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Accelerated diffusion in the centre of a vortex

Published online by Cambridge University Press:  22 June 2001

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

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The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P1/3 times the turn-over time, where P is a Péclet number. The mechanism relies on differential rotation, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the centre of the streamlines, and the time scale becomes greater. The behaviour at the centre is analysed and it is found that scalar there is only destroyed on a time scale of order P1/2. Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of the flow. Some exact solutions are presented.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 437 , 25 June 2001, pp. 395 - 411
Copyright
© 2001 Cambridge University Press