Wave Modeling

1. Wave Modeling Local Wave Transformations Billy L. Edge & Margery Overton CVEN 695-02

2. Bathymetric Data

3. Why do we need wave models? • Wave climate assessment at the project site is important to most coastal & ocean engineering projects, including - navigation and channel studies - on/offloading of ships - optimization of harbor layouts - design of structures (breakwaters, etc.) • shoreline erosion projects, etc. • Nearshore wave conditions are normally determined from deepwater conditions - long-term nearshorewave data are usually unavailable - transform offshore wave data to nearshore (wind-generation, shoaling, refraction, breaking, dissipation, bottom friction) – regional scale models - investigate local scale phenomena (refraction, wave reflection, diffraction, nonlinear wave-wave and wave-current interaction) –local scale models

4. Regional Scale Wave Modeling • Scale O(100 km~5000 km) • Spectral wind-wave models (WAM) • Scale O(10 km ~100 km) • Spectral wind-wave models (STWAVE and SWAN) • Dominant process: wind input, shoaling and refraction • Wave action: conservation equation • Assume phase-averaged wave properties vary slowly over distances of the order of a wavelength • Cannot accurately resolve rapid variations that occur at sub-wavelength scale due to wave reflection/diffraction

5. Local Scale Wave Modeling • Scale O(1 km ~ 10 km) • Elliptic mild-slope model (CGWAVE) • Parabolic mild-slope model (REFDIF) • Boussinesq wave model (BOUSS-2D) • Dominant processes: shoaling, refraction, breaking, reflection, diffraction, wave nonlinearities due to interactions of different frequencies and ambient currents and structures • All models use vertically integrated eqns for wave propagation in 2D horizontal plane • CGWAVE assumes hyperbolic cosine variation of the velocity potential over depth, and BOUSS-2D assumes a quadratic variation

7. STWAVE CGWAVE/ REFDIF BOUSS Shoaling/Refraction    Wave Breaking    Wave-Current Interaction    Nonlinear Interactions   Diffraction/Reflection   Phase averaging Phase averaging Phase resolving Summary of Model Features

8. Spectral Wind-Wave Models • Advantages • wind-wave generation • shoaling, refraction, breaking • wave-current interaction • applicable to large domains (deep to shallow water) • Disadvantages • reflection, diffraction • steady-state

9. Elliptic Mild-Slope Models • Advantages • well suited for long-period oscillations • shoaling, refraction, breaking, bottom friction • reflection, diffraction • wave-current interaction (in future version) • flexibility of finite elements • Disadvantages • nonlinear interactions in shallow water (in future version)

10. Parabolic Mild-Slope Models • Advantages • shoaling, refraction, breaking, bottom friction • Refraction, reflection, diffraction • wave-current interaction • Disadvantages • Grid limitations in size and regular gridding

11. Boussinesq Wave Models • Advantages • shoaling, refraction, breaking, bottom friction • reflection, diffraction, nonlinear interactions • wave-induced currents, wave-current interaction • Disadvantages • computationally intensive • 2-D very computationally intensive

12. Applicability • STWAVE: • ideal for wave propagation in open water • SWAN: • time dependent, larger domain • Mild-Slope: • ideal for long-period oscillations in harbors (CGWAVE) • suited for strong diffraction & reflection • more flexibility with finite element method(CGWAVE) • rapid solutions(REFDIF) • BOUSS-2D: • ideal for wave transformation near entrance channels and harbors • nonlinear interactions in shallow water • wave-induced currents near structures and surfzone

13. Engineering Practice - 1 • CORPS wave models have good physics to provide reliable estimates to projects • Integrated with tools (SMS,etc.) • Used in support of a variety of research and engineering studies • Have strengths & weaknesses – no one model can do it all! • Validated with field/lab data & checked against analytical solutions • MIKE21 wave models … • DELFT3D wave models …

14. STWAVE • Wind forcing • Current forcing • Wave-current • Regional modeling • Deepwater wave transformation up to pre-breaking depths • Finite difference • Spectral, steady state • Quick to run • Good front end STWAVE computed wave Heights

15. CGWAVE • Diffraction • Reflection • Refraction • Breaking • Bottom friction • Entrance losses • Finite element mesh • Spectral sea state • Wave-current Interaction (in testing) • Wave-wave Interaction (in testing) • No wind Input CGWAVE Sea state for Morro Bay, CA

16. BOUSS-2D • Time-dependent • Open coast, harbor and surf zone waves • Shoaling, refraction, reflection, diffraction, dissipation and run-up • Finite difference • Random spectral sea state modeling • Wave-induced currents • Nonlinear waves, sub- and super-harmonics BOUSS-2D Simulation for Everglades project

17. Engineering Practice -3 • Have to use models if no nearshore field data available • Using models that are in common practice and have acceptance in the engineering community is preferred to one of a kind models • Project-specific problems must determine the type of model for a study • Detailed model documentation is necessary

19. Grays Harbor, Washington

20. Grays Harbor, Washington

22. Entrained Sand

23. Regions of Application of Wave Models

24. Solitary/CnoidalWaves

25. Wave Prediction (Deep Water)

26. Combined Refraction and Shoaling(Dean and Dalrymple)

28. Random Waves • Analysis Methods • Eye • ZUC • ZDC • Spectral

29. Random Wave Spectra JONSWAP

30. Wave Spectra JONSWAP TMA Pierson Moskowitz Other

31. Mild Slope Equation http://www.coastal.udel.edu/refdif/img20.htm

32. CONCLUSIONS • BOUSS-2D is a powerful nonlinear model for estimating waves in shallow and intermediate water depths where wave diffraction and nonlinearities are important • Model is ready for project applications • SMS interface of BOUSS-2D • MAKE THINGS AS SIMPLE AS POSSIBLE BUT NO SIMPLER!!! – “Albert Einstein”

33. REFDIF