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The response of Hill's spherical vortex to a small axisymmetric disturbance

Published online by Cambridge University Press:  12 April 2006

H. K. Moffatt  and
D. W. Moore
H. K. Moffatt
Affiliation:
School of Mathematics, University of Bristol, England
D. W. Moore
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

The response of a Hill's spherical vortex to an irrotational axisymmetric small perturbation is examined on the assumption that viscous diffusion of vorticity is negligible. The problem of determining the response is first reduced to a system of differential equations for the evolution of the Legendre coefficients of the disturbance stream function. This system is then solved approximately and it is shown that, if the initial disturbance is such as to make the vortex prolate spheroidal, the vortex detrains a fraction ⅗ε of its original volume, where ε is the fractional extension of the axis of symmetry in the imposed distortion. The detrained fluid forms a thin spike growing from the rear stagnation point. If the vortex is initially oblate, irrotational fluid is entrained at the rear stagnation point to the interior of the vortex.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 4 , 29 August 1978 , pp. 749 - 760
Copyright
© 1978 Cambridge University Press

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