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.
quasimodes2.1.pdf - Accepted Version
turner02.pdf - Published Version
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.
|Additional Information:||Copyright 2008 Cambridge University Press.|
|Divisions:||Faculty of Engineering and Physical Sciences > Mathematics|
|Depositing User:||Matthew Turner|
|Date Deposited:||11 May 2011 13:32|
|Last Modified:||23 Sep 2013 18:41|
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