Discontinuous solutions of the “shallow water” equations for flow over a bottom step

Flows over a depth discontinuity (bottom step) are studied within the framework of a single-layer “shallow water” model. Emphasis is given to substantiation of the relations for the stationary discontinuity thus formed. Admissible stable flows over this discontinuity are distinguished. As an example, the paper gives a solution of the problem of the water flow resulting from dam failure above a bottom step over which water is flowing.