Derivation of a higher order nonlinear Schrödinger equation for weakly nonlinear Rossby waves

Abstract

In the paper, with the help of a perturbation expansion method a new higher order nonlinear Schrödinger (HNLS) equation is derived to describe nonlinear modulated Rossby waves in the geophysical fluid. Using this equation, the modulational wave trains are discussed. It is found that the higher order terms favor the instability growth of modulational disturbances superimposed on uniform Rossby wave trains, but the instability region becomes narrower. In addition, the latitude and uniform background basic flow are found to affect the instability growth rate and instability region of uniform Rossby wave train. However, for a geostrophic flow the background basic flow does not affect the modulational instability of uniform Rossby wave train.