A global variational approach to vortex core identification

We present a global variational definition of a vortex core in three-dimensional flows, and describe its implementation for tracking principal vortex cores in a viscous fluid. Our definition is motivated by the observation that the line integral of vorticity along any path worthy of being called a vortex core is likely to be large. Inverting this observation, we define a vortex core as a curve for which this line integral is a local maximum in the space of all such curves (with appropriate boundary conditions). We present an algorithm by which candidate curves are evolved using a Ginsburg–Landau equation in order to locate vortex cores. We demonstrate the implementation of this algorithm using initial vorticity fields generated with clearly identifiable vortex cores, and evolved using a lattice Boltzmann Navier–Stokes solver.