Polymeric diffusive instability leading to elastic turbulence in plane Couette flow

Abstract

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 inertialess shear flow caused by the presence of small but non-zero diffusivity of the polymer stress. Numerical simulations show that the instability leads to a three-dimensional selfsustaining chaotic state, which we believe is the first reported in a wall-bounded, parallel, inertialess viscoelastic flow.