Self-scaling generalized Townsend-Perry constants for high-order moments in turbulent boundary layers

Inspired by the thought-provoking paper of Meneveau and Marusic [J. Fluid Mech. 719, R1 (2013)], the universal expression of the self-scaling generalized Townsend-Perry constants for the high-order statistical moments is investigated. The measured results deviate from the previous attached-eddy-model–based Gaussian prediction because the wall-non-attached eddies with sub-Gaussian statistics mask the Gaussian behavior of the wall-attached eddies. Leveraging the generalized Gaussian distribution function and the logarithmic law for turbulence intensity, the universal expression of the self-scaling generalized Townsend-Perry constants, regardless of the eddy type, is derived. Moreover, asymptotic expression of the shape parameter in self-scaling generalized Townsend-Perry constants with Reynolds number is further characterized by data in boundary layers and atmospheric surface layers with Reynolds number $R{e}_{\tau }$ spanning over $O\left({10}^3\right)$ to $O\left({10}^6\right)$.