Algebraic formulas are derived here for the eddy viscosities and mixing lengths of turbulent boundary layers on flat plates. The effect of low Reynolds numbers, especially on rough surfaces, is included. The formulas are based on the similarity laws and the equations of motion. Both smooth and rough surfaces are considered. The agreement with Klebanoff's measurements is excellent.
Eddy Viscosities and Mixing Lengths for Turbulent Boundary Layers on Flat Plates, Smooth or Rough
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Granville, Paul S.. "Eddy Viscosities and Mixing Lengths for Turbulent Boundary Layers on Flat Plates, Smooth or Rough." J Ship Res 32 (1988): 229–237. doi: https://doi.org/10.5957/jsr.1918.104.22.168
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