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Asymptotic analysis of turbulent channel and boundary-layer flow

Published online by Cambridge University Press:  29 March 2006

William B. Bush  and
Francis E. Fendell
William B. Bush
Affiliation:
University of Southern California, Los Angeles, California
Francis E. Fendell
Affiliation:
TRW Systems, Redondo Beach, California
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Abstract

Asymptotic expansion techniques are used, in the limit of large Reynolds number, to study the structure of fully turbulent shear layers. The relevant Reynolds number characterizes the ratio of the local turbulent stress to the local laminar stress, so that a relatively thick outer defect layer, in which, to lowest order, there is a balance between turbulent stress and convection of momentum, may be distinguished from a relatively thin wall layer, in which, to lowest order, there is a balance between turbulent and laminar stresses. The two cases examined are channel (or pipe) flow and two-dimensional boundary-layer flow with an applied pressure gradient, upstream of any separation. Attention, for these two cases, is confined to the flow of incompressible constant property fluids. Closure is effected through the introduction of an eddy-viscosity model formulated with sufficient generality for most existing models to be special cases. Results are carried to higher orders of approximation to indicate what properties for the friction velocity, integral thicknesses, and velocity profiles, and what conditions for similarity are implied by current eddy-viscosity closures.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 4 , 28 December 1972 , pp. 657 - 681
Copyright
© 1972 Cambridge University Press

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