Exchange Flows Through a Long Shallow Channel

Edwin A. CowenDeFrees Hydraulics Laboratory, School of Civil & Environmental

Engineering, Cornell University, Ithaca, NY USA

Francisco J. RuedaGrupo de Rios y Embalses

Universidad de Granada, Granada, Spain

DBE-0083625, CTS-0093794

Fundamental Hypothesis of the Project Biocomplexity: Physical,

Biological, and Human Interactions Shaping the Ecosystems of Freshwater

Bays (DBE-0083625)

The average time water takes to move through an aquatic system is a key variable defining the extent that ecosystems are self-organized or dominated by outside influences.

R=V/Q? A Better RTD1

Embayment

WatershedLake x,t1

t0t1t2

1

2

Residence time Age

Transit time

= F(n,t0)

Exchange

dominates

1Rueda, R.J.; Cowen, E.A. (2003). Circulation and Exchange in a Freshwater Embayment: Residence Time Scales. Submitted to Limnology and Oceanography.

Lake Ontario

Ithaca

**** LITTLE SODUS BAY ****• Area - 2.96 km2 • Deepest point – 12 m• Volume (V) – 20020311 m3

• Mean daily discharge (Q) - 0.15 m3/s

V / Q ~ 1544 days (?)

Experimental Setups for Series

of Deployments 2001-2002

•5 strings with SBE-39 pressure & temperature Loggers (S1 – S5)

• Meteorological station

• RDI-1200Khz-ADCP at Channel

• Nortek & Sontek – ADVs in Channel

• SCAMP casts in Channel

x - channel

4th Mode Barotropic Seiche is Dominant Forcing at Sub-Diurnal

Time Scales

x - channel

The Long Shallow Channel Connecting Lake Ontario to Little

Sodus Bay

Lake OntarioLittle Sodus Bay

50 m

View South View North

500 m

Lake Ontario

3 m

deep

120 F 1~2

0 F

Lit

tle S

od

us B

ay

Lake O

nta

rio

The Canonical Inviscid Picture of Exchange Flows (e.g., Armi & Farmer

1986)

Baroptropically dominated residual

circulation

Baroclinically dominated two-layer

exchange flows2 2 2

0 0 0 2 1 0( )F U Hg U g H

Along Channel Velocity Profile Time Series (1200 kHz ADCP) Reveal

Barotropic `Tide´

October 11, 2002: A Wave Driven Turbulent Boundary

Layer with large-Scales Constrained to 2-D Turbulence

T=93 minDispersion Relation:

=13 m kh = 1.6

-3

-5/3

T=3.0 s

T=12 min(H2/Kv)

0.5 =15 minKv 10-4 m/s2

Is the Inviscid Internal Hydraulic Model Valid in a Long Shallow

Channel?

Ivey (2002) suggests that if

2 640 10GrA The flow is transitional between diffusive dominance (diffusion-buoyancy balance) andinternal hydraulic dominance (buoyancy-inertia balance). 23

22v

g H HGrA

K L

HydraulicDiffusive

Note H5 and L-2 dependencies

!Shallow long flows tend NOT to be inviscid!

Estimating the Vertical Diffusivity (Kv)

• Deploy 3 ADVs on a bottom mounted frame.

• Measurement Volumes at 0.3, 1.5, 2.5 m above bed.

• Apply Shaw & Trowbridge (2001) linear filtration and differencing technique to remove waves and pass turbulence.

v

vK v w

z

Vertical Diffusivity and Modified Gravity Temporal Histories for Oct. 11,

2002

October 11, 2002 Observations Suggest Inviscid Approximation was

Extremely Poor!

Importance of Bed Friction• The ratio of friction to inertia is

2 2

2 2d d

LU UC C

h L h

• Cleary bottom friction is often as or more important than inertia!

Importance of Temporal Unsteadiness

• Heilfrich (1995) suggests that if the time for long internal waves to propagate through a channel, , is the order of the time scale of the barotropic flow, 1 – 2 hours as seen in our measurements, then temporal unsteadiness can not be ignored.

• October 2002 data 3 < w < 8.

• These are weaker than typical, 2ºC across channel leads to w 1 hour, under stronger temperature gradients, w < 1 hour.

w L g H

Temporally unsteady effects cannot be ignored in Little Sodus

More on the Importance of Unsteadiness

• Ivey (2002) Defines a fluxed based unsteadiness parameter

Tb

g H HBTE

aLB

For October 2002 observations, 0.2 < ET < 1 only for very strong baroclinic events (upwelling)

is ET > 5

Where a is the amplitude of barotropic oscillations, B is the width of the channel, Bb is the width of the basin, and T is the barotropic period. Ivey suggests that for 0.5 < ET < 5 both baroclinic and unsteady forcing is important

We Have Shown

• Vertical diffusion is often important• Bed friction is often important• Unsteadiness is often important• Flow is predominantly 2-D with the

vertical and along-channel coordinates active.

To investigate the details of this flow we turn to a numerical model

The Computational Model• Princeton Ocean Model

(POM – e.g., Blumberg & Mellor, 1987).

• 3-D, hydrostatic, Boussinesq, sigma coordinates.

• x = y =25m, 24 layers in vertical (z =0.1m in channel).

• a =2cm, T=2hr, Tc ,LSB temperature set at 25ºC.

• Effect of wind stress also investigated.

N

Modeled Scenarios

Conditions

Parameter Typical Upwelling

Wind

Tc (ºC) 1-3 19 19

g´ (m/s2) 0.005 0.028 0.028

U02 (m2/s2) 0.20 0.20 0.20

F02 2.75 0.50 0.50

UA (m/s) 0 0 4 (North)

Typical

Typical

Upwelling

Upwell-ing

Wind

Wind

Channel Channel

LS

LO

F02<~1

F02>>1

Bar

ocli

nic

Bar

otro

pic

Conclusions• Long shallow channel flows are highly complex

and the result of a subtle balance between:– Barotropic forcing– Baroclinic forcing– Turbulent diffusion– Unsteadiness– Wind stress

• Extreme care should be taken when interpreting thermistor string/temperature profile data as the presence of different temperature regimes is not sufficient to conclude active layer flow.

Evidence of Strong Mean Boundary Layer (1 minute averaged

data)

Rapidly Varying Strong Shear Exists

Animation