The SWASH model for soliton splitting due to decreasing depth

Abstract

A solitary wave is a nonlinear wave that travels undisturbed in shape and velocity as a result of a balance between dispersion and nonlinearity. According to the inverse scattering theory of KdV, a solitary wave will split into N-soliton due to decreasing depth. This phenomenon is simulated using the non-hydrostatic model SWASH. Simulations are conducted for initial amplitude of 2 m with four types of slope: steep, moderately steep, mild, and linear slope. The initial depth decreases from 10 m to ∼6.14 m which make solitary wave split into two solitons. Simulations show that the solitary wave splits into two solitons for steep, moderately steep, and mild bottom slope, where as for linear slope the initial solitary wave will evolve into a solitary wave with a tail. From the simulation over a moderately steep bottom, amplitudes of the separated soliton admit a nearly quadratic ratio which is comparable with those resulting from the inverse scattering theory.