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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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References

van den Berg, B. 1975 A three-dimensional law of the wall for turbulent shear flows. J. Fluid Mech. 70, 149–160.Google Scholar
Bradshaw, P. 1967 The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625–645.Google Scholar
Bradshaw, P. 1987 Turbulent secondary flows. Ann. Rev. Fluid Mech. 19, 53–74.Google Scholar
Coleman, G. N., Ferziger, J. H. & Spalart, P. R. 1989 A numerical study of the turbulent Ekman layer. J. Fluid Mech. submitted.Google Scholar
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
Coles, D. E. 1962 The turbulent boundary layer in a compressible fluid. Appendix A: A manual of experimental practice for low-speed flow. pp. 35–74. Rand. Rep. R403-PR, ARC 24473
Coles, D. E. 1968 The young person's guide to the data. Proc. AFOSR-IFP-Stanford Conf. on Computation of Turbulent Boundary Layers, Stanford, Calif., Aug. 18–25, 1968, Vol. 2, p. 1–45.
Csanady, G. T. 1967 On the resistance law of a turbulent Ekm layer. J. Atmos. Sci. 24, 467–471.Google Scholar
Deakdorff, J. W. 1970 A three-dimensional numerical investigation of the idealized planetary boundary layer. Geophys. Fluid Dyn. 1, 377–410.Google Scholar
Kazanski, A. B. & Monin, A. S. 1961 On the dynamical interaction between the atmosphere and the earth's surface. Bull. Acad. Sci. USSR, Ser. Geophys. 5, 514–515.Google Scholar
Mason, P. J. & Thomson, D. J. 1987 Large-eddy simulations of the neutral-static-stability planetary boundary layer. Q. J. R. Met. Soc. 113, 413–443.Google Scholar
Perry, A. E. & Schofield, W. H. 1973 Mean velocity and shear stress distributions in turbulent boundary layers. Phys. Fluids. 16, 2068–2074.Google Scholar
Spalart, P. R. 1986a Numerical simulation of boundary layers. Part 1. Weak formulation and numerical method. NASA TM 88222.
Spalart, P. R. 1986b Numerical study of sink-flow boundary layers. J. Fluid Mech. 172, 307–328.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Rθ = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Spalart, P. R. & Baldwin, B. S. 1987 Direct simulation of a turbulent oscillating boundary layer. Proc. 6th Symp. on Turbulent Shear Flows, Toulouse, France, Sept. 7–9, 1987.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics (annotated edn). Stanford: Parabolic.