Modulation instability analysis of Rossby waves based on (2 + 1)-dimensional high-order Schrödinger equation

Abstract

Modulational instability is an important area of research with important practical and theoretical significance in fluid mechanics, optics, plasma physics, and military and communication engineering. In this paper, using multiscale analysis and a perturbation expansion method, starting from the quasi-geostrophic potential vortex equation, a new (2 + 1)-dimensional high-order nonlinear Schrödinger equation describing Rossby waves in stratified fluids is obtained. Based on this equation, conditions for the occurrence of modulational instability of Rossby waves are analyzed. Moreover, the effects of factors such as the dimension and order of the equation and the latitude at which Rossby waves occur on modulational instability are discussed. It is found that the (2 + 1)-dimensional equation provides a good description of the modulational instability of Rossby waves on a plane. The high-order terms affect the modulational instability, and it is found that instability is more likely to occur at high latitudes.