Evolution of breaking waves on sloping beaches

• The paper provides a solution for modeling the wave breaking processes over a beach.
• The experiment data for the wave breaking process was measured by high speed camera.
• By varying the slope and wave steepness, the post-breaking stages can be simulated.
• The present solution gets the characteristics of post-breaking waves on slopes.

This study investigates the evolution of breaking waves on sloping beaches. The motion of water particles is formulated in the Lagrangian framework that uses label and time as the independent variables. A classic perturbation scheme is employed for solutions. In this paper, a Lagrangian solution up to the first order in term of the beach slope is presented. In the solution the wave breaking criteria commonly used are adopted: waves break when the horizontal particle velocity at the wave crest is equal or greater than the wave celerity, or when a vertical tangent profile occurs at the free surface. The continuous wave deformations and breaking calculated from the Lagrangian solution are presented. A series of experiments are also conducted in a laboratory wave tank for observing wave evolution and verifying the Lagrangian solution. It shows that the Lagrangian solution and the experiment data, including the plunging, post-plunging, spilling and post-spilling breaking waves, agree reasonably well.