The linear and nonlinear properties of the high-order Bonssinesq equations for wave propagation

摘要

A study of the Boussinesq equations for waves propagating from deep water to shallow water is presented. In this paper, we rederive the Boussinesq equations with the recursion form not only appearing in the main variables but in the coefficients. This greatly reduces the efforts of the derivation of the higher-order Boussinesq equations. Parameters concerning the linear and nonlinear wave properties are also derived to analyze the accuracy of the present models. The linear properties include the phase velocity, the group velocity and the particle velocities. The forcing terms of the continuity equation and the equation of motion are developed to analyze the nonlinear properties. By choosing a suitable water-depth parameter /n, the optimal wave models are consequently determined. Our model provides an easier and more flexible method to analyze the wave mechanics than previous studies based on the Pad￡ approximation.