GALCIT Colloquium

Addition of a small amount of very large polymer molecules or micelle-forming surfactants to a liquid can dramatically reduce the energy dissipation it exhibits in the turbulent flow regime. The most striking feature of this phenomenon is the existence of a so-called maximum drag reduction (MDR) asymptote: for a given geometry and driving force, there is a maximum achievable level of drag reduction that is virtually independent of polymer properties. This universality is the major puzzle of drag reduction.

Drag reduction can occur at Reynolds numbers as low as the laminar-turbulent transition regime. The past decade has seen substantial increases in the understanding of this regime through application of ideas from the theory of nonlinear dynamical systems and we are working to extend these to the drag reduction phenomenon using simulations of channel flow of both Newtonian and viscoelastic polymeric fluids. In minimal channel simulations in the absence of polymers there are time intervals that display very low drag as well as many other features of the MDR asymptote observed in polymer solutions. As viscoelasticity increases, the frequency of these low-drag intervals also increases, leading to flows that increasingly resemble MDR. A simple mechanistic theory captures key features of the intermittent dynamics observed in the simulations. We also compute new families of Newtonian invariant states in the minimal channel flow geometry. Interestingly, the family of states around which minimal channel turbulence is organized contains solutions that approach the MDR asymptote and the classical Newtonian log-law profile, both in terms of bulk velocity and mean velocity profile. Finally, we use pattern analysis techniques to characterize the spatiotemporal intermittency within near-transition turbulence in extended domains and its relation to invariant states found in small domains. Based on these observations, we propose a tentative unified description of rheological drag reduction that sheds light on the observed universality of MDR and may ultimately lead to new flow control approaches for improving energy efficiency in a wide range of processes.