Topographic solitary waves by the shooting method and Fourier spectral method

Abstract

The influences of topography on barotropic Rossby solitary waves are discussed in this paper. A Boussinesq model equation of nonlinear Rossby wave amplitude is derived by using the perturbation expansion method and the space–time transformation. A classical problem we treat is the Sturm-Liouville type ordinary differential equation with varied coefficients and fixed boundary conditions. The shooting method is adopted, and the numerical solution of the obtained Boussinesq equation is given by using the Fourier spectral method. The effects of bottom topography and earth’s rotation are both discussed through qualitative and quantitative results, respectively. New conclusions about the topography Rossby waves are declared.

Keywords

• Topography
• Rossby solitary wave
• Shooting method
• Fourier spectral method