Near-wall similarity in two- and three-dimensional turbulent boundary layers

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Virginia Polytechnic Institute and State University


Static pressure, mean velocity, indirect wall shear from Preston tubes, direct wall shear using a two-dimensional (single line of action) floating element device, and direct wall shear measurements from an omnidirectional floating element capable of simultaneously determining magnitude and direction of a wall shear vector were completed over a modest range of two-dimensional, (near-zero) pressure gradient flows. Static pressure, mean velocity, and direct wall shear measurements using the omnidirectional meter were completed in a pressure driven, and two different shear driven three-dimensional flows. These data were combined to evaluate ten of eleven three-dimensional similarity models found in the literature. Uncertainty estimates on all the data are presented.

Two-dimensional experimental results show that the constants in the two-dimensional law of the wall formula appear to be slightly dependent on Reynolds number, and the Patel calibration formulas for Preston tubes to be better than any other available formulas. Three-dimensional results show (1) the Perry and Joubert and the White, Lessmann, and Christoph three-dimensional similarity models to give limited but overall better agreement with experimental data, (2) none of the proposed models adequately model experimental results for y⁺ < 50, (3) near-wall collateral flow does not exist, and (4) pressure gradient effects on the omnidirectional meter appear to be negligible.