Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 8 1/2 2001 10.5194/npg-8-9-2001 http://www.nonlin-processes-geophys.net/8/9/2001/ http://www.nonlin-processes-geophys.net/8/9/2001/npg-8-9-2001.html http://www.nonlin-processes-geophys.net/8/9/2001/npg-8-9-2001.pdf 9 19 0000-00-00 Formation of vortex clusters on a sphere V. Pavlov D. Buisine V. Goncharov DMF, UFR de Mathématiques Pures et Appliquées, Université de Lille 1, 59655 Villeneuve d’Ascq Cedex, France Institute of Atmospheric Physics, Russian Academy of Sciences, 109017 Moscow, Russia 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 <i>N</i> is large,&nbsp;<i><br> N </i>~ 10<sup>2</sup> - 10<sup>3</sup> , a small number of vortex collective structures <i>(cluster</i>s) 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 <i>a</i> <i>few </i>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 &quot;bursted&quot;. The system evolves to a few separated vortex &quot;spots&quot; which exist sufficiently for a long time.