Enhanced dissipation and axisymmetrization of two-dimensional viscous vortices

TL;DR

This paper analyzes the stability of the Lamb-Oseen vortex at high Reynolds numbers, showing that localized perturbations lead to rapid axisymmetrization due to enhanced dissipation from differential rotation.

Contribution

It demonstrates that vortex axisymmetrization occurs faster than viscous diffusion, providing new insights into vortex stability and dissipation mechanisms at high Reynolds numbers.

Findings

Vortex relaxes to axisymmetry in time proportional to Re^{2/3}

Enhanced dissipation is caused by differential rotation inside the vortex core

Comparison with physical literature and shear flow results

Abstract

This paper is devoted to the stability analysis of the Lamb-Oseen vortex in the regime of high circulation Reynolds numbers. When strongly localized perturbations are applied, it is shown that the vortex relaxes to axisymmetry in a time proportional to $Re^{2/3}$, which is substantially shorter than the diffusion time scale given by the viscosity. This enhanced dissipation effect is due to the differential rotation inside the vortex core. Our result relies on a recent work by Li, Wei, and Zhang, where optimal resolvent estimates for the linearized operator at Oseen's vortex are established. A comparison is made with the predictions that can be found in the physical literature, and with the rigorous results that were obtained for shear flows using different techniques.