High-order generalisation of the diagnostic scaling for turbulent boundary layers

The diagnostic scaling concept, introduced for the streamwise turbulence intensity in wall-bounded turbulent flows ( Alfredsson, Segalini and Orlu, Phys. Fluids 2011; 23: 041702), is here extended and generalised not only for the higher even-order central statistical moments, but also for the odd moments and thereby the probability density distribution of the streamwise velocity fluctuations. Turbulent boundary layer data up to a friction Reynolds number of 60,000 are employed and demonstrate the feasibility of the diagnostic scaling for the data throughout the logarithmic and wake regions. A comparison with the generalised logarithmic law for even-order moments by Meneveau and Marusic ( J. Fluid Mech. 2013; 719: R1) based on the attached-eddy hypothesis, is reported. The diagnostic plot provides an apparent Reynolds-number-independent scaling of the data, and is exploited to reveal the functional dependencies of the constants needed in the attached-eddy-based model. In particular, the invariance of the lowest order diagnostic scaling poses an intriguing incompatibility with the asymptotic constancy of the Townsend-Perry constant.