(2+1)-dimensional coupled Boussinesq equations for Rossby waves in two-layer cylindrical fluid*

In this paper, the existence and propagation characteristics of Rossby waves in a two-layer cylindrical fluid are studied. Firstly, based on the dimensionless baroclinic quasi-geostrophic vortex equations including exogenous and dissipative, we derive new (2+1)-dimensional coupled Boussinesq equations describing wave propagation in polar coordinates by employing a multiscale analysis and perturbation method. Then, the Lie symmetries and conservation laws of the coupled Boussinesq equations are analyzed. Subsequently, by using the -expansion method, the exact solutions of the (2+1)-dimensional coupled Boussinesq equations are obtained. Finally, the effects of coupling term coefficients on the propagation characteristics of Rossby waves are analyzed.