Motion of decaying vortex rings with non-similar vorticity distributions

Abstract

The motion and decay of circular vortex rings with an inner viscous core is considered by systematic matching of inner and outer asymptotic expansions. The governing Navier-Stokes equations are reduced to a coupled integro-differential system. A method of construction of solutions for the integro-differential system is presented. The initial vorticity distribution may be non-similar. Also presented is a method for introducing a time shift which makes the first term in the series solution for the vorticity to be the “best” approximation. The analysis is then applied to the motion and decay of a pair of coaxial vortex rings.