Viscous free-surface flows past cylinders

Free-surface flows of viscous liquid down an inclined plane and past cylinders of various cross-sections are studied theoretically and experimentally. For relatively wide cylinders, a pond of nearly stationary fluid forms upstream of the cylinder, and a dry region without fluid occurs downstream of it. The flow structure in the pond region depends on the cylinder cross-section and curvature at the upstream stagnation point. The theory is used to deduce simplified asymptotic expressions of the force on the cylinders. The work is relevant to volcanic lava flow deflection by barriers.