Abstract
The log-law of the wall in the overlap for wall-bounded turbulent flows is rederived from a pure dimensional analysis and functional equation based on three experimental facts: (1) in the inner flow region, the mean velocity distribution is dominated by the viscous length scale; (2) in the outer flow region, the mean velocity distribution is dominated by the largest eddy size or the boundary layer thickness; and (3) there is an overlap between the inner and outer regions. These facts lead to a functional equation that yields a universal log-law in the overlap. Hence, the log-law is independent of any turbulence model, and it is an axiom accepted widely in fluid mechanics.
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