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# Existence of asymmetric Burgers vortices and their asymptotic behavior at large circulations

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 Title: Existence of asymmetric Burgers vortices and their asymptotic behavior at large circulations Authors: Maekawa, Yasunori Browse this author Issue Date: 2008 Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 896 Start Page: 1 End Page: 34 Abstract: The asymmetric Burgers vortices are vortex solutions to the three dimensional stationary Navier-Stokes 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69705 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics