In this paper, the solitary wave deformation and breaking process along a sloping beach is investigated by using the improved volume of fluid method. As the initial conditions of the incident wave, Laitone's second order formulas for the free surface profile, velocity and pressure fields of a solitary wave are employed. Comparisons with the laboratory experimental data of the wave height on the slope are presented. The numerical computation have been carried out for several, configuration of beach slopes with m=I:2, 1:4, 1:8 and i:20. For a steep slope, the internal velocity field on the sloping beach is demonstrated in detail during run-up and run-down of the non-breaking wave. For a gentle slope, the phenomena of wave breaking such as wave steepening, overturning and bore formation have been successfully simulated by an improved VOF method.
In coastal engineering one is most often concerned about wave breaking due to shoaling as waves approach the shore. A knowledge of the internal kinematics of breaking wave is necessary for the estimation of loads on coastal structure and the prediction of near-shore water movements resulting in sediment transport. Although research has improved our understanding of many aspects of this phenomenon, theoretical information on breaking waves on a sloping beach is still inadequate. A large amount of literature has been published in the numerical models of breaking wave problem based on boundary integral equation schemes, such as Longuet-Higgins and Cokelet (1976), Vinje and Brevig, (1981), and Dold and Peregrine (1984). Recently, Grilli and Svendsen (1989) have developed an alternate approach based on a boundary element method (BEM). Although the procedure can provide details of the velocity and pressure variations within the wave immediately prior to its breaking, theoretical and mathematical difficulties remain in coping with wave deterioration after overturning.
