Plunging Flow into a Reservoir: Theory

The flow considered herein is a two‐dimensional negatively buoyant flow from a shallow channel over a sloping bottom (mild or steep) into a well‐mixed reservoir. For the analysis, a set of integral equations, in particular the equations of conservation of mass and volume, and the momentum equation, are employed. This study is concerned with the analysis of the plunging phenomenon and is directed towards prediction of the depth at the plunge point in terms of the essential independent parameters governing the problem. These predictions include the inflow densimetric Froude number, FD, the initial mixing rate, γ, the bed slope, S, and the total friction coefficient, ft. The equations for plunging depth presented in this study agree well with available laboratory and field data.