Numerical Prediction of Regular Wave Breaking on Very Gentle Slopes

摘要

Regular wave deformation and breaking on very gentle slopes is calculated by Mixed-Eulerian-Lagrangian procedure.The velocity potentials and their normal derivatives on the boundary are calculated through the mixed 0-1 boundary elementmethod. The wave elevation and the potentials of time-stepping integration are determined by the 2nd-order Taylor expansionat the nodes of free surface boundary elements. During calculation the x-coordinates of the free surface element nodes aresupposed to remain unchanged, i.e. the partial derivatives of wave elevation and potentials with respect to x are consideredas zero. The numerical results of asymmetric parameters of breaking waves are verified by experimental study. It is shownthat when the wave asymmetry is weak, the maximum horizontal velocity of water particales occurs at the wave peak and, theaverage ratio of this maximum velocity to wave celerity is 0.96. However, when the wave asymmetry is strong, the maximumhorizontal velocity of water particles occurs just before the wave crest, and the average ratio of the maximum velocity to wavecelerity is about 0.98. The numerical results also show that the asymmetry of wave profiles affects the value of the wavebreaking index (H/d)b, that is, when the asymmetric characteristics are weak, the value of wave breaking index coincideswith that given by Coda; on the contrary, when the asymmetry of wave profiles is notable, the value of wave breaking indexis close to Nelson's result. The experimental study gives the same couclusions.