Vortex Motion

Abstract

Flows at high Reynolds numbers tend to develop islands of concentrated vorticity, concisely called vortices, embedded in a low-vorticity or virtually irrotational ambient fluid. The velocity field may be decomposed into two constituents: an irrotational component prevailing in the absence of the vortices, and a rotational component associated with the localized vorticity distribution. The latter may be expressed in the convenient form of an integral over the volume occupied by the vortices, involving the vorticity distribution. At high Reynolds numbers, viscous forces are insignificant away from flow boundaries, and the vortices evolve according to simplified rules dictated by the vorticity transport equation for inviscid fluids. In this chapter, we derive the integral representation of the velocity in terms of the vorticity, discuss the simplified laws governing vortex motion in a flow with negligible viscous forces, and develop numerical methods for describing the dynamics of a prototypical class of vortex flows with specifically chosen vorticity distributions. The study of these flows will allow us to develop insights into the dynamics of more high-Reylonds-number flows characterized by vortex interactions.