Beta effect and slowly changing topography Rossby waves in a shear flow

Abstract

In barotropic fluids, based on the quasi-geostrophic potential vorticity equation, an inhomogeneous mKdV-Burgers equation including slowly changing topography and an external source is derived by employing the perturbation method and stretching transforms of time and space. With the inspection of the evolution of the amplitude of Rossby waves, it is found that beta effect, topography effect, slowly changing topography and an external source are all the important factors, and that the solitary Rossby wave is induced thought the basic stream function has a shear flow . On the assumption that the nonlinear and topographic effects are in balance, an inhomogeneous mKdV-Burgers equation is derived, the results show that the topography and Rossby wave interact in the barotropic flows. The inhomogeneous mKdV-Burgers equation describing the evolution of the amplitude of solitary Rossby wave as the change of Rossby parameter β(y) with latitude y, topographic forcing, slowly changing topography and the external source is obtained.