ON THE NONLINEAR STABILITY OF SHEAR FLOWS IN THE FRICTIONAL DISSIPATION ATMOSPHERE

From a nonlinear quasi-geostrophic equation set containing dissipation and a nonlinear shallow water wave equation set containing frictional dissipation and large topographic action,by using Serrin-Joseph's energy method and based on the variation principle,criteria for nonlinear stability of basic shear flows in the above two equation sets have been derived in terms of the total energy and total enstrophy respectively.