Numerical prediction of regular wave breaking on very gentle slopes

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 element method. The wave elevation and the potentials of Lime-stepping integration are determined by the 2nd-order Taylor expansion at the nodes of free surface boundary elements. During calculation the x-coordinates of the free surface element nodes are supposed to remain unchanged, i.e. the partial derivatives of wave elevation and potentials with respect to x are considered as zero. The numerical results of asymmetric parameters of breaking waves are verified by experimental study. It is shown that when the wave asymmetry is weak, the maximum horizontal velocity of water particales occurs at the wave peak and, the average ratio of this maximum velocity to wave celerity is 0.96. However, when the wave asymmetry is strong, the maximum horizontal velocity of water particles occurs just before the wave crest, and the average ratio of the maximum velocity to wave celerity is about 0.98. The numerical results also show that the asymmetry of wave profiles affects the value of the wave breaking index (H/d) (b), that is, when the asymmetric characteristics are weak, the value of wave breaking index coincides with that given by Goda; on the contrary, when the asymmetry of wave profiles is notable, the value of wave breaking index is close to Nelson's result. The experimental study gives the same conclusions.