By using a perturbation method, a forced mKdV equation is derived from the so-called quasi-geostrophic vorticity equation, and time evolutions of mass and energy of the mKdV solitary waves are discussed. Finally, numerical solutions of the forced mKdV equation are obtained by using the pseudo-spectral method. The calculation results show that the features of the mKdV solitary waves excited by localized external source are closely related to the detuning parameter α and the strength of the external source. The external forcing source in a forced mKdV system can excite larger amplitude and more instable disturbances than those in a forced KdV system.

It generalizes the theory developed by Helfrich and Pedlosky^[1] for time-dependent coherent structures in a marginally stable zonal flow by including forcing.Such forcing could be due to topography or to an external source.By using a perturbation method,the nonlinear differential equation is obtained for governing the evolution of a disturbance excited by those forcings.Some general features of the excited disturbance are given by numerically solving the governing equation.It further studies the interaction between solitary wave and topography and reveals that the solitary wave can always climb over the topography,but depending on the initial conditions of solitary wave and the height of topography,the initial solitary wave could keep most of its mass or be fissioned into two solitary waves traveling in opposite directions.