On two-dimensional self-similar axisymmetric vortices

Abstract

Superpositions of Lamb-Oseen axisymmetric vortices with Gaussian vorticity having zero net circulation and finite kinetic energy in unbounded domain are considered. Their evolution is described by self-similar solutions depending on a certain combination of space, time, and viscous diffusion. It is shown that the structure of a popular self-similar solution for a shielded vortex with Gaussian fluid rotation rate corresponds to two Lamb-Oseen vortices with opposite sign and nearly the same spatial scale. The radial structure of a combined vortex with different spatial scales is well suited for characterization of realistic vortical structures like atmospheric hurricanes. The linear stability of the combined vortex is investigated. The results have important implications for better understanding of vortex structures in two-dimensional flow.