On the Linear Stability of Verkley's Modons

Abstract

   Verkley (1987, 1990) constructed modons on a sphere as models of atmospheric blocking phenomena. These are exact solitary wave solutions to the barotropic potential vorticity equation on a sphere. In this paper, the linear Liapunov stability of Verkley's 1987 modons is proved by means of Arnol'd's invariant, and moreover it is shown that Verkley's 1990 modons are linearly spectrally stable. In spite of the fact that Arnol'd's invariant does not exist for the 1990 modon, it is still possible for the 1990 modon to be proved linearly spectrally stable because of the fact that the 1990 modon is a limiting case of the 1987 modon.