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

Runhua Tian,Hongwei Yang,Zongguo Zhang,Baojun Zhao

doi:10.1109/access.2020.3013925

Abstract

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.

Highlights

Many large-scale fluids in nature and engineering, such as the atmosphere and oceans, are stratified
In order to judge the practicability, veracity and reliability of the methods proposed in this study, the relative errors are discussed between the numerical solution obtained by the alternative variational iteration method and the exact solution obtained by the Jacobi elliptic function expansion method
We deduced the timefractional coupled ZK-mZK equations and analyze its conservation laws, which provides a basis for the theoretical study of the Rossby waves in two layers fluid

Summary

Introduction

Many large-scale fluids in nature and engineering, such as the atmosphere and oceans, are stratified. INDEX TERMS Two layers fluid, Rossby waves, time-fractional coupled ZK-mZK equations, alternative variational iteration method. The Lagrangian forms of the time-fractional coupled ZK-mZK equations are given as where DαT is the operator of fractional derivative, T is independent variable, α is the order of the derivative and α can be a fraction.

Results

Conclusion