Nonlinear Dynamics of Turbulent Drag Reduction

The level of energy dissipated in turbulent flow of a liquid can be dramatically reduced by low levels of certain polymer or surfactant additives. This rheological drag reduction effect is well-known, but not well-understood. Perhaps the most striking qualitative feature of turbulent drag reduction is the existence of a so-called "maximum drag reduction" (MDR) asymptote. For a given flow geometry (pipe, duct, etc.) at a given pressure drop, there is an asymptotic flow rate that can be achieved through addition of polymers. Changing the concentration, molecular weight or even the chemical structure of the additives has no effect on this asymptotic value --- it is universal. This universality is the major challenge in understanding drag reduction.

We present simulation results for Newtonian and viscoelastic turbulent channel flow that reveal important new features of the turbulent drag reduction phenomenon. Our observations indicate that at high levels of drag reduction, viscoelasticity acts to suppress normal "active" turbulence (i.e. the dynamics that dominates Newtonian turbulence), while unmasking a fundamentally different kind of turbulence (which we call hibernating turbulence); in small channels the dynamics cycles stochastically between active and hibernating. Although unmasked by viscoelasticity, hibernating turbulence is also found intermittently in Newtonian flow, and during hibernation (whether Newtonian or viscoelastic), many features of the flow closely mirror features of the MDR regime. We are also studying the dynamics of "edge states" on the boundary between the basins of attraction of turbulent and laminar flows; the dynamics on this boundary mirror many features of hibernating turbulence and thus MDR, even in Newtonian flow. Together these results point toward a unified dynamical systems picture of the turbulent drag reduction phenomenon, a picture that may also have broader implications for flow control.