Disturbance evolution and the nonlinear stability to the basic flows for two-dimensional quasi-geostrophic motion

The status of disturbances of both initial values and parameters in the models is further investigated, the exact explicit estimates on the disturbance energy and disturbance potential enstrophy are given; and while the initial disturbance fields rely only on the initial disturbance potential enstrophy, initial disturbance velocity circulation along the boundary, disturbance parameters, and the nonlinear stability criteria paralleling to Arnold's second theorem are obtained, and the main results of Mu are generalized.