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The flow in the neighbourhood of the rim of a finite rotating disc

Published online by Cambridge University Press:  26 February 2010

S. H. Smith
S. H. Smith
Affiliation:
Department of Mathematics, University of Toronto, Toronto, 181, Canada.
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Abstract

The flow in the wake of a finite rotating disc was recently investigated by Leslie [1], who showed that the structure of the wake was very similar to that found for the two-dimensional flow past the trailing edge of a flat plate by Goldstein. Here, we investigate the inner region where the Goldstein wake joins onto the flow over the plate itself. Because there is no pressure jump across the rim at the edge of the Ekman layer, no third deck is necessary, so this inner region has width O (E½) and contains just two decks, the lower thickness O(E⅔) and the upper with thickness O(E½); E is the Ekman number for the flow. The resultant differential equation in the lower deck for the radial and axial velocities is uncoupled from that for the azimuthal velocity, and has exactly the same form as the equation found by Stewartson [4] for the lower deck in the flat plate problem cited above.

Type
Research Article
Information
Mathematika , Volume 20 , Issue 1 , June 1973 , pp. 47 - 52
Copyright
Copyright © University College London 1973

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References

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