Streamwise self-similarity and log scaling in turbulent boundary layers

Abstract

High Reynolds number is thought to be a fundamental condition essential for the occurrence of log scaling in turbulent boundary layers. However, while log variation of mean velocity is seen to occur at moderate Reynolds numbers in the traditional boundary layer literature, log variations of higher-order moments are evident only at much higher Reynolds numbers, as reported in recent experiments. This observation suggests that, underlying the occurrence of log scaling in turbulent boundary layers, there exists a more fundamental condition (apart from the largeness of Reynolds number) – the requirement of self-similar evolution of a mean-flow quantity of interest along a mean-flow streamline, i.e. the mean advection of the scaled mean quantity of interest is required to be zero. Experimental data from the literature provide strong support for this proposal.