Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

We perform a linear stability analysis of viscoelastic plane Couette and Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, are driven suitable body force. find that both types flow become linearly unstable, we characterise spatial structure unstable modes. By performing condition homotopy from to no-slip boundaries, demonstrate modes directly related least stable problem, destabilised under situation. discuss how our observations can be used study recently discovered purely elastic turbulence in parallel shear flows.