Flow in a waterfall with large Froude number (Q1334753)

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in the free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz-Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half- plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated.