Inner-outer decomposition of wall shear stress fluctuations in turbulent channels

Abstract

Fluctuating wall shear stress in turbulent channel flows is decomposed into small-scale and large-scale components. The large-scale fluctuating wall shear stress is computed as the footprints of the outer turbulent motions, and the small-scale one is obtained by subtracting the large-scale one from the total, which fully remove the outer influences. We show that the statistics of the small-scale fluctuating wall shear stress is Reynolds number independent at the friction Reynolds number larger than 1000, while which is Reynolds number dependent or the low-Reynolds-number effect exists at the friction Reynolds number smaller than 1000. Therefore, a critical Reynolds number that defines the emergence of universal small-scale fluctuating wall shear stress is proposed to be 1000. The total and large-scale fluctuating wall shear stress intensities approximately follow logarithmic-linear relationships with Reynolds number, and empirical fitting expressions are given in this work.