GE0-3112GE0-3112 Sedimentary processes and products Sedimentary processes and products

Lecture 2. Fluid flow and sediment grains.Lecture 2. Fluid flow and sediment grains.

Geoff CornerGeoff CornerDepartment of GeologyDepartment of GeologyUniversity of TromsøUniversity of Tromsø20062006

Literature:Literature:- Leeder 1999. Ch. 4, 5 & 6. - Leeder 1999. Ch. 4, 5 & 6.

Sedimentological fluid dynamics.Sedimentological fluid dynamics.

ContentsContents

►2.1 Introduction - Why study fluid 2.1 Introduction - Why study fluid dynamicsdynamics

►2.2 Material properties2.2 Material properties►2.3 Fluid flow2.3 Fluid flow►2.4 Turbulent flow2.4 Turbulent flow►Further readingFurther reading

2.1 Introduction - Fluid 2.1 Introduction - Fluid dynamicsdynamics

►Concerns how fluids transport Concerns how fluids transport sedimentary particles. (NB. Fluids are sedimentary particles. (NB. Fluids are liquids liquids andand gasses) gasses)

►Fluid flows can be described using Fluid flows can be described using basic physics, although sedimentary basic physics, although sedimentary particles add complication. particles add complication.

Why study fluid dynamics?Why study fluid dynamics?

►Examples of practical problemsExamples of practical problems Pebbles on a sandy surfacePebbles on a sandy surface Slidden boulder in Death ValleySlidden boulder in Death Valley Deformation structureDeformation structure

Notes on scientific notationNotes on scientific notation

►Fundamental units of physical Fundamental units of physical dimension (dimensional analysis): M dimension (dimensional analysis): M (mass), L (length), T (time).(mass), L (length), T (time).

►System of units of measurement:System of units of measurement: Metre-kilogram-second (SI, SystMetre-kilogram-second (SI, Systèm èm

Internationale d’Unités).Internationale d’Unités). CGS, centimetre-gram-second (informal)CGS, centimetre-gram-second (informal)

►Greek letters (used in formulas).Greek letters (used in formulas).

2.2 Material properties2.2 Material properties

►Three states of matter (solid, liquid, gas); Three states of matter (solid, liquid, gas); have different properties and behaviour.have different properties and behaviour.

►Solids (e.g. rock, ice): have strength and resist Solids (e.g. rock, ice): have strength and resist shear (limited ...deformation).shear (limited ...deformation).

►Liquids (e.g. water): deform readily under shear Liquids (e.g. water): deform readily under shear stress; incompressible.stress; incompressible.

►Gasses (e.g. air): deform readily under shear Gasses (e.g. air): deform readily under shear stress; compressible stress; compressible

►NB. Some substances have behaviour NB. Some substances have behaviour intermediate between liquid and solid (e.g. mud-intermediate between liquid and solid (e.g. mud-water mixtures).water mixtures).

Material properties of fluidsMaterial properties of fluids

►DensityDensity►ViscosityViscosity

Density and viscosity are temperature dependent.Density and viscosity are temperature dependent.

DensityDensity

► DensityDensity ( (ρρ) is mass (m) per unit volume [ML-3; ) is mass (m) per unit volume [ML-3; kg/mkg/m33].].

► SolidsSolids (rock, ice, sediments) have strength and resist (rock, ice, sediments) have strength and resist shear (limited ...deformation).shear (limited ...deformation).

► LiquidsLiquids (water) deform readily under shear stress but (water) deform readily under shear stress but are incompressible.are incompressible.

► GassesGasses (air) deform readily under shear stress and (air) deform readily under shear stress and are compressible. are compressible.

► NB. Some substances have behaviour NB. Some substances have behaviour intermediateintermediate between liquid and solid (e.g. mud-water mixtures).between liquid and solid (e.g. mud-water mixtures).

► Density affects:Density affects:

►Density affects:Density affects: Fluid momentumFluid momentum Buoyancy (density ratio)Buoyancy (density ratio)

Density vs. temperature and Density vs. temperature and pressurepressure

► Water density decreases with temperature (above 4Water density decreases with temperature (above 4ooC) and increases with C) and increases with pressure.pressure.

► Air density decreases with temperature and increases with pressure. Air density decreases with temperature and increases with pressure.

Water Air

Example 1: thermal Example 1: thermal stratification in lakesstratification in lakes

Density vs. salinityDensity vs. salinity

► Water density inceases with salinity.Water density inceases with salinity.► Salinity examples:Salinity examples:

Freshwater lakes Norway: Freshwater lakes Norway: <c. 0.4‰ Brackish water fjords Norway: Brackish water fjords Norway: c. 29-3‰ Coastal seawater Norway: Coastal seawater Norway: 33-29‰ Seawater tropics: Seawater tropics: 34-35‰

Example 2a: saline stratification Example 2a: saline stratification in fjordsin fjords

Syvitski 1987

Example 2b: density driven Example 2b: density driven thermohaline circulation in the thermohaline circulation in the

ocean ocean ► Example of flow generated by density and Example of flow generated by density and

temperature differences: thermohaline flowtemperature differences: thermohaline flow

Density vs. sediment contentDensity vs. sediment content

► Density increases with sediment content Density increases with sediment content

Example 3: Hypo- and Example 3: Hypo- and hyperpycnal flows beyond river hyperpycnal flows beyond river

mouthsmouths

► Hypopycnal = less denseHypopycnal = less dense► Hyperpycnal = more denseHyperpycnal = more dense► Density differences between the inflowing and ambient water can Density differences between the inflowing and ambient water can

be caused by a combination of be caused by a combination of temperaturetemperature, , salinitysalinity and and sediment sediment concentrationconcentration differences. differences.

ViscosityViscosity

►Dynamic (or molecular) viscosity Dynamic (or molecular) viscosity ((μμ): ): [ML[ML-1-1TT-1-1; kg/m s, or N s/m; kg/m s, or N s/m22]](A measure of a fluid’s ability to resist deformation)(A measure of a fluid’s ability to resist deformation)

►Kinematic viscosity (Kinematic viscosity (νν): ): vv==μμ// [L[L22TT-1-1; m; m2/2/s]s](Ratio between a fluid’s ability to resist deformation (Ratio between a fluid’s ability to resist deformation

and its resistance to acceleration)and its resistance to acceleration)

Dynamic (molecular) Dynamic (molecular) viscosityviscosity

► Viscosity controls the rate of deformation by Viscosity controls the rate of deformation by an applied shear, or:an applied shear, or:

► Viscosity is the proportionality factor that Viscosity is the proportionality factor that links shear stress to rate of strain:links shear stress to rate of strain:

► Dimensions are: [MLDimensions are: [ML-1-1TT-1-1; kg/m s]; kg/m s]► Viscosity is much higher in water than in air.Viscosity is much higher in water than in air.

Shear stress (tau)

Viscosity (mu)

Strain rate

Viscosity vs. temperatureViscosity vs. temperature

► Viscosity varies temperature:Viscosity varies temperature: In water it decreases.In water it decreases. In air it increases. In air it increases.

Viscosity vs. sediment Viscosity vs. sediment concentrationconcentration

► Fluid viscosity increases Fluid viscosity increases with sediment content.with sediment content.

Viscosity vs. shear rate Viscosity vs. shear rate ((Newtonian and Non-Newtonian Newtonian and Non-Newtonian

behaviourbehaviour))

► Newtonian fluidsNewtonian fluids:: ConstantConstant viscosity at constant temperature and pressure. viscosity at constant temperature and pressure. Continuous deformation (irrecoverable strain) as long as shear is Continuous deformation (irrecoverable strain) as long as shear is

maintained.maintained.► Non-Newtonian fluids:Non-Newtonian fluids:

Viscosity Viscosity variesvaries with the shear rate. with the shear rate. Various types of Non-Newtonian behaviour/substances:Various types of Non-Newtonian behaviour/substances:

► Pseudoplastic, Dilatant, Thixotropic, Rheopectic. Pseudoplastic, Dilatant, Thixotropic, Rheopectic.

Non-Newtonian behaviourNon-Newtonian behaviour

► Pseudoplastic: Pseudoplastic: μμ decreases as rate of shear increases. decreases as rate of shear increases.► Dilatant: Dilatant: μμ increases as rate of shear increases. increases as rate of shear increases.► Thixotropic: Thixotropic: μμ decreases with time as shear is applied. decreases with time as shear is applied.► Rheopectic: Rheopectic: μμ increases with time as shear is applied. increases with time as shear is applied.

Examples from natureExamples from nature

Newtonian viscous fluid

Non-Newtonian

Increasing viscosity

2.3 Fluid flow2.3 Fluid flow

►Flow typesFlow types►Controlling forcesControlling forces►Dimensionless numbersDimensionless numbers►Flow steadiness and uniformityFlow steadiness and uniformity►Flow visualisation and flow linesFlow visualisation and flow lines►Laminar and turbulent flow (Reynolds Laminar and turbulent flow (Reynolds

number)number)►Turbulent flowTurbulent flow

Flow typesFlow types

► Newtonian: continuous deformation Newtonian: continuous deformation (irrecoverable strain) as long as shear stress (irrecoverable strain) as long as shear stress is maintained (linear stress-strain is maintained (linear stress-strain relationship).relationship).

► Plastic: initial resistance to shear (yield Plastic: initial resistance to shear (yield stress) followed by deformation.stress) followed by deformation. Bingham plastic: constant viscosityBingham plastic: constant viscosity Non-Bingham plastic: viscosity varies with shearNon-Bingham plastic: viscosity varies with shear

► Non-Newtonian pseudo-plasticNon-Newtonian pseudo-plastic► Non-Newtonian thixotropicNon-Newtonian thixotropic► Non-Newtonian dilatantNon-Newtonian dilatant

Fluid flow – driving forcesFluid flow – driving forces

► Momentum-driven flows (externally applied Momentum-driven flows (externally applied forces)forces)(Gravity and pressure differences drive flows)(Gravity and pressure differences drive flows)

► Buoyancy-driven flowsBuoyancy-driven flows

(Density difference drives flows)(Density difference drives flows)

Controlling forcesControlling forces

►Buoyancy forces (density controlled)Buoyancy forces (density controlled)►Viscous forces (viscosity controlled)Viscous forces (viscosity controlled)► Inertial forces (momentum controlled)Inertial forces (momentum controlled)►Gravitational forcesGravitational forces

Dimensionless numbersDimensionless numbers

►Dimensionless ratios provide scale- and Dimensionless ratios provide scale- and unit-independent measures of dynamic unit-independent measures of dynamic behaviour.behaviour.

►Two important ratios in fluid dynamics are:Two important ratios in fluid dynamics are: Reynolds number: ratio of inertial to viscous Reynolds number: ratio of inertial to viscous

forcesforces Froude number: ratio of inertial to gravity Froude number: ratio of inertial to gravity

forcesforces

Flow steadinessFlow steadiness

►Relates to change in velocity over timeRelates to change in velocity over time Steady flow - constant velocitySteady flow - constant velocity Unsteady flow – variable velocity Unsteady flow – variable velocity

Steady flow (e.g. steady turbulent river measured over hours)

Unsteady flow (e.g. decelerating turbidity current)

Flow uniformityFlow uniformity

►Relates to change in velocity over distanceRelates to change in velocity over distance Uniform flow - constant velocity (parallel Uniform flow - constant velocity (parallel

streamlines)streamlines) Non-uniform flow – variable velocity (non-Non-uniform flow – variable velocity (non-

parallel sls)parallel sls)Uniform flow (e.g. in channel)

Non-uniform (diverging) flow (e.g. at river mouth)

Flow visualisation - flow linesFlow visualisation - flow lines►Streamline Streamline - line tangential to the velocity vector of fluid - line tangential to the velocity vector of fluid

elements at any instant.elements at any instant.

►Pathline Pathline - trajectory swept out over time (e.g. long exposure - trajectory swept out over time (e.g. long exposure

of a spot tracer).of a spot tracer). ►Streakline Streakline - instantaneous locus of all fluid elements that - instantaneous locus of all fluid elements that

have passed through the same point in the flow field (e.g. short have passed through the same point in the flow field (e.g. short exposure of a continuously introduced tracer.exposure of a continuously introduced tracer.

PathlinesStreamlines Streaklines

Flow visualisation – reference Flow visualisation – reference framesframes

Streamlines for flow pattern round an object moving to the left through a stationary fluid (Langrangian velocity field)

Streamlines for flow past a stationary object (Eulerian velocity field)

Laminar and turbulent flow Laminar and turbulent flow

► Flow type changes Flow type changes with increasing with increasing velocity -velocity -

from laminar to from laminar to turbulent.turbulent.

► The relationship is The relationship is described by the described by the Reynolds number. Reynolds number.

Rapid pressure drop/ change in flow type.

Reynolds numberReynolds number

► Reynolds number (Reynolds number (ReRe) is the the ) is the the ratio of ratio of viscous forcesviscous forces (resisting (resisting deformation) to deformation) to inertial forcesinertial forces (ability of fluid mass to (ability of fluid mass to accelerate). accelerate).

► The transition from laminar to The transition from laminar to turbulent flow occurs at about turbulent flow occurs at about ReRe = 500 – 2000. = 500 – 2000.

Inertial force

Viscous forceMolecular viscosity

Velocity

Density

Depth

Flow patternsFlow patterns

► Laminar flow: parallel Laminar flow: parallel flowlines (low Re).flowlines (low Re).

► Turbulant flow: Turbulant flow: irregular flowlines irregular flowlines with eddies and with eddies and vortices (high Re).vortices (high Re).

Laminar flow

Transitional to turbulent flow

Turbulent flow

Streaklines

Velocity distribution in viscous Velocity distribution in viscous flowsflows

Parabolic Newtonian laminar flow velocity profile.

Plug-like non-Newtonian laminar flow (e.g. debris flow).

Flow retardation in a boundary layer

2.4 Turbulent flow2.4 Turbulent flow

►Turbulent eddiesTurbulent eddies►Bed roughnessBed roughness►Flow separationFlow separation

Turbulent eddiesTurbulent eddies

Backwash/rip-current eddies at Breivikeidet

Eddy movement in x-y space with time (t1-t2)

Instantaneous velocityInstantaneous velocity

Bed roughnessBed roughness

Turbulent stresses dominate

Viscous sublayer

Viscous forces dominate

+η (Boussinesq’s eddy viscosity)

Bed roughnessBed roughness

Viscous sublayer (smooth bed)

No viscous sublayer (rough bed)

Shear velocity and skin Shear velocity and skin frictionfriction

Smooth

Rough

Turbulent eddies in air

Streaklines viewed in the x-z plane (i.e. plan section)

Streaklines viewed in the x-y plane (i.e. flow-parallel vertical section)

Components of turbulent Components of turbulent eddieseddies

Sweep (fast)

Burst (slow)

Streaks (close to bed)

Turbulent eddies in water

Flow at successively higher positions above the bed (a- d)

Slow flow pattern in viscous sublayer

Flow pattern in turbulent boundary layer

Macroturbulence in outer regions of flow

Sand particle flow in viscous sublayer shown at 1/12 s time intervals

’Sweep’ event

Kelvin-Helmholz vorticesKelvin-Helmholz vortices

► Important mixing Important mixing mechanism at junction of mechanism at junction of two fluids, e.g. at two fluids, e.g. at junctions of tributaries or junctions of tributaries or mixing water masses, at mixing water masses, at fronts and tops of density fronts and tops of density currents, etc.currents, etc.

Likely causes of K-H instability: a)-c) velocty differences across boundary layer or in density-stratified flows; d)-e) shear layers produced by pressure differences.

Flow separationFlow separation

Boundary layer separation point

Boundary layer reattachment zone (downstream)

Accelerating flow, decreasing pressureDecelerating flow, increasing pressure, redardation and separation of flow closest to the bed

2.5 Sediment grains in fluids2.5 Sediment grains in fluids

►Settling (Stokes velocity)Settling (Stokes velocity)►Threshold velocityThreshold velocity►Rolling, saltation and suspensionRolling, saltation and suspension►Bedload, suspended and washload Bedload, suspended and washload

SettlingSettling

►Fall velocity Fall velocity increases with increases with increasing increasing grain sizegrain size

Stokes equation applies:- Low Re (< 0.5)- No viscous flow separation- Low sed. concentration

Silt-f.sand

Velocity increase reduced:- Higher Re (>1) - Turbulent drag- Non-spherical grains- High sed. concentration

NB! Clays flocculate

Particle transportParticle transport► Critical threshold (shear) velocityCritical threshold (shear) velocity

Lift + drag forces = resisting (gravity) forces.Lift + drag forces = resisting (gravity) forces.► Low pressure over grains (due to acceleration, Low pressure over grains (due to acceleration,

cf. Bernoulli’s equation) causes lift.cf. Bernoulli’s equation) causes lift.

Particles above the bedParticles above the bed► Instantaneous local shear varies due to Instantaneous local shear varies due to

burst/sweep events.burst/sweep events.► Once entrained, drag forces increase relative to Once entrained, drag forces increase relative to

lift forces.lift forces.

More drag

More lift

Threshold velocityThreshold velocity

►Threshold velocity for motion Threshold velocity for motion increases with increasing grain size.increases with increasing grain size.

Silt Sand Pebbles

Impact threshold in airImpact threshold in air

►Falling grains in air can induce grain Falling grains in air can induce grain motion on impact above the motion on impact above the impact impact thresholdthreshold velocity. velocity.

►Velocity for Velocity for normal thresholdnormal threshold is higher. is higher.

Grain motionGrain motion

►Rolling, saltation, suspensionRolling, saltation, suspension

Types of transport loadsTypes of transport loads

►WashloadWashload►Suspended loadSuspended load►BedloadBedload

Further readingFurther reading

► Allen, J.R.L. 1970. Physical processes of Allen, J.R.L. 1970. Physical processes of sedimentation.sedimentation. Chapter 1 covers the same ground as Leeder and Chapter 1 covers the same ground as Leeder and

explains clearly the principles involved; good explains clearly the principles involved; good supplementary reading for aquiring a sound supplementary reading for aquiring a sound grasp of the physics of fluid dynamics and grasp of the physics of fluid dynamics and sedimentation. Alternatively consult the more sedimentation. Alternatively consult the more encyclopedic:encyclopedic:

► Allen, J.R.L 1984. Sedimentary structures: Allen, J.R.L 1984. Sedimentary structures: their character and physical basis. their character and physical basis. A more encyclopedic alternative to the above if it A more encyclopedic alternative to the above if it

is unavailable.is unavailable.