Dense underflow into a lake or reservoir—Sub-critical flow.

Steady two-dimensional flow of a dense stream down a slight embankment into a lake or a reservoir is considered. The inflowing water is separated from the ambient lake water by a density interface. This work follows on from earlier work in which the flows down a steep incline with a relatively high flow rate were considered. Here, the flow is slow and the entry angle is small, resulting in waves on the interface. The fluid is assumed to be of finite depth and the incoming channel makes an angle α to the horizontal. Limiting flows are found when the fluid separates at a stagnation point or alternatively when the waves reach maximum steepness. The regions in parameter space where such solutions are obtained are delineated for different flow conditions.