Comparison between wall and dissipative scalings for fourth-order structure functions in a fully developed turbulent channel flow

The classical scaling of wall turbulence is based on wall parameters (friction velocity, friction temperature, and kinematic viscosity). Recently, a novel scaling based on dissipative scales—the mean turbulent energy dissipation rate, the mean scalar dissipation rate, and kinematic viscosity—was put forward by Tang and Antonia [“Scaling of small-scale wall turbulence,” J. Fluid Mech. 948, A25 (2022) and “Similarity for dissipation-scaled wall turbulence,” J. Fluid Mech. 960, A18 (2023)]. This new scaling is supported by extensive wall turbulence data, related mainly to the second- and third-order statistics. In this paper, we systematically compare the classical wall scaling and the dissipative scaling in the context of fourth-order statistics, specifically, the fourth-order velocity and scalar structure functions in a fully developed turbulent channel flow at a molecular Prandtl number Pr=0.71. It is found that both the wall parameter- and dissipative scale-normalized fourth-order velocity and scalar structure functions exhibit similar degrees of collapse at moderate distances from the wall. However, in the very-near-wall region, dissipative scale-normalized structure functions collapse approximately at all scales, while wall parameter-normalized distributions vary systematically with the Reynolds number. Far from the wall, dissipative scale-normalized structure functions collapse approximately at small scales, while wall parameter-normalized distributions continue to evolve with the Reynolds number at all scales. Overall, the scaling based on dissipative scales is superior to that based on wall parameters over a significant portion of the channel, except at moderate distances from the wall, where both scalings are valid in the small-scale range.