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The spiral wind-up of vorticity in an inviscid planar vortex
journal contribution
posted on 2023-05-18, 18:32 authored by Andrew BassomAndrew Bassom, Gilbert, ADThe 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 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).
History
Publication title
Journal of Fluid MechanicsVolume
371Pagination
109-140ISSN
0022-1120Department/School
School of Natural SciencesPublisher
Cambridge Univ PressPlace of publication
40 West 20Th St, New York, USA, Ny, 10011-4211Rights statement
Copyright 1998 Cambridge University PressRepository Status
- Restricted