Vortex Dipoles Colliding with Curved Walls

Abstract

Incompressible, inviscid two-dimensional flows away from boundaries possess special stationary solutions in the form of coherent, isolated vortical structures. These solutions can be classified in terms of the spatial moments of the vorticity distribution about their centers. Flows involving several such structures can be seen in nature and in the laboratory. In case the structures remain well-separated, they can be described in terms of a few collective variables (strength and location for symmetric monopoles, plus eccentricity and orientation for elliptical ones, and similarly for dipolar structures). The vorticity, distributed among these structures, acts as a source for a collective velocity field, which away from the structures is harmonic. A small viscosity does not change the dynamics of these free-space structures substantially. The resulting dynamical system has been studied extensively both analytically and numerically.