Dependence of dilution of a plunging discharge over a sloping bottom on inflow conditions and bottom friction

Abstract

A tributary flowing into a reservoir or lake is nearly always at a density different from the receiving surface water. The difference is due to temperature, dissolved and suspended materials. An understanding of density current phenomena is therefore essential to lake or reservoir water quality modeling. In this study the dependence of plunging characteristics (dilution, depth and location at plunging) on inflow conditions (densimetric Froude number and channel aspect ratio) and bottom friction is quantified by an integral jet model. The jet-like flow from a shallow channel over a sloping bottom into standing water was studied as an approximation of the flow of a tributary into a lake or reservoir. The integral jet flow analysis used similarity hypotheses for transverse (Gaussian) and vertical (power law) velocity profiles. The model especially includes momentum reductions by bottom and side wall friction and a flow development region, which were not addressed in other previous studies, and were found to have a significant effect on dilution characteristics. Depth and volumetric flow rate of the inflow were determined at the “plunge” point of negatively buoyant (sinking) inflows which in turn is characterized by a critical densimetric Froude number. These characteristics can serve as inflow boundary conditions for lake water quality or sediment transport models in reservoirs including density currents. The model predictions were validated against laboratory data and one set of field data. For slopes steeper than 0.5°, dilution at plunging (Q_P/Q₀) was found to increase linearly with inflow densimetric Froude number F₀. Dilution is sensitive to the bed friction coefficient ct and the channel aspect ratio AR₀, but insensitive to the bottom slope. Maximum dilution at plunging is given as a function of F₀ and (AR₀ c_f).