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 modes) and resolvent analyses, i.e., critical-layer structures localized where the mean fluid velocity equals the wave speed. Computations of self-sustained nonlinear Tollmien-Schlichting waves reveal 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
