Point vortices on a rotating sphere

    2005, Volume 10, Number 1, pp.  39-58

    Author(s): Laurent-Polz F.

    We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of latitudinal rings of identical vortices for the non-rotating sphere persists to be a relative equilibrium when the sphere rotates. We study the nonlinear stability of a polygon of planar point vortices on a rotating plane in order to approximate the corresponding relative equilibrium on the rotating sphere when the ring is close to the pole. We then perform the same study for geostrophic vortices. To end, we compare our results to the observations on the southern hemisphere atmospheric circulation.
    Keywords: point vortices, rotating sphere, relative equilibria, nonlinear stability, planar vortices, geostrophic vortices, Southern Hemisphere Circulation
    Citation: Laurent-Polz F., Point vortices on a rotating sphere , Regular and Chaotic Dynamics, 2005, Volume 10, Number 1, pp. 39-58

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