Abstract
We solve the so-called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency, andβeffect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipation on the evolution of envelope solitary Rossby wave is also discussed. The results show that the dissipation causes a slow decrease of amplitude of envelope solitary Rossby waves and a slow increase of width, while it has no effect on the propagation velocity. That is quite different from the KdV-type solitary waves. It is notable that dissipation has certain influence on the carrier frequency.
Highlights
In the last decades, Rossby waves theory has attracted significant attention for it can testify some of the prime events of geophysical fluid flows
If there is no shear in the basic flow (u = constant) and β is the function of latitudinal variable y, δ ≠ 0; (38) is still the nonlinear Schrodinger equation
By analyzing the evolution of amplitude of envelope solitary Rossby waves, we can find that the shear of basic flow, Brunt-Vaisala frequency, and β effect are important factors to form the envelope solitary Rossby waves
Summary
Rossby waves theory has attracted significant attention for it can testify some of the prime events of geophysical fluid flows. Song and Yang [10] derived an inhomogeneous mKdV equation including topographic forcing by employing the perturbation method and stretching transforms of time and space in stratified fluids. Luo [13, 14] derived a higher order nonlinear Schrodinger equation using a perturbation expansion method, which describes nonlinear modulated Rossby waves in the geophysical fluid. He investigated envelope solitary Rossby waves and modulational instability of a uniform Rossby wave train in two space dimensions. Yang et al [15, 16] discussed the effects of periodic external source on the generation of algebraic Rossby solitary waves in stratified fluid and studied the effects of topographic forcing and dissipation on solitary Rossby waves. We solve dissipative nonlinear Schrodinger equation by using trial function method and discuss the effects of dissipation on the evolution of envelope solitary Rossby waves
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