Polymer diffusive instability leading to elastic turbulence in plane Couette flow

Elastic turbulence is a chaotic flow state observed in dilute polymer solutions in the absence of inertia. It was discovered experimentally in circular geometries and has long been thought to require a finite amplitude perturbation in parallel flows. Here we demonstrate, within the commonly used Oldroyd-B and FENE-P models, that a self-sustaining chaotic state can be initiated via a linear instability in a simple inertia-less shear flow caused by the presence of small but nonzero diffusivity of the polymer stress. Numerical simulations show that the instability leads to a three-dimensional self-sustaining chaotic state, which we believe is the first reported in a wall-bounded, parallel, inertia-less viscoelastic flow.