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Formation of vortex clusters on a sphere
1DMF, UFR de Mathématiques Pures et Appliquées, Université de Lille 1, 59655 Villeneuve d’Ascq Cedex, France
2Institute of Atmospheric Physics, Russian Academy of Sciences, 109017 Moscow, Russia
Abstract. This paper applies the Hamiltonian Approach (HA) to two-dimensional motions of incompressible fluid in curvi-linear coordinates, in particular on a sphere. The HA has been used to formulate governing equations of motion and to interpret the evolution of a system consisting of N localized two-dimensional vortices on a sphere. If the number of vortices N is large,
N ~ 102 - 103 , a small number of vortex collective structures (clusters) is formed. The surprise is that a quasi-final state does not correspond to completely disorganized distribution of vorticity. Numerical analysis has been carried out for initial conditions taken in the form of a few axisymmetric chains of point vortices distributed initially in fixed latitudes. The scheme of Runge-Kutta of 4th order has been used for simulating an evolution of resulting flows. The numerical analysis shows that the Kelvin-Helmholtz instability appears immediately formating initial disorganized structures which are developed and finally "bursted". The system evolves to a few separated vortex "spots" which exist sufficiently for a long time.
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Citation: Pavlov, V., Buisine, D., and Goncharov, V.: Formation of vortex clusters on a sphere, Nonlin. Processes Geophys., 8, 9-19, 2001. Bibtex EndNote Reference Manager
