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

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

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Title: The spiral wind-up of vorticity in an inviscid planar vortex
Author: Bassom, Andrew P.
Gilbert, Andrew D.
Citation: Vol. 371, pp. 109-140
Publisher: Cambridge University Press
Journal: Journal of Fluid Mechanics
Date Issued: 1998
URI: http://hdl.handle.net/10036/56333
DOI: 10.1017/S0022112098001955
Links: http://www.journals.cambridge.org/abstract_S0022112098001955
Abstract: The relaxation of a smooth two-dimensional vortex to axisymmetry, also known as `axisymmetrization', is studied asymptotically and numerically. The vortex is perturbed at t = 0 and differential rotation leads to the wind-up of vorticity fluctuations to forma 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 ≥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).
Type: Article
Description: Copyright © 1998 Cambridge University Press. Published version reproduced with the permission of the publisher.
ISSN: 0022-11201469-7645


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