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

Abstract

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 flat. However for small values of F , the waves are of large amplitude. They ultimately approach the Stokes' limiting configuration with an angle of 120° at their crest as F is decreased.