Scaling of Wall Turbulence at Finite Reynolds Number

Abstract

New scaling relations for the mean velocity and Reynolds shear stress in viscous sublayer were proposed based on the application of matched asymptotic expansion method to the mean momentum balance. It was shown that the new parameter $\Lambda_+$ is relevant for the wall turbulence in addition to the friction velocity. From the proposed new scaling of the viscous sublayer the power law for the mean velocity in the overlap region was derived. The complete or incomplete similarity of the parameter $\Lambda_+$ was shown to be the key factor, which determines whether the mean velocity obeys the power law or log law in the overlap layer.