层结流体中带有耗散和地形强迫的非线性Boussinesq方程及其解

Nonlinear Boussinesq Equation with Dissipation and Topography Forcing in Stratified Fluids and Its Solutions

本文研究在层结流体中非线性Rossby波的动力学模型.利用GardnerMorikawa变换和摄动展开法,从包含耗散、地形和外热源的准地转斜压位涡方程出发,推导了强迫非线性Boussinesq方程去描述非线性Rossby波振幅的演变和发展.利用修正的Jacobi椭圆函数展开法和同伦摄动法,得到强迫非线性Boussinesq方程的解析解和近似解.解的结果表明推广的β效应、基本流剪切效应和层结效应是产生非线性Rossby孤立波的重要因素,耗散和地形是影响非线性Rossby孤立波演变的外强迫因素.

We investigate the dynamic model of nonlinear Rossby waves in stratified fluids.We derive a forced nonlinear Boussinesq equation to describe the amplitude evolution of nonlinear Rossby waves by considering the quasi-geostrophic baroclinic potential vorticity equation with dissipation and topography and external source,and by utilizing Gardner-Morikawa transform and the perturbation expansion method.The analytic and approximate solutions for the forced nonlinear Boussinesq equation are presented by the modified Jacobi elliptic function expansion method and the homotopy perturbation method.Result of solutions shows that the generalizedβ,basic flow shear and stratification are extremely important factors inducing the nonlinear Rossby waves,dissipation and topography are external forcing factors affecting the evolution of nonlinear Rossby waves.