A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids

Abstract

From rotational potential vorticity-conserved equation with topography effect and dissipation effect, with the help of the multiple-scale method, a new integro-differential equation is constructed to describe the Rossby solitary waves in deep rotational fluids. By analyzing the equation, some conservation laws associated with Rossby solitary waves are derived. Finally, by seeking the numerical solutions of the equation with the pseudospectral method, by virtue of waterfall plots, the effect of detuning parameter and dissipation on Rossby solitary waves generated by topography are discussed, and the equation is compared with KdV equation and BO equation. The results show that the detuning parameterαplays an important role for the evolution features of solitary waves generated by topography, especially in the resonant case; a large amplitude nonstationary disturbance is generated in the forcing region. This condition may explain the blocking phenomenon which exists in the atmosphere and ocean and generated by topographic forcing.

Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions

“…In the last few decades , the research on constructing mathematical models to study the generation and evolution of Rossby waves has attracted a lot of attention, and a series of mathematical models, such as KdV [4,5], mKdV [6,7], ZK [8,9], modified Kawahara equation [10], and so on [11,12], have been obtained. Meanwhile, some natural phenomena related to Rossby waves were explained with the help of mathematical models [13].…”

Three-Dimensional Coupled NLS Equations for Envelope Gravity Solitary Waves in Baroclinic Atmosphere and Modulational Instability

“…Afterward, Benny [3] amplified the conclusions and got a conclusion that velocity and amplitude of solitary waves were related. Recently, a variety of equation models which described the solitary waves, such as ILWBurgers equation and ZK-Burgers equation, were discussed by Yang et al [4,5]. Meanwhile the generation and evolution of solitary waves in different topography condition and different fluid depths were discussed.…”

Algebro-Geometric Solutions for a Discrete Integrable Equation

“…As we all know, the generation of integrable system, determination of exact solution, and the properties of the conservation laws are becoming more and more rich [1][2][3][4][5]; in particular, the discrete integrable systems have many applications in statistical physics, quantum physics, and mathematical physics [6][7][8][9][10][11]. It is worth discussing the properties of discrete integrable systems, such as Darboux transformations [12,13], Hamiltonian structures [14][15][16], exact solutions [17], and the transformed rational function method [18].…”