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Accelerated scalar dissipation in a vortex

Published online by Cambridge University Press:  10 October 1997

P. FLOHR  and
J. C. VASSILICOS
P. FLOHR
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, UK
J. C. VASSILICOS
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, UK
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Abstract

A scalar patch forms spiral structure when it wraps around an isolated vortex. It is shown that this wind-up process leads to accelerated diffusion during a time range TS<t<TD. The lower limit TS is the time needed to create a well-defined spiral, and the upper limit TD is the diffusive time scale of the scalar field θ in the vortex. Whereas the scaling TD∼Pe1/3 is independent of the particular spiral topology, the accelerated decay of the scalar variance θ2[bar](t) for earlier times is directly linked to the space-filling property of the spiral and is found to scale as θ2[bar](0)−θ2[bar](t)∼ (Pe1/3t) 3(1−D′K). D′K is the Kolmogorov capacity of the spiral; it is defined in the range 1/2<D′K<1 and it is the most suitable measure of the spiral's space-filling property.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 348 , 10 October 1997 , pp. 295 - 317
Copyright
© 1997 Cambridge University Press

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