Solitary waves of nonlinear barotropic–baroclinic coherent structures

Abstract

This study describes the evolutionary mechanisms of nonlinear barotropic–baroclinic interactions, especially, on the excitations, propagations, and decreases of nonlinear coherent structures. Starting from the classical two-layer quasi-geostrophic potential vorticity conservation model equations, the barotropic and baroclinic model equations are derived from the classical work of Pedlosky and Thomson [J. Fluid Mech. 490, 189–215 (2003)]. By considering the effects of bottom topography and beta-plane approximation, the coupled nonlinear Korteweg–de Vries model equations for the evolutions of barotropic and baroclinic coherent structures are obtained by using the methods of multiple scales and perturbation expansions, respectively. Solitary wave solutions are given according to the method of elliptic function expansions, and the physical mechanisms for the evolutions of the nonlinear barotropic–baroclinic interactive coherent structures are analyzed based on the obtained solitary wave solutions. It will be potentially useful for further theoretical investigations on atmospheric blocking phenomena or wave–flow interactions.