Obstructed free-surface viscoplastic flow on an inclined plane

The interaction of steady free-surface flows viscoplastic material with a surface-piercing obstruction square cross-section on an inclined plane is investigated theoretically. flow thickness increases upstream the and decreases in its lee. depends two dimensionless parameters: aspect ratio that relates thickness, width inclination; Bingham number quantifies magnitude yield stress relative to gravitationally induced stresses. Flows non-vanishing always form static ‘dead’ zone neighbourhood downstream stagnation points. For relatively wide obstructions, deep ‘ponded’ region develops small dead zone, while deflected reconnects over long distances downstream. depth pond both obstruction, unyielded varies primarily stress. Both are predicted asymptotically by balancing volume flux fluid into out ponded region. When narrow, perturbation oncoming reduced. It exhibits fore–aft antisymmetry, symmetric leading order. Increasing leads larger zones eventually encompass all upstream- downstream-facing boundaries fully divert flow. Results for obstructions circular rhomboidal cross-sections also presented illustrate effects boundary shape properties