Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Topology change of vortices using stochastic differential equations

N.K.-R. Kevlahan*
Department of Mathematics & Statistics, McMaster University, Hamilton, Canada

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We propose two semi-analytic models for the interaction of N three-dimensional vortex filaments. These models allow for topology change of the vortices, e.g. reconnection. Both models are stochastic differential equations where the effect of diffusion is modelled via a Gaussian white noise forcing of the inviscid equations. The vorticity distribution is the ensemble average of many realizations, each of which contains N vortices. The first model is a straightforward extension of the semi-inviscid asymptotic approximation of Klein et al. [1] for nearly parallel vortices, while the second may be used for vortex filaments of arbitrary geometry.

Keywords:  Vortex filament; Merging; Reconnection; Stochastic differential equation