Stability of stationary barotropic modons by Lyapunov's direct method
- 1 February 1990
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 211, 393-416
- https://doi.org/10.1017/s0022112090001628
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.Keywords
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