Stability of a class of solutions of the barotropic vorticity equation on a sphereequation on a sphere

The linear and nonlinear stability of modons and Wu-Verkley waves, which are weak solutions of the barotropic vorticity equation on a rotating sphere, are analyzed. Necessary conditions for normal mode instability are obtained, the growth rate of unstable modes is estimated, and the orthogonality of unstable modes to the basic flow is shown. The Liapunov instability of dipole modons in the norm associated with enstrophy is proven.

Keywords

barotropic vorticity equation on a sphere, modons and Wu-Verkley waves, linear and Liapunov instability

2010 Mathematics Subject Classification

35B10, 35D30, 76B47, 76E09

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Received 11 April 2021

Published 21 May 2024