Identification and calculation of the universal asymptote for drag reduction by polymers in wall bounded turbulence.
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+) approximately 11.7logy+ - 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.
Benzi
Roberto
R
Dipartimento di Fisica and INFN, Università Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy.
De Angelis
Elisabetta
E
L'vov
Victor S
VS
Procaccia
Itamar
I