Mathematical modeling of plunging reservoir flows

Flow into and through a reservoir with a sloping bottom is modeled in two dimensions. The inflow is denser than the reservoir water and plunges below the surface to form a density current. The unsteady momentum and continuity equations are formulated in cylindrical coordinates. The standard k-∊ turbulence model is used with an extension to include production or destruction of turbulent kinetic energy by buoyancy forces. The equations are solved numerically. Simulations were carried out for a range of flow conditions and bottom slopes. The numerically generated plunge depths follow the expected basic trend, but the actual plunge depth values are about 20 percent greater than experimentally determined values. Initial entrainment values at plunging were also computed and found to be of the same order of magnitude as measured values.