Existence and Stability of Viscous Vortices

Thierry Gallay () and Yasunori Maekawa ()
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Thierry Gallay: Institut Fourier, Université Grenoble Alpes, UMR 5582 – Mathematics Laboratory
Yasunori Maekawa: Graduate School of Sciences, Kyoto University, Department of Mathematics

Chapter 13 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 687-727 from Springer

Abstract: Abstract Vorticity plays a prominent role in the dynamics of incompressible viscous flows. In two-dimensional freely decaying turbulence, after a short transient period, evolution is essentially driven by interactions of viscous vortices, the archetype of which is the self-similar Lamb-Oseen vortex. In three dimensions, amplification of vorticity due to stretching can counterbalance viscous dissipation and produce stable tubular vortices. This phenomenon is illustrated in a famous model originally proposed by Burgers, where a straight vortex tube is produced by a linear uniaxial strain field. In real flows, vortex lines are usually not straight, and can even form closed curves, as in the case of axisymmetric vortex rings which are very common in nature and in laboratory experiments. The aim of this chapter is to review a few rigorous results concerning existence and stability of viscous vortices in simple geometries.

Date: 2018
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DOI: 10.1007/978-3-319-13344-7_13

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