Enhanced Dissipation and Axisymmetrization of Two-Dimensional Viscous Vortices

Enhanced Dissipation and Axisymmetrization of Two-Dimensional Viscous Vortices 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 $${Re^{2/3}}$$ R e 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 et al. (Pseudospectral and spectral bounds for the Oseen vortices operator, 2017, arXiv:1701.06269 ), 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Rational Mechanics and Analysis Springer Journals

Enhanced Dissipation and Axisymmetrization of Two-Dimensional Viscous Vortices

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Physics; Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics
ISSN
0003-9527
eISSN
1432-0673
D.O.I.
10.1007/s00205-018-1262-0
Publisher site
See Article on Publisher Site

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 $${Re^{2/3}}$$ R e 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 et al. (Pseudospectral and spectral bounds for the Oseen vortices operator, 2017, arXiv:1701.06269 ), 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.

Journal

Archive for Rational Mechanics and AnalysisSpringer Journals

Published: Jun 1, 2018

References

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