wave-current interactions and sediment dynamics juan m. restrepo mathematics department physics...
Post on 20-Dec-2015
213 views
TRANSCRIPT
![Page 1: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/1.jpg)
Wave-Current Interactions and Sediment Dynamics
Juan M. RestrepoMathematics Department
Physics DepartmentUniversity of Arizona
Support provided by NSF, DOE, NASA
![Page 2: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/2.jpg)
CollaboratorsCollaborators
• Jim McWilliams (UCLA)Jim McWilliams (UCLA)
• Emily Lane (UCLA)Emily Lane (UCLA)
• Doug Kurtze (St. Johns)Doug Kurtze (St. Johns)
• Paul Fischer (ANL)Paul Fischer (ANL)
• Gary Leaf (ANL)Gary Leaf (ANL)
• Brad Weir (Arizona)Brad Weir (Arizona)
![Page 3: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/3.jpg)
WAVESWAVES ANDAND MATHMATH Nonlinear and Dissipative WavesNonlinear and Dissipative Waves
dissipative Burgersdissipative Burgers Nonlinear and Dispersive WavesNonlinear and Dispersive Waves
Korteweg de VriesKorteweg de Vries Eikonal Equations/RaysEikonal Equations/Rays Amplitude EquationsAmplitude Equations
WHAT NEXT?
![Page 4: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/4.jpg)
• Climate Dynamics Climate Dynamics (HEAT,TRANSPORT)(HEAT,TRANSPORT)
days-100 yrs, 1 Km-6 Kmdays-100 yrs, 1 Km-6 Km
• Shelf-Ocean DynamicsShelf-Ocean Dynamics
(TRANSPORT/WAVES-CURRENTS)(TRANSPORT/WAVES-CURRENTS)
10 sec-season, 10 m-100 Km10 sec-season, 10 m-100 Km
• Shoaling Zone Dynamics Shoaling Zone Dynamics
(RADIATION STRESSES,TRANSPORT)(RADIATION STRESSES,TRANSPORT)
5 sec-season, 1 m- 2 Km5 sec-season, 1 m- 2 Km
![Page 5: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/5.jpg)
• Advection: waves, causal effects, Advection: waves, causal effects,
• Multiscale: resolving dynamicsMultiscale: resolving dynamics
• Stochasticity: turbulence, Stochasticity: turbulence, parametrizations, quantifying parametrizations, quantifying uncertainty, data assimilation.uncertainty, data assimilation.
ADVECTIVE/MULTISCALE ADVECTIVE/MULTISCALE STOCHASTIC FOCUSSTOCHASTIC FOCUS
![Page 6: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/6.jpg)
Can Gravity Waves Can Gravity Waves Influence Basin Scale Influence Basin Scale Circulation?Circulation?• Climate lore: Climate lore: nono
• Data: Data: not availablenot available
• Lab: no Lab: no experimentsexperiments
• Basin scale Basin scale circulation models circulation models do not incorporate do not incorporate this aspectthis aspect
![Page 7: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/7.jpg)
Ocean circulation is forced by radiation and surfacefluxes and results from balance of Earth’s rotation, viscous and buoyancy forces
![Page 8: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/8.jpg)
Hemispheric, 2D Ocean Basin
TS)
![Page 9: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/9.jpg)
The Conveyor BeltThe Conveyor Belt
![Page 10: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/10.jpg)
Stommel’s 2-Box ModelStommel’s 2-Box Model
![Page 11: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/11.jpg)
2-Box Steady Solutions2-Box Steady Solutions
f = (R x – y)dx/d = (1-x) - |f|xdy/d = 1–y - |f| y
Stommel’sEquations
Steady State Solutions:
densitydensity
temperature
salt
![Page 12: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/12.jpg)
Steady State Solutions:
Haline
Temp
![Page 13: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/13.jpg)
Advective EffectsAdvective Effects
f = (R x – y)dx/d = (1-x) - |f|[x(-s)-x()]dy/d = 1–y - |f|[y(-s)-y()]
Kurtze, Restrepo, JPO, vol 31,’01
![Page 14: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/14.jpg)
Conclusions?Conclusions?
• Advective effects potentially Advective effects potentially contribute to climate variabilitycontribute to climate variability
• Advective effects: important in THC?Advective effects: important in THC?
• Teleconnections in ENSO? (Tropical Teleconnections in ENSO? (Tropical Climate)Climate)
• Teleconnections in NAO? (North Teleconnections in NAO? (North Atlantic Oscillation)Atlantic Oscillation)
![Page 15: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/15.jpg)
Wave Effects on ClimateWave Effects on Climate• Thermohaline Thermohaline
teleconnectionteleconnection• Residual flow due Residual flow due
to wavesto waves
McWilliams Restrepo, JPO, vol 32, ‘99
![Page 16: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/16.jpg)
Air/Sea InterfaceAir/Sea Interface
• Momentum: waves, thermocline Momentum: waves, thermocline mixing, wind.mixing, wind.
• Mass: water evaporation and Mass: water evaporation and precipitation, river inflows, precipitation, river inflows, chemicals.chemicals.
• Energy: sun radiation, other thermal Energy: sun radiation, other thermal balances.balances.
![Page 17: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/17.jpg)
Air/Sea Interface BudgetsAir/Sea Interface Budgets
![Page 18: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/18.jpg)
Energy BudgetEnergy Budget
![Page 19: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/19.jpg)
Transport Velocity due to Transport Velocity due to Oscillatory FlowsOscillatory Flows• Linear Waves: Linear Waves:
particle paths closeparticle paths close• Nonlinear Waves: Nonlinear Waves:
particle paths do particle paths do not closenot close
![Page 20: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/20.jpg)
Restrepo, Leaf, JPO, vol 32, ‘02
![Page 21: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/21.jpg)
Quasi-Geostrophic CaseQuasi-Geostrophic Case
![Page 22: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/22.jpg)
![Page 23: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/23.jpg)
![Page 24: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/24.jpg)
![Page 25: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/25.jpg)
![Page 26: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/26.jpg)
Estimates on Wave/Driven Estimates on Wave/Driven FlowFlow
Wind driven transport:
Stokes transport:
![Page 27: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/27.jpg)
Empirical EstimatesEmpirical Estimates
Planetary Geostrophic Balance
![Page 28: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/28.jpg)
![Page 29: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/29.jpg)
Wind-driven SpectraWind-driven Spectra
![Page 30: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/30.jpg)
![Page 31: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/31.jpg)
![Page 32: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/32.jpg)
![Page 33: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/33.jpg)
MathematicsMathematics• Vortex force representationVortex force representation UU¢r¢rU = 1/2U = 1/2rr|U|U22|+|+r£r£UU££ U U Radiation stress Radiation stress
representationrepresentation UU¢r¢rU = U = r¢r¢(UU)+U (UU)+U r¢r¢ U U
• Introduction of stochastic Introduction of stochastic componentcomponent
•Lagrangian/Eulerian mapping
Capturing multiscalebehavior of systemof hyperbolic pde’s
![Page 34: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/34.jpg)
Shelf Wave/Current Shelf Wave/Current DynamicsDynamics
• 10 secs-months, 100m-100 10 secs-months, 100m-100 KmKm
• Speed: waves > currentsSpeed: waves > currents
• kH ~ 1kH ~ 1
• Applications: Applications:
erodible bed dynamicserodible bed dynamics
river plume evolutionriver plume evolution
algal/plankton blooms algal/plankton blooms
pollutionpollution
McWilliams, Restrepo, Lane, JFM 2004
![Page 35: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/35.jpg)
Shelf Wave/Current ModelShelf Wave/Current Model
• Start with Shallow Water Equations Start with Shallow Water Equations (ignore dissipation, for now)(ignore dissipation, for now)
• Velocity field separation:Velocity field separation:
waveswaves
currentscurrents
long wave componentlong wave component
![Page 36: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/36.jpg)
• 2 space scales, average over smaller ones2 space scales, average over smaller ones
• 3 time scales, average over faster ones3 time scales, average over faster ones
• Waves (amplitude equations)Waves (amplitude equations)
• Waves and Currents have depth and Waves and Currents have depth and stratification dependencestratification dependence
• Frequency/wavenumber evolution Frequency/wavenumber evolution equationsequations
Restrepo, Continental Shelf Res, 2001
![Page 37: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/37.jpg)
![Page 38: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/38.jpg)
![Page 39: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/39.jpg)
![Page 40: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/40.jpg)
Current Effects on WavesCurrent Effects on Waves
Current forcing:
Fixed bottom topography
![Page 41: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/41.jpg)
Effect of CURRENTS
WAVEAmplitude
WAVEPhase
NO CURRENTS
![Page 42: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/42.jpg)
Wave Effects on CurrentsWave Effects on Currents
![Page 43: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/43.jpg)
NO WAVES WAVES
![Page 44: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/44.jpg)
Inner Shelf/Shoaling RegionInner Shelf/Shoaling Region
• 5 seconds-6 hours, 5 seconds-6 hours, 1m-2Km1m-2Km
• Traditional Radiation Traditional Radiation Stress:Stress: wave-averaged wave-averaged effects on currents: effects on currents: divergence of a stress divergence of a stress tensortensor
• Vortex Force Vortex Force RepresentationRepresentation: wave-: wave-average effects: average effects: decomposed in terms decomposed in terms of a Bernoulli head of a Bernoulli head and a vortex force.and a vortex force.
Lane, Restrepo, McWilliams, JFM 2005
![Page 45: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/45.jpg)
Radiation StressesRadiation Stresses
• Compared RS (Hasselmann), GML Compared RS (Hasselmann), GML (MacIntyre), VF (McWilliams, (MacIntyre), VF (McWilliams, Restrepo, Lane).Restrepo, Lane).
• Waves >> currents new Waves >> currents new interpretationinterpretation
• Revisit old problems: rip currents, Revisit old problems: rip currents, longshore currents.longshore currents.
![Page 46: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/46.jpg)
Dissipative EffectsDissipative Effects
White capping
Zt =f(Zt,t)dt+s(Zt)dW
with
f(x,t) = a cos(k x - t)<Wt Wx> = (t-s)<Wt> = 0
Yields dissipative coupling of the total rotation of the current and the Stokes drift velocity uS
r £ [uS £ ]
Dissipative effect…but how does it manifest itself?
![Page 47: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/47.jpg)
BASIC DISSIPATION MODELBASIC DISSIPATION MODEL
• New particle motion:New particle motion:
dZdZtt = = ( ( u,w) dt + u,w) dt + 22 v dt + B(Z v dt + B(Ztt,T) ,T) dWdWtt
Sea Elevation: = a cos (k x - = a cos (k x - t – [ 2 t – [ 2 ]]1/21/2 W Wtt) e) e-- t t
dxdxtt = = u dt + [2 B(X,T)] u dt + [2 B(X,T)]1/21/2 dW dWhhtt
dzdztt = = w www dt dt
![Page 48: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/48.jpg)
Stokes Drift with DissipationStokes Drift with Dissipation
VVStSt = A = A22 k/2 sinh k/2 sinh22[kH] [kH]
[cosh [2k(z+H)]+1/[cosh [2k(z+H)]+1/22(2 (2 22+[+[--DD22/2])/2])DD
WWstst = - A = - A22 k/ 2 sinh k/ 2 sinh22[kH] (16 [kH] (16 //) ) DD
D D = e= e-- T T [1 + ( [1 + ( + D + D22/2)/2)22//22]]-1-1
![Page 49: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/49.jpg)
Effect of DissipationEffect of Dissipation
DRIFT, NO DISSIPATION
Dissipation
DRIFT, DISSIPATION
![Page 50: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/50.jpg)
Effect of DissipationEffect of Dissipation
No dissipation
With dissipationInitial vorticity
![Page 51: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/51.jpg)
NO DISSIPATION WITH DISSIPATION
VELOCITY VELOCITY VELOCITY + DRIFTVELOCITY + DRIFT
![Page 52: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/52.jpg)
Future WorkFuture Work
• Regional Ocean Model (ROMS)Regional Ocean Model (ROMS)
• Dissipative Mechanisms in Dissipative Mechanisms in Wave/Currents: wave breaking, Wave/Currents: wave breaking, bottom drag, surface pollution, bottom drag, surface pollution, stratification.stratification.
• Wind ForcingWind Forcing
![Page 53: Wave-Current Interactions and Sediment Dynamics Juan M. Restrepo Mathematics Department Physics Department University of Arizona Support provided by NSF,](https://reader031.vdocument.in/reader031/viewer/2022032704/56649d485503460f94a23c29/html5/thumbnails/53.jpg)
Further Information:Further Information:
Juan M RestrepoJuan M Restrepo
www.math.arizona.edu/~restrepowww.math.arizona.edu/~restrepo