1. National Center for Computational Hydroscience and Engineering The University of Mississippi Wave Model of CCHE2D-Coast For Model Training Course Yan Ding, Ph.D. Research Assistant Professor National Center for Computational Hydroscience and Engingeering The University of Mississippi, Oxford, MS 38677 March, 2008

2. Deformation of Irregular Waves Deformation of waves from offshore to onshore Shoaling Refraction Diffraction Reflection Wave Breaking Wave Transmission through structure Bottom Friction Wave-Current Interaction …… Incident Wave

3. Wave Transmission through a Nonsubmerged Structure Wave transmission coefficient K t = H r /H f Transmission through and over a riprap structure H r = Wave height transmitted to the water body in the rear side of the structure H f = Wave height in front of the structure Overtopping K t can be determined by means of the experimental studies on the features of structures; The values can be found from most of coastal textbooks and coastal engineering manuals

4. Irregular Wave Models Phase-averaged models 1. Short-wave-averaged models dealing with irregular and multidirectional waves developed on a statistical basis; 2.Spectral Energy Balance Equation (SEB); 3.The models can predict irregular wave transformation in a large- scale region (1-100km), but not time-varying wave conditions Phase-resolving models 1.Simulate the time-varying processes of short waves, and even wave breaking process; 2.It’s suitable for small region and can give highly spatial resolutions.

5. Multidirectional Wave Spectral Model (1) Energy Balance Equation + Diffraction The variations of wave energy density S(x,y, ,f) under the attack of irregular/multi-directional incident waves, can be represented as follows, (Mase 2001) where  = wave direction (-0.5  – 0.5  ), v = energy transport velocity, Q = source term arisen from energy dissipation, e.g., wave breaking and bottom friction.  = empirical coefficient (=2.0-3.0). C=wave celerity, Cg=wave group celerity Diffraction Term Fig. Coordinate System

6. Wave Spectrum S(f,θ) and Wave Properties S(f)= Wave Frequency Spectrum D(θ,f)  = Wave Directional Spreading Function Multidirectional Wave Spectrum Energy Significant Wave Height H 1/3 Based on the Rayleigh Distribution Total Wave Energy Mean Wave Direction Averaged Wave Period

7. Wave Spectral Model (2) Frequency Spectra S(f) Bretschneider-Mitsuyasu (1970) (B-M Spectrum) Texel Marsen Arsole (TMA) Spectrum (Bouws et al. 1985) h=water depth f p =peak frequency  = peak enhancement factor

8. Bretschneider-Mitsuyasu (B-M) Spectrum Texel Marsen Arsole (TMA) Spectrum (Bouws et al. 1985) Wave Spectral Model (3) Directional Spreading Function D(q,f)  m =mean wave direction; J=number of terms in the series (=20)  m = spreading parameter

9. Wave Breaking Criteria Goda’s Criterion (Goda 1975) H b = Breaking Wave Height L 0 = Wave Length A = Empirical Coefficient (0.12 – 0.18)  = Sea Bed Slope Saturated Wave Breaking h = water depth γ = empirical coefficient, 0.6-0.8

10. Generation of Non-Orthogonal Mesh Covering Touchien Estuary CCHE2D Mesh Generator http://www.ncche.olemiss.ed u/index.php?page=freesoftw are#mesh

11. Close-up View of Mesh

12. Wave Spectrum Input x y Onshore Offshore +θ+θ -θ-θ Offshore wave spectral properties: Wave height (m) Period (s) Mean Direction (Deg) Tide Elevation (m)

13. Input Data (1) Filename = *_wave.dat, where * = a project name, e.g. touchien

14. Input Data (2) Filename = n_karl.dat

15. Output Filename = wave_res.plt

16. Demonstration Dialogue Input

17. Contact Information Yan Ding, Ph.D National Center for Computational Hydroscience and Engineering The University of Mississippi Carrier Hall, Room 102 University, MS 38677 U.S.A. Email: ding@ncche.olemiss.eduding@ncche.olemiss.edu Phone: +1 (662) 915-1339 Website: http://www.ncche.olemiss.eduhttp://www.ncche.olemiss.edu