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On the mixing length eddies and logarithmic mean velocity profile in wall turbulence

Published online by Cambridge University Press:  21 January 2020

Michael Heisel Open the ORCID record for Michael Heisel [Opens in a new window] ,
Charitha M. de Silva Open the ORCID record for Charitha M. de Silva [Opens in a new window] ,
Nicholas Hutchins Open the ORCID record for Nicholas Hutchins [Opens in a new window] ,
Ivan Marusic Open the ORCID record for Ivan Marusic [Opens in a new window]  and
Michele Guala Open the ORCID record for Michele Guala [Opens in a new window]
Michael Heisel*
Affiliation:
St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414, USA Department of Civil, Environmental, and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455, USA
Charitha M. de Silva
Affiliation:
School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney2052, Australia
Nicholas Hutchins
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria3010, Australia
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria3010, Australia
Michele Guala
Affiliation:
St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414, USA Department of Civil, Environmental, and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: heise070@umn.edu
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Abstract

Since the introduction of the logarithmic law of the wall more than 80 years ago, the equation for the mean velocity profile in turbulent boundary layers has been widely applied to model near-surface processes and parameterize surface drag. Yet the hypothetical turbulent eddies proposed in the original logarithmic law derivation and mixing length theory of Prandtl have never been conclusively linked to physical features in the flow. Here, we present evidence that suggests these eddies correspond to regions of coherent streamwise momentum known as uniform momentum zones (UMZs). The arrangement of UMZs results in a step-like shape for the instantaneous velocity profile, and the smooth mean profile results from the average UMZ properties, which are shown to scale with the friction velocity and wall-normal distance in the logarithmic region. These findings are confirmed across a wide range of Reynolds number and surface roughness conditions from the laboratory scale to the atmospheric surface layer.

JFM classification

Turbulent Flows: Turbulent boundary layers Boundary Layers: Boundary layer structure Geophysical and Geological Flows: Atmospheric flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 887 , 25 March 2020 , R1
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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