## 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 language | English |
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Pages (from-to) | 669-705 |

Number of pages | 37 |

Journal | Mathematical Models and Methods in Applied Sciences |

Volume | 19 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2009 May |

## Keywords

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

## ASJC Scopus subject areas

- Modelling and Simulation
- Applied Mathematics