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

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

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dc.contributor.author Turner, M. R. en_GB
dc.contributor.author Gilbert, Andrew D. en_GB
dc.date.accessioned 2009-03-17T14:50:46Z en_GB
dc.date.accessioned 2011-01-25T10:33:35Z en_US
dc.date.accessioned 2013-03-20T12:32:07Z
dc.date.issued 2007 en_GB
dc.description.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. en_GB
dc.identifier.citation Vol. 593, pp. 255-279 en_GB
dc.identifier.doi 10.1017/S0022112007008944 en_GB
dc.identifier.uri http://hdl.handle.net/10036/55973 en_GB
dc.language.iso en en_GB
dc.publisher Cambridge University Press en_GB
dc.relation.url http://dx.doi.org/10.1017/S0022112007008944 en_GB
dc.relation.url http://www.journals.cambridge.org/abstract_S0022112007008944 en_GB
dc.title Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles en_GB
dc.type Article en_GB
dc.date.available 2009-03-17T14:50:46Z en_GB
dc.date.available 2011-01-25T10:33:35Z en_US
dc.date.available 2013-03-20T12:32:07Z
dc.identifier.issn 0022-1120 en_GB
dc.identifier.issn 1469-7645 en_GB
dc.description Copyright © 2007 Cambridge University Press. Published version reproduced with the permission of the publisher. en_GB
dc.identifier.journal Journal of Fluid Mechanics en_GB


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