LAUSR

Abstract We investigate the dynamics of nonlinear Rossby waves in zonally varying background jet flow under generalized beta approximation. Potential forcing, topography and dissipation are all included as influential physical factors. We derive a new modified (2 + 1) dimensional Zakharov-Kuznetsov model equation with variable coefficients in describing the spatial-temporal evolution of Rossby wave amplitude. Qualitative analysis declares the complex evolutionary processes of the nonlinear Rossby waves affected by multiple physical factors. First, it indicates that the generalized beta and basic topography are essential factors in exciting the nonlinear solitary Rossby waves, especially, for the case without shear basic flow. Second, the zonal variation of basic flow affects the zonal linear phase speed of the Rossby wave amplitude, it also affects the linear growth or decay characteristics of the three dimensional nonlinear Rossby waves, and it plays as a forcing factor on the nonlinear Rossby waves. Third, the spatial-temporal variation for higher order topography affects the evolution of solitary Rossby wave amplitude in different ways. It reveals that the weakly varying topography represents an unstable physical mechanism for the evolution of solitary Rossby waves. Besides, numerical simulations are also given to analyse the dynamics of nonlinear Rossby waves.