We derive a rigorous upper bound on the energy dissipation rate in a smoothed version of plane Poiseuille flow in which a minimum length scale parallel to the walls is imposed. Due to the smaller number of degrees of freedom, much higher Reynolds numbers can be reached in numerical simulations of this system. These indicate that the turbulent energy dissipation rate achieves the upper bound scaling except for an extra logarithmic factor of Assuming that this discrepancy in scaling between the best known upper bound and true dissipation carries over to the full plane Poiseuille problem, this result presents further evidence that the viscous dissipation rate there is (in inertial units) and hence vanishes as the Reynolds number The mean flow profiles which emerge from this smoothed system are strikingly similar to those which arise by adding stress-reducing additives to a wall-bounded shear flow. Both show familiar log regions with essentially the same gradient as the undisturbed (polymer free or no minimum length scale) system but which are now displaced vertically in the traditional diagram.
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January 2003
Research Article|
January 01 2003
On smoothed turbulent shear flows: Bounds, numerics and stress-reducing additives
R. R. Kerswell;
R. R. Kerswell
Department of Mathematics, University of Bristol, Bristol, BS8 1TW, England, United Kingdom
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D. Obrist;
D. Obrist
Cray Inc., Panamaweg 7, 5034 Suhr, Switzerland
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P. J. Schmid
P. J. Schmid
Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-2420
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Physics of Fluids 15, 78–83 (2003)
Article history
Received:
December 05 2001
Accepted:
October 03 2002
Citation
R. R. Kerswell, D. Obrist, P. J. Schmid; On smoothed turbulent shear flows: Bounds, numerics and stress-reducing additives. Physics of Fluids 1 January 2003; 15 (1): 78–83. https://doi.org/10.1063/1.1524182
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