The dilution of a jet-like flow from a shallow channel over a sloping bottom into standing water has been simulated. This geometry approximates the flow of a tributary into a lake/reservoir or bay. The integral jet flow analysis includes similarity hypotheses for transverse (Gaussian) and vertical (power law) velocity profiles. Especially, this integral jet model also includes the flow development region and momentum reductions by bottom and side-wall friction, which were ignored in most previous integral models. It is assumed that the inflow and the ambient (receiving) water have different densities, although only negatively buoyant (sinking) inflows are considered herein. The "plunging" point of these inflows is determined by a critical densimetric Froude number, and the width, depth and volumetric flow rate of the inflow are determined at that location. These characteristics can serve as inflow boundary conditions for lake/reservoir water quality or sediment transport models including density currents. The model predictions are validated against laboratory data and one set of field data. When the integral model is applied to laboratory flow conditions with small channel aspect ratio AR_O, it does not need to include the flow development region, while for field conditions with larger channel aspect ratio, it has to include the flow development region. For slopes steeper than 0.5° (slope of 0.0087), maximum dilution at plunging was found as a function of inflow densimetric Froude number F_O, channel aspect ratio AR_O and bed friction coefficient c_f.
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