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Revisiting the mixing-length hypothesis in the outer part of turbulent wall layers: mean flow and wall friction

Published online by Cambridge University Press:  19 March 2014

Sergio Pirozzoli
Sergio Pirozzoli*
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma ‘La Sapienza, Via Eudossiana 18, 00184 Roma, Italy
*
†Email address for correspondence: [email protected]
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Abstract

We reconsider foundations and implications of the mixing length theory as applied to wall-bounded turbulent flows in uniform pressure gradient. Based on recent channel-flow direct numerical simulation (DNS) data at sufficiently high Reynolds number, we find that Prandtl’s hypothesis of linear variation of the mixing length with the wall distance is rather inaccurate, hence overlap arguments are stronger in justifying the formation of a logarithmic layer in the mean velocity profile. Regarding the core region of the wall layer, we find that Clauser’s hypothesis of uniform eddy viscosity is strictly connected with the observed size of the eddy structures, and it delivers surprisingly good agreement with DNS and experiments for channels, pipes, and boundary layers. We show that the analytically derived composite mean velocity profiles can be used to accurately predict skin friction in canonical wall-bounded flows with a minimal number of adjustable parameters directly related to the mean velocity profile, and to obtain some insight into transient growth phenomena.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 745 , 25 April 2014 , pp. 378 - 397
Copyright
© 2014 Cambridge University Press 

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