New model and dynamics of higher-dimensional nonlinear Rossby waves

Abstract

In this work, the propagation of higher-dimensional nonlinear Rossby waves under the generalized beta effect is considered. Using the methods of weak nonlinear perturbation expansions and the multiple scales, we obtain a new (2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation for the first time. Furthermore, a new dispersion relation for the linear Rossby waves is given corresponding to the linearized Boussinesq equation. More importantly, based on the methods of the traveling wave setting and the Jacobi elliptic function expansions, several kinds of exact traveling wave solutions for the higher-dimensional nonlinear Rossby waves, including the periodic solutions, solitary solutions and others are obtained. Finally, we simulate the solitary solutions obtained by using the method of the Jacobi elliptic function. The numerical results show that the amplitude of the Rossby solitary waves is decreasing with the increase of generalized beta effect.