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Nonlinear stability of continuously stratified quasi-geostrophic flow

Published online by Cambridge University Press:  26 April 2006

Liu Yongming ,
Mu Mu  and
Theodore G. Shepherd
Liu Yongming
Affiliation:
Institute of Mathematics, Anhui University, Hefei 230039, China
Mu Mu
Affiliation:
LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
Theodore G. Shepherd
Affiliation:
Department of Physics, University of Toronto, Toronto M5S 1A7, Canada
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 325 , 25 October 1996 , pp. 419 - 439
Copyright
© 1996 Cambridge University Press

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