Potential flow for a steady jet in a wedge

Potential flow theory is used to model the steady free surface of water which turns in the interior of a wedge formed by the angle between two impermeable, plane walls. The model describes simply the violent flow encountered in a crack in a seawall struck by an ocean wave. Analytic results are obtained for the free surface position when the interior angle of the wedge, β = 0°, 60° and 45°. Numerical results are illustrated for the streamlines. Two approximate theories are developed which accurately bracket the exact position of the free surface. When the wedge angle, β, is small the free surface is shown to be remote from the point of intersection of the asymptotes of the free surface. The fluid forces on the walls are found, with and without fluid leakage through the crack apex. The forces on the walls are reduced by leakage, but the forces increase without bound as β → 0. The plane flow can be supplemented by the addition of a uniform velocity component in the third dimension.