Parametrizing the probability density function of wall-shear stress in turbulent channel flows

Parametrization of the probability density function (PDF) of streamwise wall-shear stress (WSS) in turbulent channel flows at the friction Reynolds number from 180 to 5200 is investigated. Lognormal parametrization is found to be more accurate than Gaussian for both the original and rescaled PDF of WSS. The original PDF of the inner WSS fluctuations can be well parametrized by a lognormal distribution. The rescaled PDF of the outer WSS fluctuations can be precisely parametrized by a Gaussian distribution.