Generalized logarithmic law for high-order moments in turbulent boundary layers

High-Reynolds-number data in turbulent boundary layers are analysed to examine statistical moments of streamwise velocity fluctuations u . Prior work has shown that the variance of u exhibits logarithmic behaviour with distance to the surface, within an inertial sublayer. Here we extend these observations to even-order moments. We show that the $2p$ -order moments, raised to the power $1/ p, $ also follow logarithmic behaviour according to (u⁺ )²ᵖ 1/ p = Bₚ - Aₚ ln (z/ δ ) , where u⁺ is the velocity fluctuation normalized by the friction velocity, δ is an outer length scale and Bₚ are non-universal constants. The slopes Aₚ in the logarithmic region appear quite insensitive to Reynolds number, consistent with universal behaviour for wall-bounded flows. The slopes differ from predictions that assume Gaussian statistics, and instead are consistent with sub-Gaussian behaviour.