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

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