Forced dissipative Boussinesq equation for solitary waves excited by unstable topography

In the paper, the effects of topographic forcing and dissipation on solitary Rossby waves are studied. Special attention is given to solitary Rossby waves excited by unstable topography. Based on the perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies a forced dissipative Boussinesq equation. By using the modified Jacobi elliptic function expansion method and the pseudo-spectral method, the solutions of homogeneous and inhomogeneous dissipative Boussinesq equation are obtained, respectively. With the help of these solutions, the evolutional character of Rossby waves under the influence of dissipation and unstable topography is discussed.