Free-surface flow over a step

Abstract

A transformation technique is used to solve the problem of steady free-surface flow of an ideal fluid over a semi-infinite step in the bottom. Application of the exact free-surface condition results in a nonlinear integro-differential equation for the free-surface angle and solutions of this equation are dependent on step height and Froude number. Linearized solutions, based upon small step height are presented and indicate that the nature of the free surface formed depends on whether the upstream flow is subcritical or supercritical. As the step height is increased, solutions to the exact nonlinear equations are obtained using the predictions of the linear theory, or possibly a previous nonlinear solution, as an initial estimate.