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Vortex motion in a weak background shear flow

Published online by Cambridge University Press:  07 June 2004

KONRAD BAJER ,
ANDREW P. BASSOM  and
ANDREW D. GILBERT
KONRAD BAJER
Affiliation:
Institute of Geophysics, Warsaw University, Poland
ANDREW P. BASSOM
Affiliation:
Department of Mathematical Sciences, University of Exeter, North Park Road, Exeter, Devon EX4 4QE, UK
ANDREW D. GILBERT
Affiliation:
Department of Mathematical Sciences, University of Exeter, North Park Road, Exeter, Devon EX4 4QE, UK
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Abstract

A point vortex is introduced into a weak background vorticity gradient at finite Reynolds number. As the vortex spreads viscously so the background vorticity becomes wrapped around it, leading to enhanced diffusion of vorticity, but also giving a feedback on the vortex and causing it to move. This is investigated in the linear approximation, using a similarity solution for the advection of weak vorticity around the vortex, at finite and infinite Reynolds number. A logarithmic divergence in the far field requires the introduction of an outer length scale $L$ and asymptotic matching. In this way results are obtained for the motion of a vortex in a weak vorticity field modulated on the large scale $L$ and these are confirmed by means of numerical simulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 509 , 25 June 2004 , pp. 281 - 304
Copyright
© 2004 Cambridge University Press

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