New Mixing-Length Approach for the Mean Velocity Profile of Turbulent Boundary Layers

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 $δ+$ and the dimensionless wall normal coordinate $y+$⁠. 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.