Numerical study on the breaking of solitary wave on slopes

Abstract

Numerical study of the breaking criterion of solitary waves propagating on slopes was carried out by means of boundary element method, the algorithm was based on the Lagrangian description and finite differencing to time. The shoaling and breaking processes of solitary waves on various kinds of slopes are studied. According to the criterion defined as the horizontal velocity of water particle on wave crest equals to the wave celerity, our suggestions of breaking indices for slopes 1:10 to 1:50 are laid out, with which an empirical formula for the breaking indices was presented. In this article, the deformation of the wave profiles as well as the distribution of fluid velocities at the breaking region for slopes 1:30 to 1:50 are shown. Our results showed that when slope varies from 1:10 to 1:25, the breaker type was classified by the angle of wave profile on the wave crest at breaking, it was considered as plunging breakers if the angle is smaller than 90°, otherwise they are classified as surging breaker. Furthermore, when the slope varies from 1:30 to 1:50, the breakers are mostly classified as spilling breaker.