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The boundary layer on a paraboloid of revolution

Published online by Cambridge University Press:  24 October 2008

D. R. Miller
D. R. Miller
Affiliation:
Department of Applied Mathematics, University of Western Ontario
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Abstract

An analytical study is made of the boundary-layer approximation for the steady laminar flow of a viscous incompressible fluid past a paraboloid of revolution. The functional form of the vorticity distribution is found and shown to involve exponential decay with distance from the surface of the body, and inequalities are established concerning the displacement thickness.

The exact results are compared with various linearizations. The Oseen linearization (12) turns out to be incorrect except in the limit of vanishing Reynolds number; this result is connected with the infinite drag of any paraboloid of non-zero thickness. An alternate linearization, related to a method of Burgers (3) and allowing for the displacement effect of the body and of its boundary layer, is shown to give the correct functional form for these quantities. Numerical results are included which bear out these conclusions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 285 - 299
Copyright
Copyright © Cambridge Philosophical Society 1969

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