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
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+)≈ 11.7 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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