A Stokesian viscoelastic flow: Transition to oscillations and mixing

► Viscoelastic fluids are studied computationally using the Stokes-Oldroyd-B model. ► Stress diffusion is added to the model to control large gradient growth. ► Symmetry-breaking instabilities are found for sufficiently large Weissenberg number. ► Instabilities lead to periodic and quasi-periodic temporal structures. ► Consequences for mixing are investigated and quantified.