Mean velocity and length-scales in the overlap region of wall-bounded turbulent flows

Abstract

The length scales of the spectra and correlation functions of the velocity fluctuations in the overlap region of turbulent wall-bounded flows are analyzed. It is found that a mixing length based on the mean local shear works better as a normalization than the distance to the wall. To define an overlap range sufficiently long and independent of the Reynolds number to allow the two scalings to be tested, the classical asymptotic expansion of the mean shear is extended to include a near-wall virtual origin and a wake component. The result represents well the velocity profile in y+ > 70 and y/δ < 0.3 – 0.5 for Reτ≿2000, and the spectral scales for Reτ≿500. It is suggested that the scaling with a local mixing length could be interpreted as an indication that the size of the eddies is more related to the local shear time scale than to the interaction with the wall. It is also noted that the linearity of the mixing length is a more robust indicator of a logarithmic regime than those that rely on a zero virtual origin.