Simulations of elastoinertial turbulence (EIT) of a polymer solution at low Reynolds number are shown to display localized polymer stretch fluctuations. These are very similar to structures arising from linear stability (Tollmien-Schlichting (TS) modes) and resolvent analyses: i.e., critical-layer structures localized where the mean fluid velocity equals the wavespeed. Computation of selfsustained nonlinear TS waves reveals that the critical layer exhibits stagnation points that generate sheets of large polymer stretch. These kinematics may be the genesis of similar structures in EIT.Turbulent drag reduction is an important and puzzling phenomenon in the non-Newtonian flow of complex fluids. Addition of polymers or micelle-forming surfactants to a liquid can lead to dramatic reductions in energy dissipation during turbulent flow while having a negligible effect on laminar flow[1].In Newtonian channel or pipe flow, transition to turbulence occurs by a so-called subcritical or "bypass" transition mechanism as flow rate, measured nondimensionally by Reynolds number, Re, increases: turbulence is initiated by finite-amplitude perturbations to the laminar flow profile, while the laminar flow remains linearly stable. While channel flow exhibits a two-dimensional linear instability leading to so-called Tollmien-Schlichting (TS) waves, the critical Reynolds number Re = 5772 is much higher than that observed for transition, so these are not traditionally viewed as playing an important role in Newtonian transition.For flowing polymer solutions under some conditions (low concentration, short polymer relaxation times), transition to turbulence occurs via the usual bypass transition. With further increase in Re, drag reduction sets in, and the flow eventually approaches the so-called maximum drag reduction (MDR) asymptote, an upper bound on the degree of drag reduction that is insensitive to the details of the fluid.Under other conditions, flow transitions directly from laminar flow into the MDR regime, and can do so at a Reynolds number where the flow would remain laminar if Newtonian [2][3][4][5]. Recent experiments and simulations [6][7][8] suggest that turbulence in this regime has structure very different from Newtonian, denoting it as "elastoinertial turbulence" (EIT). Choueiri et al.[4] experimentally observed that at transitional Reynolds numbers and increasing polymer concentration, turbulence is first suppressed, leading to relaminarization, and then reinitiated with an EIT structure and a level of drag corresponding to MDR. Therefore, there are actually two distinct types of turbulence in polymer solutions, one that is suppressed by viscoelasticity, and one that is promoted.The present work reports computations and analysis that elucidate the mechanisms underlying EIT. We show that EIT at low Re has highly localized polymer stress fluctuations. Surprisingly, these strongly resemble linear Tollmien-Schlichting modes as well as the most strongly amplified fluctuations from the laminar state. Furthermore, the kinematic...

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Direct simulations of two-dimensional channel flow of a viscoelastic fluid have revealed the existence of a family of Tollmien-Schlichting (TS) attractors that is nonlinearly self-sustained by viscoelasticity [Shekar et al., J. Fluid Mech. 893, A3 (2020)]. Here, we describe the evolution of this branch in parameter space and its connections to the Newtonian TS attractor and to elastoinertial turbulence (EIT). At Reynolds number Re = 3000, there is a solution branch with TS-wave structure but which is not connected to the Newtonian solution branch. At fixed Weissenberg number, Wi and increasing Reynolds number from 3000-10000, this attractor goes from displaying a striation of weak polymer stretch localized at the critical layer to an extended sheet of very large polymer stretch. We show that this transition is directly tied to the strength of the TS critical layer fluctuations and can be attributed to a coil-stretch transition when the local Weissenberg number at the hyperbolic stagnation point of the Kelvin cat's eye structure of the TS wave exceeds 1 2 . At Re = 10000, unlike 3000, the Newtonian TS attractor evolves continuously into the EIT state as Wi is increased from zero to about 13. We describe how the structure of the flow and stress fields changes, highlighting in particular a "sheet-shedding" process by which the individual sheets associated with the critical layer structure break up to form the layered multisheet structure characteristic of EIT.

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