University:
Boston University
Course:
CAS EE 144 | Introduction to Oceanography
Academic year:

2024
Views:

126

Pages:

25
Author:

Adriel Kelley

Large-Scale Coastal Modeling: Wind Wave Applications Presentation Outline  Numerical setup for large-scale coastal wave problems    Bathy, wave generation, etc. Which equations to use? Applications    Hurricane waves and levee overtopping Nearshore waves and wave-induced circulation Harbor resonance studies How to generate waves  Hot start   Earthquake sources – ∆h = ∆η With velocity (e.g. Solitary Wave) our without (EQ) How to generate waves  Internal Source  Add a forcing term to the equations, adding either mass or momentum, along a strip inside the domain Linear Boussinesq-type equations over constant depth How to generate waves  Internal Source  Add a forcing term to the equations, adding either mass or momentum, along a strip inside the domain Boundary conditions   For lateral boundaries, little success with local radiation boundary conditions (nonlinear dispersive waves) Use sponge layers – another source term in both mass and momentum equations to remove mass & energy along the boundaries Boundary conditions   For lateral boundaries, little success with local radiation boundary conditions (nonlinear dispersive waves) Use sponge layers – another source term in both mass and momentum equations to remove mass & energy along the boundaries Dissipation Parameters  Bottom Friction …+ Dissipation Parameters  Breaking (ad-hoc “tack-on” to momentum equation) …+ Fb=0  Tune parameters in eddy viscosity model based on comparisons with lab & field data   See: Kennedy, A. B., Chen, Q., Kirby, J. T., and Dalrymple, R. A. (2000).‘‘Boussinesq modeling of wave transformation, breaking, and runup. I:1D.’’ J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 126(1), 39– 47. …Or just use limiters Which Equations to use?  Which Equations to use?  Weakly nonlinear, “extended” Boussinesq-type model (Nwogu, O., 1993. Alternative form of Boussinesq equations for nearshore wave propagation. Journal of Waterway, port, Coastal, and Ocean Engineering 119 (6), 618–638.     Continuity equation has as truncation error = O(εµ2,µ4) , includes 1st to third (uxxx) derivatives. Momentum equation has truncation error = O(εµ2 ,µ4) w/ ε=a/h, µ=h/L, includes 1st to third (uxxt) derivatives. (same as Peregrine’s model) Needed a differencing scheme with truncation error derivative order at least (uxxxx) and time integration of at least (utttt) Considerably better dispersion properties that Peregrines model (usually important) Which Equations to use?  Highly nonlinear, “extended” Boussinesqtype model (Wei, G., Kirby, J.T., Grill, S.T., Subramanya, R., 1995. A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. Journal of Fluid Mechanics 294, 71–92.)     Continuity equation has as truncation error = O(µ4) , includes 1st to third (uxxx) derivatives. Nonlinear high-order derivatives as well, e.g (vux)xy Momentum equation has truncation error = O(µ4) includes 1st to third (uxxt) derivatives. Need a differencing scheme with truncation error derivative order at least (uxxxx) and time integration of at least (utttt) Better prediction of very nonlinear waves (e.g. near breaking) [sometimes important, but near the “noise” level of field data] Which Equations to use?  Weakly nonlinear, Peregine model      Weakly nonlinear, “extended” model      Memory cost per 100x100 grid points (using 2nd order FV method, not memory optimized) ~ 2 MB Intermediate variable “groups” size (nx,ny) ~20 Stencil is 3 points wide CPU time / time step ~ 0.0025 s (single core, simple problem) Memory cost per 100x100 grid points (using 4th order FV method, not memory optimized) ~ 5 MB Intermediate variable “groups” size (nx,ny) ~25 Stencil is 5 points wide CPU time / time step ~ 0.01 s (single core, simple problem) Highly nonlinear, “extended” model     Memory cost per 100x100 grid points (using 4th order FV method, not memory optimized) ~ 15 MB Intermediate variable “groups” size (nx,ny) ~80 Stencil is 9 points wide CPU time / time step ~ 0.025 s (single core, simple problem) Which Equations to use?  Weakly nonlinear, “extended” model     Memory cost per 100x100 grid points (using 4th order FV method, not memory optimized) ~ 5 MB Intermediate variable “groups” size (nx,ny) ~25 Stencil is 5 points wide CPU time / time step ~ 0.01 s (single core, simple problem) For the Boussinesq-type class of model to have a future it must be favorably competitive (in terms of computational time) with 3D models. Can this equation set be accurately (and efficiently) solved on GPU? If not… Hurricane Katrina • Max sustained winds 175 mph (280 km/h) • Made landfall just west of New Orleans with winds of 125 mph (205 km/h) • Max storm surge (just east of the eye) was 28 ft (8.5 m) • Max storm surge in eastern New Orleans ~20 ft (6 m); surge in northern New Orleans, Lake Pontchartrain ~14 ft (4 m) Hurricane Katrina -Damage in Mississippi Hurricane Katrina -Damage in Mississippi Hurricane Katrina -Damage in Mississippi Hurricane Katrina -Damage in Mississippi Hurricane Katrina -Damage in Mississippi Hurricane Katrina – Damage in New Orleans • Most of New Orleans is below sea level, and requires a complex system of flood walls and levees to protect against hurricane surges Hurricane Katrina – Damage in New Orleans Hurricane Katrina – Damage in New Orleans Hurricane Katrina – Damage in New Orleans • U.S. Army Corps of Engineers organized a large forensic study of Katrina & its impact – Interagency Performance Evaluation Task Force (IPET) – Goals were to examine: • • • • The System The Storm The Performance The Consequences • Many different aspects, hydrodynamic, structural, geotech, social science,… • Nearshore wave forces & impact through detailed hydrodynamic modeing Hurricane Katrina – IPET Hydrodynamics • Multi-model, multi-scale simulation approach: – Surge predicted by ADCIRC, based on the observed/simulated wind and pressure field • Resolution ~100m, but as low as ~1m in certain areas – Wave generation predicted by STWAVE, based on wind and water levels • Coupled with ADCIRC • Resolution ~100m, cannot resolve nearshore hydrodynamics – For the nearshore, Boussinesq is used • Water level provided by ADCIRC • Incident waves provided by STWAVE • Resolution ~1m • Simulate the entire Gulf of Mexico (1 million square miles = 2.5*1012 m2) with refined resolution ~ 1m

Large-Scale Coastal Modeling - Wind Wave Applications

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