Approximate predictions of gravity flows over irregular topography for large Froude number

Abstract

Approximate predictions are reported for two-dimensional, steady, incompressible flows over backward-facing bottom, of small slope, at high Froude number. Schwartz-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 are used as a basis for the approximate solution of the problem for large Froude number, and small slope of the bottom. General equations, in integral form, for any order of approximation are obtained. Solution up to first-order approximation is discussed and illustrated.