Forced solitary wave and vorticity with topography effect in quasi-geostrophic modelling

Abstract

A forced KdV equation including the special topography effect is derived to describe nonlinear long wave and solitary eddy based on the quasi-geostrophic potential vorticity model. We obtain the theoretical solution of the equation and the concrete form of stream function through perturbation theory and multi-scale analysis methods. It is found that the joint effect of weak shear basic flow and topography can change the cyclone and anticyclone structure of eddy, and in the meantime topographic structure affects the East-West propagation direction of solitary wave. Finally, according to the interaction between nonlinear long wave and topography by pseudo spectral numerical method, the topographic height is related to the amplitude, wavelength and wave velocity of the excited wave train, and the topography affects not only the spatial structure of wave, but also the amplitude of wave.