Three-dimensional viscoelastic flow instabilities at extensional stagnation points

Simulations of viscoelastic fluid models in the Stokes limit exhibit instabilities at extensional stagnation points. We present simulations of both the Oldroyd-B and FENE-P models in a 3D periodic domain with cylindrical 4-roll mill background forcing. Beyond a critical Weissenberg number (non-dimensional relaxation time) we find an instability in the z-direction (note that the background force is constant in z). We present both simulations and linear stability analysis and identify criteria for the occurrence of this instability.