Exchange Flows Through a Long Shallow Channel
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Transcript of Exchange Flows Through a Long Shallow Channel
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
Litt
le S
odus
Bay
Lake
Ont
ario
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 min Dispersion Relation: =13 m kh = 1.6
-3
-5/3
T=3.0 s
T=12 min(H2/Kv)0.5 =15 min
Kv 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 HGrAK 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.
vvK v wz
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 Ch 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 ScenariosConditions
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
oclin
icB
arot
ropi
c
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