Advertisement

The turbulent Couette flow from asymptotic theory viewpoint

  • K. Gersten
III. Instability and Turbulence
Part of the Lecture Notes in Physics book series (LNP, volume 235)

Abstract

The turbulent Couette flow is considered from the point of view of the asymptotic theory for turbulent shear flows at large Reynolds numbers. According to this theory the flow has a two-layer structure which can be treated by the method of matched asymptotic expansions. Without specifying a turbulence model the analysis leads to boundary conditions which have to be satisfied by the solution and hence by any turlence modelling. It is shown that some of the existing turbulence models do not satisfy these conditions. A new turbulence model is proposed which leads to analytical solutions.

Keywords

Wall Shear Stress Turbulent Kinetic Energy Asymptotic Theory Couette Flow Turbulent Shear 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Van Dyke, M., Higher-Order Boundary-Layer Theory, Annual Review of Fluid Mechanics, Vol. 1, pp. 265–292, 1969.Google Scholar
  2. 2.
    Gersten, K. Advanced Boundary-Layer Theory in Heat Transfer, in Proc. 7th Intern. Heat Transfer Conference, München, Vol. 1, pp. 159–179, 1982.Google Scholar
  3. 3.
    Afzal, N., and Yajnik, K., Analysis of Turbulent Pipe and Channel Flows at Moderately Large Reynolds Numbers, J. Fluid Mech., Vol. 61, pp. 23–31, 1973.Google Scholar
  4. 4.
    Lund, K.O., Bush, W.B., Asymptotic Analysis of Plane Turbulent Couette-Poiseuille Flows, J. Fluid Mech., Vol. 96, pp. 81–104, 1980.Google Scholar
  5. 5.
    Henry, F. S., and Reynolds., A. J., Analytical Solution of Two Gradient-Diffusion Models Applied to Turbulent Couette Flow, J. Fluid Engng., Vol. 106, pp. 211–216, 1984.Google Scholar
  6. 6.
    Launder, B.E., and Spalding, D.B., Lectures in Mathematical Models of Turbulence, Academic Press, London, 1972.Google Scholar
  7. 7.
    Hanjalic, K., and Launder, B.E., A Reynolds Stress Model of Turbulence and its Application to Thin Shear Flows, J. Fluid Mech., Vol. 52, pp. 609–638, 1972.Google Scholar
  8. 8.
    El Telbany, M.M.M., and Reynolds, A.J., The Structure of Turbulent Plane Couette Flow, J. of Fluids Engineering, Vol. 104, pp. 367–372, 1982.Google Scholar
  9. 9.
    Townsend, A.A., The Structure of Turbulent Shear Flow, Cambridge University Press, 1976.Google Scholar
  10. 10.
    Schlichting, H., Boundary Layer Theory, Verlag G. Braun, Karlsruhe, 1979.Google Scholar
  11. 11.
    Rotta, J.C., Recent Attempts to Develop a Generally Applicable Calculation Method for Turbulent Shear Flow Layers, AGARD-CP-93, pp. A-1 to A-11, 1971.Google Scholar
  12. 12.
    Laufer, J., The Structure of Turbulence in Fully Developed Pipe Flow, NACA Rep. 1174, 1954.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • K. Gersten
    • 1
  1. 1.Institut für Thermo- und FluiddynamikRuhr-Universität BochumBochum 1Germany

Personalised recommendations