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