Vortex motion

Abstract

Flows at high Reynolds number typically develop islands of concentrated vorticity, concisely called vortices, embedded in a low-vorticity or virtually irrotational ambient fluid. The velocity field can be resolved into two constituents: an irrotational component prevailing in the absence of the vortices, and a rotational component associated with the localized vorticity distribution. The velocity field of the latter can be expressed conveniently as an integral over the volume of fluid occupied by the vortices. At high Reynolds numbers, viscous forces are insignificant away from flow boundaries, and the vortices evolve according to simple rules dictated by the vorticity transport equation.