Exchange Flows Through a Long Shallow Channel Edwin A. Cowen DeFrees Hydraulics Laboratory, School of Civil & Environmental Engineering, Cornell University, Ithaca, NY USA Francisco J. Rueda Grupo de Rios y Embalses Universidad de Granada, Granada, Spain DBE , CTS

Fundamental Hypothesis of the Project Biocomplexity: Physical, Biological, and Human Interactions Shaping the Ecosystems of Freshwater Bays (DBE ) 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 RTD 1 Embayment WatershedLake x,t 1 t0t0 t1t1 t2t2 11 22 Residence timeAge Transit time = F(  n,t 0 ) Exchange dominates 1 Rueda, 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 km 2 Deepest point – 12 m Volume (V)– m 3 Mean daily discharge (Q) m 3 /s    V / Q ~ 1544 days (?)

Experimental Setups for Series of Deployments 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

4 th 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 Ontario Little Sodus Bay 50 m View South View North 500 m Lake Ontario 3 m deep

Little Sodus Bay Lake Ontario The Canonical Inviscid Picture of Exchange Flows (e.g., Armi & Farmer 1986) Baroptropically dominated residual circulation Baroclinically dominated two-layer exchange flows

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 min Dispersion Relation: =13 m  kh = /3 T=3.0 s T=12 min (H 2 /K v ) 0.5 =15 min K v  m/s 2

Is the Inviscid Internal Hydraulic Model Valid in a Long Shallow Channel? Ivey (2002) suggests that if The flow is transitional between diffusive dominance (diffusion-buoyancy balance) and internal hydraulic dominance (buoyancy-inertia balance). Hydraulic Diffusive Note H 5 and L -2 dependencies! Shallow long flows tend NOT to be inviscid!

Estimating the Vertical Diffusivity ( K v ) 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.

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 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. Temporally unsteady effects cannot be ignored in Little Sodus

More on the Importance of Unsteadiness Ivey (2002) Defines a fluxed based unsteadiness parameter For October 2002 observations, Where a is the amplitude of barotropic oscillations, B is the width of the channel, B b is the width of the basin, and T is the barotropic period. Ivey suggests that for 0.5 < E T < 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,  T c,LSB temperature set at 25ºC. Effect of wind stress also investigated. N

Modeled Scenarios Conditions ParameterTypicalUpwellingWind  T c (ºC) g´ (m/s 2 ) U 0 2 (m 2 /s 2 ) 0.20 F02F U A (m/s ) 00 4 (North)

Typical

Upwelling

Upwell- ing

Wind

Channel LS LO F 0 2 <~1 F 0 2 >>1 Baroclinic Barotropic

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