Elasto-inertial turbulence: Reentrant transition and connection to linear mechanisms*

We describe direct numerical simulations (DNS) of channel flow turbulence in a FENE-P fluid.  At Reynolds numbers very close to transition, the flow first relaminarizes upon increasing Weisenberg number (Wi) or polymer concentration, but then becomes turbulent again, displaying features of elasto-inertial turbulence (EIT). At higher Reynolds number, the flow evolves as Wi increases from displaying intermittency and streamwise vortex structure characteristic of Newtonian flow to EIT, while at intermediate Wi, a spatiotemporal mixture of the two structures is observed. We tie these observations to the 2D stability of the  laminar flow and characterize the observed disturbance amplification which starts to show up at intermediate Wi. Observations point at a bypass transition with turbulent flow structure that resembles that of a discrete eigenmode close to the real axis in the eigenvalue spectrum. Further, we present a tentative phase diagram of polymer drag reduction and draw links to Tollmien-Schlichting modes in the Newtonian limit and Gorodtsov-Leonov modes in the elastic limit.