Stirring Vortices with Vorticity Holes

Abstract

A vorticity hole is a region with, in absolute value, significantly lower vorticity than its surroundings. Here we discuss the dynamics of a Rankine vortex with two equal circular holes. Since a symmetric initial condition is assumed, the evolution depends on three parameters only: the vorticity drop, the hole radius and the distance between the holes. We computed the evolution with a contour-dynamics model and analysed the stirring of fluid particles using the Lagrangian flow geometry, i.e., the set of hyperbolic trajectories and associated manifolds of the time-dependent velocity field. The vorticity holes evolve similarly to a pair of vortices in an otherwise quiescent fluid; their interaction with the boundary of the Rankine vortex being relevant only when they are close to it. We found that the strongest stirring occurs when the holes interact elastically and that it always takes place in the centre of the Rankine vortex. This result contradicts the generally accepted notion that vortices are regions of null to weak stirring.