Negatively Buoyant Flow in Diverging Channel. III: Onset of Underflow

If they are negatively buoyant (denser than ambient water), inflows to lakes and reservoirs sink (plunge) below the water surface after entering. The location of the plunge line or maximum penetration into the lake or reservoir is related to the ratio of inertial to buoyant forces, and lake or reservoir geometry. Experiments have been conducted in diverging horizontal laboratory channels, and the plunging phenomenon has been reproduced. For flows separating from the channel wall the relationship $x_p/B_0=0.52F_0^4$ has been found to describe the maximum horizontal penetration $x_p\text{.}$ The basic form and exponent of this relation was developed from jet flow theory, and the coefficient was experimentally determined. $F_0$ is the inflow densimetric Froude number and $B_0$ is the inflow channel width. Experimental data for $x_p/B_0$ are also reported for attached flows. In this case the distance to plunging can be expressed as $x_p/B_0==(0.74F_0-0.5)(\tan \delta {)}^{-1}\text{.}$