Thresholds for the formation of satellites in two--dimensional vortices
Turner, MR and Gilbert, AD (2008) Thresholds for the formation of satellites in two--dimensional vortices J. Fluid Mech, 614. pp. 381-405.
![]()
|
Text
quasimodes2.1.pdf - Accepted version Manuscript Available under License : See the attached licence file. Download (1MB) |
|
![]() |
Text (licence)
licence.txt Download (1kB) |
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.
Item Type: | Article |
---|---|
Divisions : | Faculty of Engineering and Physical Sciences > Mathematics |
Authors : | Turner, MR and Gilbert, AD |
Date : | 1 June 2008 |
Depositing User : | Symplectic Elements |
Date Deposited : | 24 Jun 2011 16:15 |
Last Modified : | 06 Jul 2019 05:07 |
URI: | http://epubs.surrey.ac.uk/id/eprint/2913 |
Actions (login required)
![]() |
View Item |
Downloads
Downloads per month over past year