Abstract

Rossby-Haurwitz waves on the sphere S2 form a set of exact time-dependent solutions to the Euler equations of hydrodynamics and generate a family of non-stationary geodesics of the L2 metric in the volume preserving diffeomorphism group of S2. Restricting to a particular subset of Rossby-Haurwitz waves, this article shows that under certain conditions on the physical characteristics of the waves each corresponding geodesic contains conjugate points. In addition, a physical interpretation of conjugate points is given and links the result to the stability analysis of meteorological Rossby-Haurwitz waves.

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