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Removal of Goldstein's singularity at separation, in flow past obstacles in wall layers

Published online by Cambridge University Press:  20 April 2006

F. T. Smith  and
P. G. Daniels
F. T. Smith
Affiliation:
Mathematics Department, Imperial College, London SW7 2BZ
P. G. Daniels
Affiliation:
Mathematics Department, City University, St John Street, London EC1V 4PB
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Abstract

It is shown that, in the flow of a viscous wall layer past a relatively steep obstacle at the wall, the Goldstein (1948) singularity generated in the classical boundary-layer approach to separation is removable in a physically sensible fashion. The removal is effected by means of a sequence of local double structures, the last of which arises just beyond separation owing to the occurrence of a further singularity which is also removable and describes the necessary complete breakaway of the viscous layer from the wall. The novel forms of the local pressure–displacement relations are the key elements allowing the solution to retain physical reality throughout. Beyond the breakaway the reattachment process takes place only at a relatively large distance downstream, before the motion returns to its original uniform shear form. The present flow configuration, the first we know of where Goldstein's singularity proves to be removable, has important applications in both internal and external flows at high Reynolds numbers and these are also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 110 , September 1981 , pp. 1 - 37
Copyright
© 1981 Cambridge University Press

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