Role of elasto-inertial turbulence in viscoelastic drag-reducing turbulence

Abstract

Two kinds of nonlinearities coexist in viscoelastic fluid flows, i.e., inertia and elasticity, which can engender different types of chaotic states including inertial turbulence (IT), drag-reducing turbulence (DRT), elastic turbulence, and elasto-inertial turbulence (EIT). The state of maximum drag reduction (MDR), the ultimate state of DRT of viscoelastic fluids, is recently regarded as EIT. This Letter quantitatively demonstrates the role of IT and EIT in drag-reducing turbulent flows passing through the parallel plane channels via the contributions of Reynolds shear stress and the nonlinear part of elastic shear stress to flow drag. The nature of DRT is reexamined under a wide range of flow conditions covering a series of flow regimes from the onset of DR to MDR with the Oldroyd-B model. We argue that EIT-related dynamics appears in DRT long before settling to MDR state and competitively coexists with IT in both spatial and temporal domains at moderate and high Reynolds number (Re). More specifically, under a low DR condition, EIT first emerges close to the channel walls. With the increase in elasticity, low-drag EIT gradually replaces a high-drag IT from channel walls to center, resulting in a drastic decrease in flow drag comparing with IT. When EIT dynamics dominates the whole channel, MDR phenomenon occurs. Our findings provide evidence that DRT phenomenon is the result of IT and EIT interaction.