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Lyapunov instability of the Rossby-Haurwitz waves and dipole modons. (English) Zbl 0819.76030

Summary: A study has been made of the properties of the wave solutions to the vorticity equation in the model of the ideal incompressible fluid on a sphere: the Rossby-Haurwitz waves and the Verkley modons. Formulae have been derived for determining the distance in the phase space between a modon and a Rossby-Haurwitz wave, or between two modons. Necessary and sufficient conditions are given for conservation of this distance. Lyapunov instability has been proven for any dipole modon and for each nonzonal Rossby-Haurwitz wave including spherical harmonics of a degree higher than unity. The results are of interest also for meteorology in connection with the low-frequency variability of the large-scale atmospheric circulation.

MSC:

76E20 Stability and instability of geophysical and astrophysical flows
76B65 Rossby waves (MSC2010)
86A10 Meteorology and atmospheric physics
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