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Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles

Published online by Cambridge University Press:  22 February 2011

B. ROLLIN ,
Y. DUBIEF  and
C. R. DOERING
B. ROLLIN*
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87544, USA
Y. DUBIEF
Affiliation:
School of Engineering, University of Vermont, Burlington, VT 05405, USA
C. R. DOERING
Affiliation:
Department of Mathematics, Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109-1107, USA
*
†Email address for correspondence: bertrand@lanl.gov
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Abstract

The relation between the form of a body force driving a turbulent shear flow and the dissipation factor β = ϵℓ/U3 is investigated by means of rigorous upper bound analysis and direct numerical simulation. We consider unidirectional steady forcing functions in a three-dimensional periodic domain and observe that a rigorous infinite Reynolds number bound on β displays the same qualitative behaviour as the computationally measured dissipation factor at finite Reynolds number as the force profile is varied. We also compare the measured mean flow profiles with the Stokes flow profile for the same forcing. The mean and Stokes flow profiles are strikingly similar at the Reynolds numbers obtained in the numerical simulations, lending quantitative credence to the notion of a turbulent eddy viscosity.

JFM classification

Turbulent Flows: Turbulence modelling Mathematical Foundations: Variational methods
Type
Papers
Information
Journal of Fluid Mechanics , Volume 670 , 10 March 2011 , pp. 204 - 213
Creative Commons
This is a work of the U.S. Government and is not subject to copyright protection in the United States.
Copyright
Copyright © Cambridge University Press 2011. This is a work of the U.S. Government and is not subject to copyright protection in the United States.

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References

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