Nonlinear stability of continuously stratified quasi-geostrophic flow
Yongming, L., Mu, M. and Shepherd, T. G. (1996) Nonlinear stability of continuously stratified quasi-geostrophic flow. Journal Of Fluid Mechanics, 325. pp. 419-439. ISSN 0022-1120
To link to this article DOI: 10.1017/S002211209600818X
Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established.