Viscoelastic instabilities in a 3D Stokes-Oldroyd-B fluid

The consequences of three-dimensional viscoelastic instabilities are examined numerically using the Oldroyd-B model in the low Reynolds number (Stokes) regime. The fluid is driven by a simple time-independent forcing that, in the absence of viscoelastic stresses, creates a four-roll mill in (x,y) which is constant in z. It is now known that such forcing will force the 2d version of this system into symmetry breaking and flow mixing. Here we find that at sufficiently large, but O(1), Weissenberg number, 3d perturbations grow exponentially and lead to complex three-dimensional flow dynamics which can differ markedly from the 2d case.