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Renewed studies on the unsteady boundary layers governed by singular parabolic equations

Published online by Cambridge University Press:  20 April 2006

J. C. T. Wang
J. C. T. Wang
Affiliation:
Department of Fluid and Flight Dynamics, Avco Systems Division, Wilmington, Massachusetts 01887, U.S.A. Present address: The Aerospace Corporation, P.O. Box 92957, Los Angeles, California 90009.
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Abstract

Two classic problems in unsteady boundary layers, the Stewartson and the Lam & Crocco problems, are formulated with a unified new semi-similar transformation using velocity and static enthalpy as dependent variables. By this formulation, the resulting governing equations – singular parabolic in nature – for these two physically different problems are shown to closely resemble one another in all essential aspects. For both cases, the domain of the streamwise independent variable is mapped onto [0, 1] for all t. The existence of the Reynolds analogy and the exact energy integral are given; their relations are shown to be different from those in the steady boundary layers. Uniformly valid solutions are shown to be obtainable, accurately, by a standard relaxation method commonly applied to the solution of elliptical partial differential equations. Characteristics of the transition from non-similar solutions to downstream similar solutions are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 155 , June 1985 , pp. 413 - 427
Copyright
© 1985 Cambridge University Press

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