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Viscous flow through unsteady symmetric channels

Published online by Cambridge University Press:  19 April 2006

P. W. Duck
P. W. Duck
Affiliation:
Department of Mathematics Imperial College, London, S.W. 7 Present address: Department of Mathematics, University of Manchester, England.
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Abstract

The high-Reynolds-number (K) flow through a symmetric channel, with walls whose shape is time dependent, is studied. The distortion of the walls is of non-dimensional height $O(K^{-\frac{1}{3}}$) and length O(1), this particular size of perturbation being chosen such that (for the first regime of unsteadiness studied) the effects of the unsteadiness, viscous diffusion and advection all interact nonlinearly in the region of the fluid near the walls.

For this first regime of unsteadiness the problem is solved numerically. This leads on to analytic descriptions for progressively faster time variations of wall shape, and in fact the entire range of unsteadiness is covered for this particular size of distortion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 4 , 27 December 1979 , pp. 635 - 653
Copyright
© 1979 Cambridge University Press

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References

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