Capillary waves past a flat plate in water of finite depth

Free‐surface flow past a semi‐infinite flat plate in a channel of finite depth is considered. The fluid is assumed to be inviscid and incompressible, and the flow to be two‐dimensional and irrotational. Surface tension is included in the dynamic boundary condition but the effects of gravity are neglected. It is shown that there is a three‐parameter family of solutions with waves in the far field and a discontinuity in slope at the separation point. This family includes as particular cases the solutions previously computed by Osborn & Stump (2001, Phys. Fluids, 13, 616–623) and by Andersson & Vanden‐Broeck (1996, Proc. R. Soc., 452, 1985–1997).