On disturbance evolution and nonlinear stability of the multilayer quasi-geostrophic basic flows

The status of disturbances of both initial values and parameters in the mod el is further investigated, and the exact explicit estimates on the disturb ance energy and disturbance potential enstrophy are given, while the initia l disturbance fields depend only on the initial disturbance potential enstr ophy, initial disturbance velocity circulation along the boundary, and dist urbance parameters. And based on the generalized nonlinear stability concep t in the sense of Lyapunov, the nonlinear stability criteria paralleling to Arnold's set-end theorem are obtained.