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

Michael Heisel, Charitha M. De Silva, Nicholas Hutchins, Ivan Marusic, Michele Guala

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9 Scopus citations

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.

Original languageEnglish (US)
Article number1DUMMY
JournalJournal of Fluid Mechanics
Volume887
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
The authors acknowledge funding support from the Institute on the Environment (IonE) and the Australian Research Council. M.G. is supported by a National Science Foundation CAREER grant (NSF-CBET-1351303). M.H.’s visit to the University of Melbourne was supported by the University of Minnesota Graduate School. The authors are grateful to J. A. Sillero for allowing public access to the DNS data. The new PIV measurements from St. Anthony Falls Laboratory are publicly available online at the University of Minnesota data repository ( http://hdl.handle.net/11299/211303 ).

Keywords

  • Atmospheric flows
  • Boundary layer structure
  • Turbulent boundary layers

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