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_GB |
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_GB |
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 |