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Identification and Calculation of the Universal Maximum Drag Reduction Asymptote by Polymers in Wall Bounded Turbulence

Roberto Benzi·Elisabetta deAngelis·Victor S. L'vov·Itamar Procaccia
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Abstract

Drag reduction by polymers in wall turbulence is bounded from above by a universal maximal drag reduction (MDR) velocity profile that is a log-law, estimated experimentally by Virk as $V^+(y^+)\approx 11.7 \log y^+ -17$. Here $V^+(y)$ and $y^+$ are the mean streamwise velocity and the distance from the wall in "wall" units. In this Letter we propose that this MDR profile is an edge solution of the Navier-Stokes equations (with an effective viscosity profile) beyond which no turbulent solutions exist. This insight rationalizes the universality of the MDR and provides a maximum principle which allows an ab-initio calculation of the parameters in this law without any viscoelastic experimental input.

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Roberto Benzi, Elisabetta deAngelis, Victor S. L'vov, Itamar Procaccia. 2005-05-04. Identification and Calculation of the Universal Maximum Drag Reduction Asymptote by Polymers in Wall Bounded Turbulence. https://doi.org/10.1103/physrevlett.95.194502

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