TY - JOUR

T1 - Existence of asymmetric burgers vortices and their asymptotic behavior at large circulations

AU - Maekawa, Yasunori

PY - 2009/5

Y1 - 2009/5

N2 - 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.

AB - 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.

KW - Asymptotics at large circulations

KW - Burgers vortices

KW - Navier-Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=67650077663&partnerID=8YFLogxK

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U2 - 10.1142/S0218202509003577

DO - 10.1142/S0218202509003577

M3 - Article

AN - SCOPUS:67650077663

SN - 0218-2025

VL - 19

SP - 669

EP - 705

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 5

ER -