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The law of the wall in turbulent shear flow

  • Donald Coles
Chapter

Summary

The boundary-layer equations of continuity and momentum are integrated for a general turbulent shear flow whose mean-velocity profile is given by the law of the wall, u/u τ — f (yu τ /v), with u = v = 0 at y = 0. It is found that u/u τ and yu τ /v are constant on streamlines of the mean flow.

A streamline hypothesis for turbulent shear flow is introduced in the form D (u/u τ) /D t = 0. Assuming Newtonian friction at the wall, a unique generalization of the law of the wall is obtained for compressible flow along a smooth plate.

The generalization involves the Howarth transformation \( \eta = \int\limits_o^y {\varrho dy} \) and a friction density defined by τ w = ϱ τ u τ 2. The special case ϱμ = constant appears to be significant for turbulent as well as for laminar flow. Experimental data are used to evaluate the ratio ϱ τ /ϱ u for Mach numbers up to about six.

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Referrences

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    von Karman, T., Über laminare und turbulente Reibung. ZAMM, Vol. 1, No. 4 (1921), pp. 233–252, NACA TM 1092, 1946.CrossRefADSGoogle Scholar
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    Ludwieg, H. and Tillmann, W., Untersuchungen über die Wandschubspannung in turbulenten Reibungsschichten. Ing.-Arch., Vol. 17, No. 4 (1949), pp. 288—299, NACA TM 1285, 1950.CrossRefzbMATHGoogle Scholar
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    Coles, D., Measurements in the boundary layer on a smooth flat plate in supersonic flow. Thesis, California Inst. Tech., Pasadena, 1953.Google Scholar
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    Korkegi, B., Transition studies and skin friction measurements on an insulated flat plate at a hypersonic Mach number. Thesis, California Inst. Tech., Pasadena, 1954.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1955

Authors and Affiliations

  • Donald Coles
    • 1
  1. 1.Guggenheim Aeronautical LaboratoryCalifornia Institute of TechnologyPasadenaUSA

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