Existence of asymmetric burgers vortices and their asymptotic behavior at large circulations

Yasunori Maekawa

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

The asymmetric Burgers vortices are vortex solutions to the three-dimensional stationary NavierStokes equations for viscous incompressible fluids in the presence of an asymmetric background straining flow. The asymmetry of the straining flow is expressed by a non-negative parameter less than 1. The Burgers vortices have been used as a model which expresses tube-like structures of concentrated vorticity fields in turbulence, and they are numerically well investigated especially in the case of large circulation numbers. However, their existence was proved mathematically only when either the asymmetry of the straining flow is not so strong or the circulation number is sufficiently small. In this paper, we prove the existence of asymmetric Burgers vortices for all circulation numbers and each asymmetry parameter less than 1. We also obtain their asymptotic expansion at large circulation numbers, which gives an explanation for a symmetrizing effect by a fast rotation.

Original languageEnglish
Pages (from-to)669-705
Number of pages37
JournalMathematical Models and Methods in Applied Sciences
Volume19
Issue number5
DOIs
Publication statusPublished - 2009 May

Keywords

  • Asymptotics at large circulations
  • Burgers vortices
  • Navier-Stokes equations

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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