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

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...

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Bibliographic Details
Published in:Journal of fluid mechanics 1983-10, Vol.135 (1), p.389-405
Main Author: Cowley, S. J.
Format: Article
Language:English
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112083003146