Universal mean velocity profile in polymeric flows at maximum drag reduction

Turbulent wall-bounded flows of dilute polymer solutions achieve a universal state known as Maximum Drag Reduction (MDR). At MDR, elongated polymers primarily sustain velocity fluctuations, destroy the classical path of turbulent kinetic energy of wall-bounded Newtonian turbulence, and induce a mean linear effective viscosity, whose slope defines a new inner length scale for the. system. Analogously to Newtonian turbulence, the mean velocity shows a universal logarithmic behavior (Virk's law) in the case of a large separation between the inner and the outer scale of the system.