Rapid relaxation of an axisymmetric vortex

Abstract

In this paper it is argued that a two-dimensional axisymmetric large Reynolds number (Re) monopole when perturbed will return to an axisymmetric state on a time scale (Re1/3) that is much faster than the viscous evolution time scale (Re). It is shown that an arbitrary perturbation can be broken into three pieces; first, an axisymmetric piece corresponding to a slight radial redistribution of vorticity; second, a translational piece which corresponds to a small displacement of the center of the original vortex; and finally, a nonaxisymmetric perturbation which decays on the Re1/3 time scale due to a shear/diffusion averaging mechanism studied by Rhines and Young [J. Fluid Mech. 133, 133 (1983)] for a passive scalar and Lundgren [Phys. Fluids 25, 2193 (1982)] for vorticity. This mechanism is verified numerically for the canonical example of a Lamb monopole. This result suggests a physical explanation for the persistence of monopole structures in large Reynolds flows, such as decaying turbulence. © 1994 American Institute of Physics.