There has been considerable controversy during the past few years concerning the validity of the universal logarithmic law that describes the mean velocity profile in the overlap region of a turbulent wall-bounded flow (1,2). The present authors recently advanced a generalized logarithmic law to describe such overlap region (3,4). This law was derived based on a consequent extension of the classical two-layer approach to higher-order terms involving the Kármán number and the dimensionless wall normal coordinate . As compared to either the simple log law or the power law, the Reynolds-number-dependent generalized law provides a superior fit to existing high-fidelity data.
New Mixing-Length Approach for the Mean Velocity Profile of Turbulent Boundary Layers
Buschmann, M. H., and Gad-el-Hak, M. (January 17, 2005). "New Mixing-Length Approach for the Mean Velocity Profile of Turbulent Boundary Layers." ASME. J. Fluids Eng. March 2005; 127(2): 393–396. https://doi.org/10.1115/1.1881701
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