High-Reynolds-number flow about a submerged circular cylinder induced by free-surface travelling waves on finite depth

Abstract

We consider the fluid flow induced when free-surface travelling waves, on fluid whose depth is finite and uniform in its undisturbed state, pass over a submerged circular cylinder. The wave amplitude is assumed to be small, and a suitably defined Reynolds number large. Thus, the inviscid flow may be pursued by perturbation methods, as may viscous effects that are confined to thin boundary layers on the cylinder and bed beneath it. Particular attention is focused on the steady streaming motion, which induces a circulation about the cylinder. The consequences of this on bed scouring beneath the cylinder, when the bed is erodible, are considered.