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 either one elliptic hole or two equal circular holes. If we assume symmetry and null vorticity within the holes, the evolution only depends on the hole size and either the aspect ratio of the elliptic hole or the separation of the circular holes. We computed the evolution with a contour-dynamics model and found that it is analogous to either that of the Kirchhoff vortex or that of the vortex pair, but the vorticity holes are additionally affected by their interaction with the boundary of the Rankine vortex. To quantify the stirring of fluid particles, both inside and outside the vortex, we analysed the set of hyperbolic trajectories and associated manifolds of the time-evolving velocity field. The strongest stirring always occurred in the areas of highest vorticity, which contradicts the generally accepted notion that vortices are regions of null to weak stirring.