Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles

Turner, M.R. and Gilbert, A.D. (2007) Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles Journal of Fluid Mechanics, 593 . pp. 255-279. ISSN 0022-1120

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Abstract

This paper considers the evolution of smooth, two-dimensional vortices subject to a rotating external strain field, which generates regions of recirculating, cat's eye stream line topology within a vortex. When the external strain field is smoothly switched off, the cat's eyes may persist, or they may disappear as the vortex relaxes back to axisymmetry. A numerical study obtains criteria for the persistence of cat's eyes as a function of the strength and time-scale of the imposed strain field, for a Gaussian vortex profile. In the limit of a weak external strain field and high Reynolds number, the disturbance decays exponentially, with a rate that is linked to a Landau pole of the linear inviscid problem. For stronger strain fields, but not strong enough to give persistent cat's eyes, the exponential decay of the disturbance varies: as time increases the decay slows down, because of the nonlinear feedback on the mean profile of the vortex. This is confirmed by determining the decay rate given by the Landau pole for these modified profiles. For strain fields strong enough to generate persistent cat's eyes, their location and rotation rate are determined for a range of angular velocities of the external strain field, and are again linked to Landau poles of the mean profiles, modified through nonlinear effects.

Item Type:Journal article
Additional Information:© 2007 Cambridge University Press
Subjects:G000 Computing and Mathematical Sciences > G100 Mathematics
DOI (a stable link to the resource):10.1017/S0022112007008944
Faculties:Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Engineering and Product Design Research > Automotive Engineering
ID Code:6470
Deposited By:Dr Matthew Turner
Deposited On:26 Nov 2009
Last Modified:08 Oct 2013 12:49

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