Numerical Simulation of Nonlinear Sea Wave Model in Shallow Water

We present a nonlinear shallow water numerical wave model based on the purpose of radar monitoring in shallow sea. The model is based on the ocean dynamics boundary conditions of finite water depth. Firstly, we used the perturbation method to educe the "nonlinear long wave" discrete solution of the modulation between a long wave and a short wave at different depth, the "nonlinear long wave" will modulate another short wave and it produces a new "nonlinear long wave". And then, using the same method we derived the nonlinear wave expression of linear mild slope, and educed the nonlinear shallow sea wave model. Finally, we achieved relatively good simulation results. This model avoids the limitation of the analytical solution which is used to solve the nonlinear sea wave model of modulation just between a single long-wave and a single short-wave. In theory, it can characterize the sea wave model that a long wave modulates infinite short waves. Establishing an accurate model of the shallow sea is essential to improve the accuracy of monitoring.