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The spiral wind-up of vorticity in an inviscid planar vortex

Citation

Bassom, AP and Gilbert, AD, The spiral wind-up of vorticity in an inviscid planar vortex, Journal of Fluid Mechanics, 371 pp. 109-140. ISSN 0022-1120 (1998) [Refereed Article]

Copyright Statement

Copyright 1998 Cambridge University Press

DOI: doi:10.1017/S0022112098001955

Abstract

The relaxation of a smooth two-dimensional vortex to axisymmetry, also known as Ďaxisymmetrizationí, is studied asymptotically and numerically. The vortex is perturbed at t=0 and differential rotation leads to the wind-up of vorticity fluctuations to form a spiral. It is shown that for infinite Reynolds number and in the linear approximation, the vorticity distribution tends to axisymmetry in a weak or coarse-grained sense: when the vorticity field is integrated against a smooth test function the result decays asymptotically as t−λ with λ=1+(n2+8)1/2, where n is the azimuthal wavenumber of the perturbation and n[gt-or-equal, slanted]1. The far-field stream function of the perturbation decays with the same exponent. To obtain these results the paper develops a complete asymptotic picture of the linear evolution of vorticity fluctuations for large times t, which is based on that of Lundgren (1982).

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:108013
Year Published:1998
Web of Science® Times Cited:54
Deposited By:Mathematics and Physics
Deposited On:2016-04-04
Last Modified:2016-07-08
Downloads:0

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