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Stability of stationary barotropic modons by Lyapunov's direct method

Published online by Cambridge University Press:  26 April 2006

H. Sakuma
Affiliation:
Climate Dynamics Center, Department of Atmospheric Sciences, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024-1565, USA
M. Ghil
Affiliation:
Climate Dynamics Center, Department of Atmospheric Sciences, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024-1565, USA

Abstract

A new Lyapunov stability condition is formulated for the shallow-water equations, using a gauge-variable formalism. This sufficient condition is derived for the class of perturbations that conserve the total mass. It is weaker than existing stability criteria, i.e. it applies to a wider class of flows. Formal stability to infinitesimally small perturbations of arbitrary shape is obtained for two classes of large-scale geophysical flows: pseudo-eastward flow with constant shear, and localized coherent structures of modon type.

Type
Research Article
Copyright
© 1990 Cambridge University Press

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