Thresholds for the formation of satellites in two-dimensional vortices

Turner, M.R. and Gilbert, A.D. (2008) Thresholds for the formation of satellites in two-dimensional vortices Journal of Fluid Mechanics, 614 . pp. 381-405. ISSN 0022-1120

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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 infection 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 proles based on the tanh function.

Item Type:Journal article
Additional Information:© The Author(s) and Cambridge University Press, 2008
Subjects:G000 Computing and Mathematical Sciences > G100 Mathematics
H000 Engineering
DOI (a stable link to the resource):10.1017/S0022112008003558
Faculties:Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Engineering and Product Design Research > Automotive Engineering
ID Code:6462
Deposited By:Dr Matthew Turner
Deposited On:10 Nov 2009
Last Modified:08 Oct 2013 15:52

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