Author(s): Richard A. Denton

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Abstract: One method for obtaining solutions for single- and multi-layer flow over bottom humps and through sidewall contractions is to consider the variation in mechanical energy with layer thickness at key cross-sections. However, previous models of gradually-varying multi-layer flow have been restricted to flows which remain subcritical with respect to all but the slowest internal wave speed. This paper shows how the energy extrema method can be used over the full range of flow conditions; from subcritical with respect to all internal wave speeds to supercritical with respect to the free surface wave. The complete energy curves for three-layer flow are found to have up to seven different energy extrema at a given cross-section. The energy extrema are classified according to whether the flow is critical with respect to the first- or second-mode internal wave or the free-surface wave, whether the energy is a local maximum or minimum, and which layers are active. Froude numbers based on the actual wave speeds are used to determine whether the flow at a given cross-section is subcritical, critical or supercritical with respect to each of the three possible wave modes. All seven energy extrema represent possible energy conditions at a hydraulic control. Which energy extrema are applicable for a particular three-layer flow depends on the obstruction geometry and the upstream and downstream boundary conditions.

DOI: https://doi.org/10.1080/00221688909499114

Year: 1989