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〉 = 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.