The KdV Equation Of Rossby Wave In Barotropic Fluid

In this paper,the KdV equations of Rossby wave in barotropic fluid are derived from barotropic quasi-geostrophic vorticity equation by using weakly nonlinear method. First, the vorticity equation is converted into non-dimensional 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 deals mainly with six problem:(1) The effect of β is a nonlinear function of latitude ,and without shear flow.(2) The effect of β is a nonlinear function of latitude, and with a shear flow.(3) The effect of topography is a nonlinear function of latitude, and with a shear flow.(4) The effect of topography is a linear function of latitude, and with a shear flow.(5) The effect of topography is a nonlinear function of latitude, and with a shear flow.(6) The effect of β is a nonlinear function of latitude,the effect of topography is anonlinear function of latitude, and with a shear flow. Owning to the balance of nonlinear effect and dispersion effect,the nonlinear Korteweg-deVries(KdV) equation,controlling the amplitude of nonlinear Rossby waves,is derived in barotropic fluid,at the same time,we can see that the effect of β and topography effect areequivalent.