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The spiral wind-up and dissipation of vorticity and a passive scalar in a strained planar vortex

Published online by Cambridge University Press:  10 November 1999

ANDREW P. BASSOM  and
ANDREW D. GILBERT
ANDREW P. BASSOM
Affiliation:
School of Mathematical Sciences, University of Exeter, North Park Road, Exeter, Devon EX4 4QE, UK
ANDREW D. GILBERT
Affiliation:
School of Mathematical Sciences, University of Exeter, North Park Road, Exeter, Devon EX4 4QE, UK
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Abstract

The response of a Gaussian vortex to a weak time-dependent external strain field is studied numerically. The cases of an impulsive strain, an on–off step function, and a continuous random strain are considered. Transfers of enstrophy between mean and azimuthal components are observed, and the results are compared with an analogous passive scalar model and with Kida's elliptical vortex model.

A ‘rebound’ phenomenon is seen: after enstrophy is transferred from mean to azimuthal component by the external straining field, there is a subsequent transfer of enstrophy back from the azimuthal component to the mean. Analytical support is given for this phenomenon using Lundgren's asymptotic formulation of the spiral wind-up of vorticity. Finally the decay of the vortex under a continuous random external strain is studied numerically and compared with the passive scalar model. The vorticity distribution decays more slowly than the scalar because of the rebound phenomenon.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 398 , 10 November 1999 , pp. 245 - 270
Copyright
© 1999 Cambridge University Press

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