NONLINEAR STABILITY OF CONTINUOUSLY STRATIFIED QUASI-GEOSTROPHIC FLOW

Nonlinear stability theorems analogous to Arnol'd's second stability t heorem are established for continuously stratified quasi-geostrophic f low with general nonlinear boundary conditions in a vertically and hor izontally confined domain. Both the standard quasi-geostrophic model a nd the modified quasi-geostrophic model (incorporating effects of hydr ostatic compressibility) are treated. The results establish explicit u pper bounds on the disturbance energy, the disturbance potential enstr ophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear sta bility in the sense of Liapunov is also established.