Viscoplastic corner eddies

When viscous fluid in a corner is disturbed, eddies can form the absence of inertia. Examples flow configurations which this motion occurs include through an abrupt contraction and over cavity. Six decades ago, Moffatt ( J. Fluid Mech. , vol. 18, 1964, pp. 1–18) calculated slow Newtonian fluids sharp corners, detailing his eponymous ‘Moffatt eddies’. In study we examine flows viscoplastic materials, class non-Newtonian exhibit solid-like behaviour for stresses below yield stress. Specifically, consider Bingham fluid, material perfectly rigid at While static unyielded plug forms tip corner, analogous to those found by also form. We these numerically, computing finite element solutions using augmented-Lagrangian method, analytically, employing boundary layer formulation scaling arguments. measure depth as function number (dimensionless stress), show that process new eddy forming decreased driven pressure yielded adjacent plug, provide heuristic argument critical occurs.