Universal mean velocity profile in polymeric flows at maximum drag reduction

Abstract

Provided a sufficient concentration of long-chain polymers in a Newtonian solvent, turbulent wall-bounded flows exhibit a universal state known as Maximum Drag Reduction (MDR). Through direct numerical simulations, we show that the wall-normal kinetic energy flux characterising Newtonian wall-bounded turbulence is suppressed at MDR, and that the polymers mainly sustain velocity fluctuations. In agreement with the experimental data, we derive a universal expression for the mean velocity profile no longer dependent on characteristic quantities of wall-bounded turbulence.