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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 13, issue 1
Nonlin. Processes Geophys., 13, 41–51, 2006
https://doi.org/10.5194/npg-13-41-2006
© Author(s) 2006. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Complex dynamics in geosciences: analysis techniques for observational...

Nonlin. Processes Geophys., 13, 41–51, 2006
https://doi.org/10.5194/npg-13-41-2006
© Author(s) 2006. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  10 Mar 2006

10 Mar 2006

Evolution of localized vortices in the presence of stochastic perturbations

E. Bécu1 and V. Pavlov2 E. Bécu and V. Pavlov
  • 1Laboratoire de Mécanique de Lille, Boulevard Paul Langevin, 59 655 Villeneuve d'Ascq, France
  • 2UFR de Mathématiques Pures et Appliquées, Université de Lille 1, 59 655 Villeneuve d'Ascq, France

Abstract. We consider the evolution of a distribution of N identical point vortices when stochastic perturbations in the Hamiltonian are present. It is shown that different initial configurations of vorticity with identical integral invariants may exist. Using the Runge-Kutta scheme of order 4, it is also demonstrated that different initial configurations with the same invariants may evolve without having any tendency to approach to a unique final, axially symmetric, distribution. In the presence of stochastic perturbations, if the initial distribution of vortices is not axially symmetric, vortices can be trapped in certain domains whose location is correlated with the configuration of the initial vortex distribution.

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