Instabilities in viscoelastic parallel shear flows with free-slip boundary conditions

Elastic turbulence is a strongly non-linear, turbulent-like flow state recently observed in polymer solutions at vanishing Reynolds numbers. Despite its relevance for industrial processing of viscoelastic materials and our general understanding of flows of complex fluids, available numerical results on elastic turbulence are scarce due to numerical instabilities. To ease the numerical complexity of such simulations, here we study free-slip plane Couette (pCF) and plane Poiseuille flows (pPF) of Oldroyd-B fluids. We perform a temporal linear stability analysis of free-slip pCF and pPF. Although their no-slip counterparts are generally linearly stable, we find that both geometries exhibit linear instabilities. By performing a boundary conditions homotopy, we show that these instabilities are caused by the least stable modes of no-slip flows loosing their stability under free-slip conditions. We perform direct numerical simulations to study the states that appear at the instability. We report a sequence of coherent structures from 2D to 3D periodic orbits to flows of yet higher complexity. We speculate that the 3D structures we observe in free-slip flows could be traced back to the no-slip setup, where they would form a dynamical scaffold for purely elastic turbulence.