Abstract
It is shown that a family of formally derived similarity solutions describe to leading order the outer region of a turbulent boundary layer for all Reynolds numbers for which the layer satisfies the logarithmic law-of-the-wall. The family includes Coles' [1] hypothesis. For consistency with this hypothesis and the logarithmic law-of-the-wall, it is further shown that the constants in the latter form the product κC=2+O(ε), suggesting the logarithmic law of the wall be written
A range of data are reprocessed to determine the skin friction coefficientC f using κC = 2 and these collapse well when plotted against momentum thickness Reynolds number, Re θ . It is also shown that the form parameter, Π, in Coles hypothesis is not unique but is determined by history effects peculiar to the boundary layer. Expressions are derived forC f (Re θ ) and the shape factorH (Re θ ); both agree closely with the data and are valid over all Reynolds numbers for which the logarithmic law of the wall is satisfied.
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Phillips, W.R.C. On the logarithmic-law constants and the turbulent boundary layer at low Reynolds numbers. Appl. Sci. Res. 52, 279–293 (1994). https://doi.org/10.1007/BF00936833
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DOI: https://doi.org/10.1007/BF00936833