A mathematical model for the flow development upstream of the region of air entrainment on a spillway is presented. The model is based on numerical solutions of the time-averaged two-dimensional form of the Navier-Stokes equations. Predictions from the model of mean velocity distributions, boundary layer growth, and water surface profiles are compared with experimental data, both model and prototype. Excellent agreement is obtained. Furthermore, it is shown conclusively that self-aeration in a spillway flow commences at the point where the bed induced turbulence reaches the free surface.
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Keller et al. (1975) studied this question.
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