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

ABSTRACT

The diagnostic scaling concept, introduced for the streamwise turbulence intensity in wall-bounded turbulent flows (Alfredsson, Segalini and Örlü, 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.

KEYWORDS:

• Turbulent flows
• turbulent boundary layers

Acknowledgments

Ramis Örlü acknowledges the support from the Swedish Research Council (VR), Antonio Segalini the support from STandUP for Wind, and Joseph Klewicki the support from the US National Science Foundation (NSF) and the Australian Research Council.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. While the Princeton Superpipe facility suggests generally higher values for the von Kármán constant,[22] recent high Re pipe flow experiments [23] yield values that are close to those of ZPG TBL [20] and channel [21] flows.