Approximate solution of a flow over a ramp for large Froude number

摘要

An approximate method is presented to solve the problem of steady free-surface flow of an ideal fluid over a semi-infinite ramp in the bottom. Schwartz-Christoffel transformation is used to map the region of flow, 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 inclination angle of the ramp. General equations, in integral form, for any order of approximation are obtained. Solution up to first-order approximation is discussed and illustrated.Elevation of the free-surface for different ramp heights, different inclination angles of the ramp and different Froude numbers are plotted. An approximate formula of maximum elevation of the free-surface in terms of the ramp heights and its inclination angle is found.