scaling laws for residual flows and cross-shelf exchange at an isolated submarine canyon
DESCRIPTION
Scaling Laws for Residual Flows and Cross-shelf Exchange at an Isolated Submarine Canyon. Dale Haidvogel, IMCS, Rutgers University Don Boyer, Arizona State University. With support from: NSF, ONR, Coriolis Lab. Gordon Research Conference, 2003. Premise and Approach. - PowerPoint PPT PresentationTRANSCRIPT
Scaling Laws for Residual Scaling Laws for Residual Flows and Cross-shelf Flows and Cross-shelf
Exchange at an Isolated Exchange at an Isolated Submarine CanyonSubmarine Canyon
Dale Haidvogel, IMCS, Rutgers University
Don Boyer, Arizona State University
Gordon Research Conference, 2003
With support from: NSF, ONR, Coriolis Lab
Premise and ApproachPremise and Approach
Laboratory datasets complement datasets obtained in the ocean, and are a valuable resource for model testing and
validation, and the study of fundamental processes.
The approach therefore is the combined application of laboratory and numerical models to idealized, but
representative, processes in the coastal ocean.
The Physical SystemThe Physical System
The physical system considered is the interaction of an oscillatory, along-slope, barotropic current with an isolated
coastal canyon.
References
Perenne, N., D. B. Haidvogel and D. L. Boyer, 2000. JAOT, 18, 235-255.
Boyer, D. L., D. B. Haidvogel and N. Perenne, 2003. JPO, submitted.
Haidvogel, D. B., 2003. JPO, submitted.
The flows here are considered to be laminar; however, a subsequent study is underway to consider the effects of
boundary layer turbulence.
The questionsThe questions
What processes and parameters control residual circulation and cross-shelf exchange at an isolated submarine canyon?
Do the laboratory and numerical datasets complement each other (e.g., corroborate each other and tell the same
dynamical story)?
The Laboratory Model
Temporal Rossby Numberf
Rot0
Rossby Number
fW
uRo 0
Burger Number 22
22
Wf
hNBu D
Ekman Number Sfh
Ek
GeometricalW
L
h
h
W
h
D
SD ,,.
Non-dimensional parameters
Parameter values (central case)
The Numerical Model : The Numerical Model : Spectral Element Ocean Spectral Element Ocean
ModelModel
Hydrostatic primitive equations
Unstructured quadrilateral grid
High-order interpolation (7th-order)
(Essentially) zero implicit smoothing
Terrain-following vertical coordinate(but via isoparametric mapping)
0.90 m
-0.90 m
Elemental partition
Isobaths (CI = 1 cm)
(Each element contains an 8x8 grid of “points”.)
Vertical partition: 25 points (8 @ 4)
Time step ~ 1 ms
Grid spacing ~ 2 mm
Experimental procedureExperimental procedure
Spin up for 10 forcing periods (240 seconds)
Run an additional two forcing periods collecting snapshots at 1/20th period
Post-process time series for:
- residual circulation (Lab/Numerical)
- residual vorticity and divergence (L/N)
- on-shelf transport of dense water (N only)
- mean and eddy density fluxes (N only)
- mean energy budget
Repeat for parameter variations
Density at the shelf-break level (first two periods)
Colors show the density of water just above the continental shelf break(red: lighter, blue: heavier, grey: unchanged from initial)
Figure 2: Vorticity (left) and horizontal divergence (right) fields for the central experiment discussed by PHB (Experiment 01 in the present study) as obtained from (a) the laboratory, (b) the SEOM model using a parameterized shear stress condition along the model floor and (c) the SEOM model using a no-slip condition, including a highly resolved Ekman layer, along the model floor.
(a)
(b)
(c)
Time-mean vorticity Time-mean divergence
Laboratory
Numerical
(stress law)
Numerical
(no-slip)
Scaling Laws for Residual Flows
• Conservation of Vorticity
• Conservation of Energy
• Ekman layer dynamics
*
1/ 2~d
z Roz
h Bu
DSS h
Bu
Roh
f
h
f
2/1
~
LuBuRo
Ro
h
h
tS
D02/1
~
Water parcel passing over canyon rim has a natural vertical length scale set by the depth change it would take to convert KE to PE
Conservation of potential vorticity assuming that water column stretches by an amount proportional to this vertical distance
Solve for relative vorticity of a parcel, and integrate over the length of the canyon and over a forcing cycle to get total vorticity
WLED B2/1~
2/12/1
0
1
)/(~
EBuRohh
Ro
u
U
tDS
2/1
2/30
0
1
Nfu
u
U
WUB /~ 1
Equate gain of cyclonic vorticity over a forcing cycle to the loss expected in a laminar Ekman bottom boundary layer
Solve for ratio of residual flow strength to magnitude of oscillatory current
The equivalent expression in dimensional form
0
0.1
0.2
0.3
0 5 10 15
0
1
u
U
L1
L2L3
L4N1
N2
N3
N4
N6
N7N9
N10
N11
Characteristic speed of the normalized time-mean flow at the shelf break level as obtained from the laboratory experiments and the numerical model against the scaling relation . The symbols near the data points correspond to either laboratory (L) or numerical (N) experiments The dashed line is the best fit = (0.9 + 12.7) 10-2.
Scaling Laws for Cross-shelf Transport
• Linear viscous arguments do not suffice to give a scaling for cross-shelf transport of dense water
- role of advection
- independent roles of mean and eddies
• The association of on-shelf pumping with a local increase in potential energy suggests an energy approach
What can we do to make progress?
• Let’s assume:
• PE gained by cross-shelf transport is proportional to KE in the incident oscillatory current
• PE gained is independent of stratification
•Conclude: cross-shelf transport is proportional to the square of Ro, inversely proportional to Ro_t, and
independent of Bu
• Since we do not know the answer, we try a minimalist dynamical explanation (aka, guesswork) and hope for a
lucky break
Lucky Break!!!
SummarySummary
Scalings are proposed for residual circulation and cross-shelf transport of dense water
The numerical and laboratory models are consistent (e.g., produce the same scaling for the residual flows)
Complicating issues: relationship of laboratory analogue to the “real ocean”; omission of (e.g.) small-scale topographic roughness, multiple canyons, boundary layer
turbulence, etc.
Rotating tank at the Coriolis Laboratory Grenoble, France
Tank is 13m (43 ft) in diameter