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 mod els is further investigated, the exact explicit estimates on the disturbanc e energy and disturbance potential enstrophy are given; and while the initi al disturbance fields rely only on the initial disturbance potential enstro phy, initial disturbance velocity circulation along the boundary, disturban ce parameters, and the nonlinear stability criteria paralleling to Arnold's second theorem are obtained, and the main results of Mu are generalized.