Polymeric diffusive instability (PDI) leading to viscoelastic chaos in planar wall-bounded flows*

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 wall-bounded parallel flows. In this talk we will discuss, within the commonly-used FENE-P model, 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 self-sustaining chaotic state. We will discuss how this instability might present a generic pathway to experimentally observed viscoelastic chaotic states, i.e. elastic turbulence and elasto-inertial turbulence.