Topology change of vortices using stochastic differential equations

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. © 2005 Elsevier Ltd.