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.

Written in terms of inner variables, the generalized log law reads
$u+=∑j=0∞εj[1κjln(y++Dj)+Aj...$