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Theoretical and numerical study of a three-dimensional turbulent boundary layer

Published online by Cambridge University Press:  26 April 2006

Philippe R. Spalart
Philippe R. Spalart
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
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Abstract

The boundary layer is created on an infinite flat plate by a time-dependent free-stream velocity vector, whose magnitude is independent of time but whose direction (as seen in plan view) changes at a constant angular velocity. The pressure gradient, at right angles to the free-stream velocity, induces a skewing of the velocity profile; all components of the Reynolds-stress tensor are non-zero (using axes aligned with the wall and the flow direction). This flow has never been produced experimentally, but it has the merit of being simply defined and of having only the Reynolds number as a parameter, which greatly simplifies the analysis. The flow is studied theoretically using Reynolds-number scaling laws, and by direct numerical simulation over a range of Reynolds numbers. The simplest version of the theory is equivalent to existing theories of the Ekman layer. A higher-order version is presented and yields excellent agreement with the numerical results at three Reynolds numbers, with just one adjustable constant in each equation. The theory allows the extrapolation of the results to high Reynolds numbers. The Reynolds-averaged equations reduce to a one-dimensional steady problem, so that turbulence-model testing will be easy and accurate. Detailed data are provided for that purpose.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 205 , August 1989 , pp. 319 - 340
Copyright
© 1989 Cambridge University Press

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