CORMIX2 and = 1.8 for UDKHDEN. The latterresult, together with the fact that the model — whilepredicting plume dimensions of the order of the waterdepth — does not address the constraint of the limitedambient depth, indicates that UDKHDEN is not applica-ble in this case. More generally, it appears thatUDKHDEN is an unreliable model for most multiportdiffuser applications in unstratified ambients. The samereservation would hold for the model UMERGE (notplotted here). ULINE indicates slightly more conserva-tive dilution values than CORMIX2. It may be overlyconservative, however, since the ULINE model coeffi-cients are based on a single set of experiments byRoberts (1977) which did not include the additionalmixing effect of the high velocity discharge jets as iscommon in actual diffuser installations (this has beenpointed out in a discussion by Jirka, 1979).

The far-field behavior of the diffuser plume is plotted inFigure 9-9. While the plume is fully mixed in the near-

Figure 9-9. Cases BB1 and BB2: predicted (CORMIX2) far-field behavior for multiport diffuser plume in stratified and uniformconditions.

field (about 100 m downstream; see Figure 9-10) itrestratifies and lifts off from the bottom. At a distanceof 1.5 km downstream the vertical thickness has re-duced to 22.0 m (compared to the initial thickness of30.0 m equal to the water depth). At 10 km downstreamthe plume has thinned to about 11.3 m while spreadingto a half-width of 4.0 km and attaining an averagedilution of 703.

9.4 Case CC -Single Port Discharge: BrineDischarge From an Oil Field

9.4.1 Ambient and Discharge Conditions

Brine from drilling operations in a coastal oil field is tobe discharged into coastal waters. The proposed dis-charge site is 250 m offshore at a local water depth of20 m. The ocean water is weakly stratified with apycnocline at 15 m above the bottom. However, be-cause of the strongly negatively buoyant brine dis-charge the density distribution above the pycnoclineappears unimportant and the ambient can, in fact, beassumed at a constant density of 1,025.0 kg/m3 corre-sponding to the lower layer density. Ambient designvelocities range from 0.1 m/s to 0.25 m/s. The bottomis sandy with a Darcy-Weisbach friction factor of 0.015.

The brine flow rate is 0.03 m3/s with a density of1,070.0 kg/m3, thus much heavier than the oceanwater. The effluent contains several toxic metals, in-cluding copper at a concentration of 380 ppb. Theextent of the LMZ corresponds to the water depth of20 m. The TDZ is governed by a CMC concentrationfor copper of 40 ppb.

The initial design proposes a low velocity discharge(3.8 m/s) with a port of 0.1 m diameter at a 2.0 m heightabove the bottom, angled at 60° above horizontal and

pointing laterally across the cross-flow (cross-flowingdischarge).

9.4.2 Case CC1: Low Discharge VelocityDesign, Weak Current

Even though, in principle, they ought to be applicablefor negatively buoyant discharges the USEPA models(UOUTPLM and UDKHDEN) do not provide any pre-dictions for this cross-flowing upwardly angled dis-charge with a complex three-dimensional trajectory.Predictions are limited to CORMIX1 and the Jirka-Fong (JF) integral model. The near-field plume con-figuration for the two model predictions is shown inFigure 9-11a with (i) longitudinal and (ii) transverseside views, respectively. CORMIX1 predicts a flowclass NV2 with buoyant upstream intrusion along thebottom after impingement of the falling jet. The twobuoyant jet trajectories (JF and CORMIX2) are inreasonably good agreement prior to impingement. Thepredicted minimum dilution is lower for CORMIX1( = 22) than for JF (56). The extent of the upstreamintrusion is of the order of 20 m from the impingementpoint. A thin bottom layer of about 0.5 m thickness isformed and spreads laterally as the bottom plume isadvected downstream. The TDZ is very short, of theorder of 1 m from the efflux point. The conditions at theLMZ (not shown in Figure 9-11a) indicate a thin layerof 0.35 m thickness, 18.0 m half-width with an averagedilution of 40.

9.4.3 Case CC2: Low Discharge VelocityDesign, Strong Current

When the ambient current increases from 0.1 m/s to0.25 m/s the downstream buoyant jet deflection isaccentuated while the upstream buoyant extension is

Figure 9-10. Case BB2: multiport diffuser discharge in uniform ambient; comparison of jet integral models and CORMIX2.

minimized. Figure 9-11b shows CORMIX1 (flow classNV2) and JF predictions. The discrepancy betweenpredicted minimum dilutions is further increased( = 22 versus 140). Such complex three-dimen-sional trajectories represent some of the most severetests for model application, and in the absence ofdetailed experimental data for such phenomena it isdifficult to favor one model over another.

The upstream intrusion along the bottom is minimal inthe present case (order of 2 m) and the bottom densitycurrent is thicker and less wide. At the LMZ distancethe plume half-width is only 8.0 m with a thickness of0.60 m and an average dilution of 45.

9.4.4. Case CC3: High Discharge VelocityDesign, Strong Current

In order to maximize near-field dilution a high exitvelocity design (15.2 m/s) is evaluated by halving theport diameter to 0.05 m. The results are shown inFigure 9-12. When compared to Figure 9-11b, thisshows the significant effect of increased jet diffusion in

the near-field. The buoyant jet shows much more rapidmixing, and, consequently, is more liable to advectionby the ambient current. CORMIX1 (flow class NV1) nolonger predicts an upstream intrusion after the moregradual bottom approach. There are differences in thepredicted jet trajectories, as far as maximum height ofrise and bottom approach are concerned. At the LMZthese buoyant jets are predicted to be in the watercolumn without any bottom contact yet. The minimumdilution values are = 247 for JF and 119 forCORMIX1, respectively. The comparison betweenFigure 9-11b and 9-12 illustrates how LMZ constraintssometimes are met in the hydrodynamic near-field andat other times in the far-field, depending on the inter-play of ambient and discharge conditions.

9.5 Case DD Multiport Diffusers: CoolingWater Discharge into Shallow Sound

9.5.1 Ambient and Discharge Conditions

A once-through cooling water system for a thermal-electric power plant discharges the heated cooling

Figure 9-11. Cases CC1 and CC2: negatively buoyant discharge from single port; low exit velocity design under a) weak and b)stronger ambient current.

water through a submerged multiport diffuser. At adistance of 500 m offshore, a shallow relatively flatarea exists with an ambient water depth of 10.3 m.

The water is unstratified with an average temperatureof 20°C and ocean salinity. The velocity field is tidalranging from slack tide (0.0 m/s) to weak velocities(about 0.1 m/s) to a maximum velocity (0.5 m/s). Thecooling water flow rate is 67 m3/s with a dischargetemperature rise of 20.5°C above ambient and thesame salinity.

A staged diffuser design of 260 m length is proposedwith a perpendicular alignment relative to the tidalcurrents. The diffuser consists of 32 ports with a portheight of 0.5 m, port diameter of 0.6 m and a verticalangle of 20° above horizontal.

No LMZ is specified. Rather, the predictive results areto be interpreted so as to make an LMZ proposal to thestate regulatory authority.

9.5.2 Case DD1: Weak Tidal Current

None of the USEPA diffuser models are applicable forsuch shallow water diffusers with strong momentumflux and unstable near-field mixing. If they were used,UOUTPLM and UDKHDEN would predict verticalplume width far in excess of the available water depth.ULINE, on the other hand, is limited to pure plumedischarges without any directed discharge momentumflux.

Thus, reliable predictions are limited to CORMIX2 asshown in the plan view of Figure 9-13. For this case ofa weak current, CORMIX2 (flow class MU5) indicatesan initially, vertically fully mixed diffuser plume. Theplume gets gradually deflected by the weak crossflowand begins to re-stratify (lift off the bottom) after adistance. Gradual, lateral spreading and vertical thin-ning of the diffuser plume takes place. The inducedtemperature rise is 2.7°C in the near-field and drops to1.0°C at a distance of about 1500 m. (Any potentialheat loss to the atmosphere is neglected in theseconservative mixing predictions).

Figure 9-12. Case CC3: negatively buoyant discharge from single port; high exit velocity design with strong ambient current.

Figure 9-13 illustrates vividly the strong effect of thedirected momentum flux from shallow multiport dif-fusers and the ability to induce currents over consider-able distances.

9.5.3 Case DD2: Slack Tide

Stagnant ambient conditions always represent a limit-ing case for any mixing analysis. Since there is noambient advective mechanism they are always asso-ciated with an unsteady flow field and mixing process,including potential large scale recirculation effects.

The CORMIX2 (flow class MU5) predictions are givenin Figure 9-14 for unsteady conditions. The plume isnow undeflected, but has similar mixing characteristicsas the slightly deflected plume of Case DD1. However,at some distance (about 680 m) the predictions areterminated since the induced plume velocities havebecome negligibly small so that a transient recirculat-ing flow would be set up. Corresponding messages areprinted out by the expert system along with the adviceto conduct predictions for stagnant ambients only as aspecial limiting condition.

9.5.4 Case DD3: Strong Tidal Current

The effect of a strong tidal current (0.5 m/s) is togenerate a strongly deflected diffuser plume (Figure9-15) as predicted by CORMIX2 (flow class MU6). Arapid deflection and greatly increased mixing takeplace within the diffuser vicinity. The re-stratifyingplume is then advected by the ambient current andgrows in width and diminishes in vertical thickness, inform of a surface buoyant spreading process.

Figure 9-14. Case DD2: staged multiport diffuser for coolingwater discharge; CORMIX2 predictions for slacktidal conditions.

Figure 9-15. Case DD3: staged multiport diffuser for coolingwater discharge; CORMIX2 predictions forstrong tidal current.

Figure 9-13. Case DD1: staged multiport diffuser for coolingwater discharge; CORMIX2 predictions for weaktidal current.

In summary, the great variability among diffuser plumepatterns (Figures 9-13, 9-14, and 9-15) suggests thata complete assessment of initial mixing processesshould, indeed, include the whole spectrum of ambientconditions. It is often difficult to define a single “typical”design condition for mixing analysis. On the otherhand, a rapid evaluation of several ambient conditionsand of alternative designs is readily possible within theframework of presently available models.

9.6 ReferencesDoneker, R.L., and G.H. Jirka. 1990. CORMIX1: AnExpert System for Hydrodynamic Mixing Zone Analy-sis of Conventional and Toxic Submerged Single PortDischarges. Technical Report, U.S. EPA, Environ-mental Research Laboratory, Athens, GA.

Jirka, G.H. 1979. Discussion of “Line Plume andOcean Outfall Dispersion” by P.J.W. Roberts, J. of theHydraulics Div., ASCE, Vol. 105, HY 12.

Lee, J.H.W. and P. Neville-Jones. 1987. Initial Dilutionof Horizontal Jet in Crossflow. J. Hydraulic Engrg.,ASCE, Vol. 113, No. 5.

Muellenhoff, W.P., et al. 1985. Initial Mixing Charac-teristics of Municipal Ocean Discharges (Vol. 1&2).U.S.E.P.A., Environmental Research Laboratory, Nar-ragansett, R.I.

Roberts, P.J.W. 1977. Dispersion of Buoyant WasteDischarge from Outfall Diffusers of Finite Length. Rep.No. KH-R-35. W.M. Keck Lab. of Hydraulics and WaterResources, California Institute of Technology,Pasadena, CA, 183 pp.

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