Super-critical free-surface flow over a trapezoidal obstacle

A numerical method based on series truncation is presented to solve the problem of an irrotational, inviscid, incompressible and steady flow over a two-dimensional trapezoidal obstacle, with obstacle height W, lying on the bottom of the running stream. The suggested numerical method for the solution of the fully nonlinear problem is presented for which the flow is super-critical both upstream and downstream. It is found that solutions exist for symmetric trapezoidal for arbitrary size. The results are plotted for different trapezoidal shapes and different values of Froude number F > 1. The effect of the Froude number, the bottom height and the shape of the bottom are discussed.