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The three-dimensional turbulent boundary layer near a plane of symmetry

Published online by Cambridge University Press:  26 April 2006

A. T. Degani ,
F. T. Smith  and
J. D. A. Walker
A. T. Degani
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University. Bethlehem, PA 18015, USA
F. T. Smith
Affiliation:
Department of Mathematics, University College, London WC1E 6BT, UK
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University. Bethlehem, PA 18015, USA
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Abstract

The asymptotic structure of the three-dimensional turbulent boundary layer near a plane of symmetry is considered in the limit of large Reynolds number. A selfconsistent two-layer structure is shown to exist wherein the streamwise velocity is brought to rest through an outer defect layer and an inner wall layer in a manner similar to that in two-dimensional boundary layers. The cross-stream velocity distribution is more complex and two terms in the asymptotic expansion are required to yield a complete profile which is shown to exhibit a logarithmic region. The flow in the inner wall layer is demonstrated to be collateral to leading order; pressure gradient effects are formally of higher order but can cause the velocity profile to skew substantially near the wall at the large but finite Reynolds numbers encountered in practice. The governing set of ordinary differential equations describing a self-similar flow is derived. The calculated numerical solutions of these equations are matched asymptotically to an inner wall-layer solution and the results show trends that are consistent with experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 234 , January 1992 , pp. 329 - 360
Copyright
© 1992 Cambridge University Press

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