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 nearshore wave 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. Summary of Model Features Phase resolvingPhase averaging Diffraction/Reflection Nonlinear Interactions Wave-Current Interaction Wave Breaking Shoaling/Refraction BOUSS CGWAVE/ REFDIF STWAVE

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. 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 STWAVE

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 -2 Modeling waves in navigation channels/inlets is most challenging -- need reliable lab & field data to check complex physics of models WIS data suitable for open-coast, but may be transformed and used in navigation projects Use STWAVE or SWAN to transform deepwater wind/wave climate to nearshore (10 to 30 m) depth contour

18. 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

20. Grays Harbor, Washington

23. Entrained Sand

24. Local Wave Kinematics

25. Regions of Application of Wave Models

26. Solitary/Cnoidal Waves

27. Wave Prediction (Deep Water)

28. Combined Refraction and Shoaling (Dean and Dalrymple)

29. Wave Decay

31. Random Waves Analysis Methods –Eye –ZUC –ZDC –Spectral

32. Random Wave Spectra JONSWAP

33. Wave Spectra TMA Pierson Moskowitz Other JONSWAP

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

35. 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”

36. REFDIF