Self-Sustained Elastoinertial Tollmien-Schlichting Waves

Direct simulations of two-dimensional plane channel flow of a viscoelastic fluid at Reynolds number Re=3000 reveal the existence of a family of attractors whose structure closely resembles the linear Tollmien-Schlichting (TS) mode, and in particular exhibits strongly localized stress fluctuations at the critical layer position of the TS mode. At the parameter values chosen, this solution branch is not connected to the nonlinear TS solution branch found for Newtonian flow, and thus represents a solution family that is nonlinearly self-sustained by viscoelasticity. Evidence indicates that this branch is connected through an unstable solution branch to two-dimensional (2D) elastoinertial turbulence (EIT). Further, at Re=10000, where the laminar base state displays a TS linear instability, we show that the viscoelastic extension of the Newtonian nonlinear TS branch is directly connected to 2D EIT. These results suggest that, in the parameter range considered here, the transition leading to EIT is mediated by nonlinear amplification and self-sustenance of perturbations that excite the Tollmien-Schlichting mode.