ON THE NONLINEAR STABILITY OF SHEARING BASIC FLOW IN THE FRICTIONAL DISSIPATION ATMOSPHERE

From a nonlinear quasi-geostrophic equation set including frictional dissipation and a nonlinear shallow water equation including frictional dissipation and large topography,using Serrin-Joseph's energy method,by means of the variational principle,the nonlinear stability criterions of the shearing basic flows both above two equation sets with the total energy and total enstrophy respectively are found.