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

The status of disturbances of both initial values and parameters in the model is further investigated, and the exact explicit estimates on the disturbance energy and disturbance potential enstrophy are given, while the initial disturbance fields depend only on the initial disturbance potential enstrophy, initial disturbance velocity circulation along the boundary, and disturbance parameters. And based on the generalized nonlinear stability concept in the sense of Lyapunov, the nonlinear stability criteria paralleling to Arnold’s second theorem are obtained. Project supported by the National Natural Science Foundation of China (Grant No. 49776286).