Vorticity distributions for thick and thin viscous vortex pairs and rings

摘要

Unsteady vorticity distributions inside the viscous core of vortex pairs and rings are presented. All of them are solutions of the Stokes slow-flow equations, which are valid for the viscous core in the first approximation even in the case of slender vortices. It is explicitly shown that the condition of conservation for the impulse of vorticity is fulfilled for such distributions. The obtained solutions for thick viscous vortices are the direct generalizations of the classical self-similar distribution. Another form of vorticity distribution for slender vortices is identical both in the plane and in the axi-symmetric case.