Evolution of localized vortices in the presence of stochastic perturbations
- 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.