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Computer extension and analytic continuation of Blasius’ expansion for impulsive flow past a circular cylinder

Published online by Cambridge University Press:  20 April 2006

S. J. Cowley
S. J. Cowley
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW Present address: Department of Mathematics, University College London, London WC1E 6BT.
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Abstract

Boundary-layer flow past an impulsively started cylinder is studied by extending the Blasius time-series expansion to many terms. The ordinary differential equations that result from this expansion are solved using an O(h6)-accurate numerical method. The validity of the simple series expansions for the wall shear, displacement thickness and viscous displacement velocity is extended by recasting the series using rational functions. The solutions so obtained are in good agreement with previous authors’ work. In particular, an examination of the poles and zeros of the rational functions confirms that a singularity develops within a finite time. The analytic structure of the singularity is found to be in agreement with the asymptotic expansion proposed by van Dommelen & Shen.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 389 - 405
Copyright
© 1983 Cambridge University Press

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References

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