Propagation and modulational instability of Rossby waves in stratified fluids

In recent years, the research of Rossby waves gradually attracted people’s interest, and the study of modulational instability of Rossy waves had become a popular problem. Perturbation analysis and scale expansion are used in this paper to derived the the (2+1)-dimensional coupled nonlinear Schrödinger(CNLS) equations that can describe interactions of two Rossby waves propagation in stratified fluids. The (2+1)-dimensional equations can reflect and describe waves propagation more intuitively and accurately. The properties of the two waves in the process of propagation can be analyzed by the solution that obtained from the equations by using Hirota bilinear method，and the influence factors of modulational instability are analyzed. The results suggest that when the two Rossby waves with slightly different wave numbers propagate in the stratified fluids, the intensity of bright soliton decreases with the increases of dark soliton coefficients. In addition, the size of the modulational instable area is related to the amplitude and wave number that in Y-direction.