MKdV Equation For The Amplitude Of Rossby Wave In Stratified Fluid

In this thesic the mKdV equation for the amplitude of Rossby wave in stratified fluid are derived from stratified quasi-geostrophic vorticity equation by using wealky nonlinear method .First ,the vorticity equation is converted into non-dimerisional form.Then,long time and space scales are introduced.At last,the amplitude of Rossby wave is discussed under the long time and space variable X,T by using perturbation method.We deal mainly with four problems(1) The effect of β is nonlinear function of latitude, the basic flow is not a shear flow ,and the frequency of V(a|¨)is(a|¨)l(a|¨)—Brunt remains a constant.(2)The effect of β is nonlinear function of latitude with a shear flow ,and the frequency of V(a|¨)is(a|¨)l(a|¨)—Brunt remains a constant.(3)The effect of β is a nonlinear function of latitude ,the basic flow is not a shear flow, and the frequency of V(a|¨)is(a|¨)l(a|¨)—Brunt is a function of z.(4)The effect of β is a nonlinear function of latitude ,with a shear flow and the frequency of V(a|¨)is(a|¨)l(a|¨)—Brunt is a function of z.Owing to the balance of nonlinear effect and dispersion effection,the nonlinear mKdV equation controlling the amplitude of nonlinear Rossby waves is derived in stratified fluid.