Thresholds for the formation of satellites in two-dimensional vortices

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Thresholds for the formation of satellites in two-dimensional vortices

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dc.contributor.author Turner, M. R. en_GB
dc.contributor.author Gilbert, Andrew D. en_GB
dc.date.accessioned 2010-06-11T14:50:32Z en_GB
dc.date.accessioned 2011-01-25T10:33:53Z en_US
dc.date.accessioned 2013-03-20T12:30:33Z
dc.date.issued 2008 en_GB
dc.description.abstract This paper examines the evolution of a two-dimensional vortex which initially consists of an axisymmetric monopole vortex with a perturbation of azimuthal wavenumber m = 2 added to it. If the perturbation is weak, then the vortex returns to an axisymmetric state and the non-zero Fourier harmonics generated by the perturbation decay to zero. However, if a finite perturbation threshold is exceeded, then a persistent nonlinear vortex structure is formed. This structure consists of a coherent vortex core with two satellites rotating around it. The paper considers the formation of these satellites by taking an asymptotic limit in which a compact vortex is surrounded by a weak skirt of vorticity. The resulting equations match the behaviour of a normal mode riding on the vortex with the evolution of fine-scale vorticity in a critical layer inside the skirt. Three estimates of inviscid thresholds for the formation of satellites are computed and compared: two estimates use qualitative diagnostics, the appearance of an inflection point or neutral mode in the mean profile. The other is determined quantitatively by solving the normal mode/critical-layer equations numerically. These calculations are supported by simulations of the full Navier–Stokes equations using a family of profiles based on the tanh function. en_GB
dc.identifier.citation Vol. 614, pp. 381-405 en_GB
dc.identifier.doi 10.1017/S0022112008003558 en_GB
dc.identifier.uri http://hdl.handle.net/10036/104734 en_GB
dc.language.iso en en_GB
dc.publisher Cambridge University Press en_GB
dc.relation.url http://www.journals.cambridge.org/abstract_S0022112008003558 en_GB
dc.relation.url http://dx.doi.org/10.1017/S0022112008003558 en_GB
dc.title Thresholds for the formation of satellites in two-dimensional vortices en_GB
dc.type Article en_GB
dc.date.available 2010-06-11T14:50:32Z en_GB
dc.date.available 2011-01-25T10:33:53Z en_US
dc.date.available 2013-03-20T12:30:33Z
dc.identifier.issn 0022-1120 en_GB
dc.identifier.issn 1469-7645 en_GB
dc.description Copyright © 2008 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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