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Elastic turbulence is a chaotic flow state observed in dilute polymersolutions in the absence of inertia. It was discovered experimentally incircular geometries and has long been thought to require a finite amplitudeperturbation in parallel flows. Here we demonstrate, within the commonly-usedOldroyd-B and FENE-P models, that a self-sustaining chaotic state can beinitiated via a linear instability in a simple inertialess shear flow caused bythe presence of small but non-zero diffusivity of the polymer stress. Numericalsimulations show that the instability leads to a three-dimensionalselfsustaining chaotic state, which we believe is the first reported in awall-bounded, parallel, inertialess viscoelastic flow.

Polymeric diffusive instability leading to elastic turbulence in plane Couette flow