Linear instability leading to elastic turbulence in plane Couette flow

Elastic turbulence (ET) is a chaotic flow state observed in dilute polymer solutions in the absence of inertia, which was originally discovered experimentally in curved geometries. It has long been thought that triggering ET in parallel flows requires a finite amplitude perturbation to generate streamline curvature. We demonstrate here that self-sustaining ET can be initiated via a linear instability in inertialess planar Couette flow, a flow configuration which has previously been assumed to be stable to all initial perturbations. The new linear instability is associated with the existence of finite polymer diffusivity and exists for a wide range of realistic parameter settings and different choices of boundary conditions on the polymer conformation tensor. Numerical simulations show that the instability leads to a three-dimensional self-sustaining chaotic state, which we believe is the first reported numerical evidence of ET in a parallel flow.