A Kind of New Coupled Model for Rossby Waves in Two Layers Fluid

In this article, a new model for Rossby waves in two layers fluid is studied. Form the dimensionless baroclinic quasi-geostrophic vortex equations include exogenous and dissipative, the new (2 + 1)-dimensional coupled ZK-mZK equations are established by multiscale analysis and perturbation method. Based on the semi-inverse and Agrawal's method, the time-fractional coupled ZK-mZK equations are derived. Then, Lie symmetries and conservation laws of time-fractional equations are analyzed. Finally, the exact and numerical solutions of the time-fractional coupled ZK-mZK equations are obtained by the Jacobi elliptic function expansion method and alternative variational iteration method. The relative errors between solutions show that the alternative variational iteration method gives a high-precision numerical solution. Further, propagation of Rossby waves in two layers fluid is affected by time, order of fractional derivative and coefficient of coupling term.