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

Published online by Cambridge University Press:  19 February 2013

Charles Meneveau  and
Ivan Marusic
Charles Meneveau
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia
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Abstract

High-Reynolds-number data in turbulent boundary layers are analysed to examine statistical moments of streamwise velocity fluctuations ${u}^{\prime } $. Prior work has shown that the variance of ${u}^{\prime } $ 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 $\langle \mathop{({u}^{\prime + } ){}^{2p} \rangle }\nolimits ^{1/ p} = {B}_{p} - {A}_{p} \ln (z/ \delta )$, where ${u}^{\prime + } $ is the velocity fluctuation normalized by the friction velocity, $\delta $ is an outer length scale and ${B}_{p} $ are non-universal constants. The slopes ${A}_{p} $ 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.

JFM classification

Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulent boundary layers
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , R1
Copyright
©2013 Cambridge University Press

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