Numerical calculations of the free-surface flow under a sluice gate

The free-surface flow under a sluice gate is considered. The fluid is assumed to be inviscid and incompressible. The problem is solved numerically by using a boundary integral equation technique. Accurate numerical solutions are obtained when the intersection of the upstream free surface with the gate is a stagnation point. It is shown that the radiation condition is not satisfied far upstream and that there is a train of waves on the upstream free surface. For large values of the downstream Froude number F, the amplitude of the waves is so small that the upstream free surface is essentially hat. However for small values of F, the waves are of large amplitude. They ultimately approach the Stokes' limiting configuration with an angle of 120 degrees at their crest as F is decreased.