Title: Role of Elasto-Inertial Turbulence in Maximum Drag Reduction
Abstract:Minute concentrations of high molecular weight polymers have one exceptional and one intriguing properties in turbulent ows. Polymers show exceptional friction drag reduction capability (up to 80%). Yet, since the discovery of polymer drag reduction in 1949, the community has been intrigued by the asymptotic state called maximum drag reduction or MDR that appears to be universal to all polymer molecules tested so far. Whilst the mechanism of the polymer drag reduction is now considered understood , MDR remains somewhat a controversial topic. One school of thought argues that the dynamics of MDR is of Newtonian nature, i.e. the building blocks are the fundamental instabilities that create streaks and vortices as observed in turbulence with Newtonian uids. Support for this theory stems from numerical simulations using a specic approach to stabilize the polymer eld governing equation. This approach is the achilles' heel of the claim that MDR is of Newtonian nature and an interesting tool to study MDR. Indeed this presentation will show that most simulations of polymer drag reduction have numerically ltered out a small scale phenomenon, called Elasto-Inertial Turbulence (EIT). EIT is a recently discovered new state of turbulence, where interactions between inertia and elastic eects can sustain a turbulence-like state in channel and pipe ows at Reynolds numbers much lower than the critical Reynolds at which Newtonian ows undergo a transition from laminar to turbulent state. The dynamics of EIT is an interesting and fairly unique inverse cascade system driven by the interplay of pressure, viscoelastic eects and velocity perturbations. EIT is found over a large range of Reynolds numbers from close to unity to well above critical, and not only in parallel, wall bounded shear ows but also in natural convection ows and surmised to exist in free shear ows. This presentation will introduce the second school of thought which argues that EIT is the cause of MDR. The relation between EIT and Elastic Turbulence (ET), a turbulent state discovered 17 years ago in inertia-less ows with curved streamlines, will also be discussed in the light of recent advances, in particular from Prof. Arratia, showing that ET may exist in parallel flows.