An open-channel flow meeting a barrier and forming one or two jets

A steady two-dimensional free-surface flow in a channel of finite depth is considered. The channel ends abruptly with a barrier in the form of a verti cal wall of finite height. Hence the stream, which is uniform far upstream, is forced to go upward and then falls under the effect of gravity. A confi guration is examined where the rising stream splits into two jets, one fall ing backward and the other forward over the wall, in a fountain-like manner . The backward-going jet is assumed to be removed without disturbing the in cident stream. This problem is solved numerically by an integral-equation m ethod. Solutions are obtained for various values of a parameter measuring t he fraction of the total incoming fur that goes into the forward jet. The l imit where this fraction is one is also examined, the water then all passin g over the wall, with a 120 degrees corner stagnation point on the upper fr ee surface.