The brink of a river (or brink of a waterfall) is the exact lip or edge where the river's bed abruptly drops vertically or near-vertically. It is the precise geometric line where:
The brink is a dynamic erosion zone. The turbulence and hydraulic action at the lip undercut the resistant caprock (often sandstone, limestone, or basalt), causing it to fracture and collapse. This causes the waterfall to migrate upstream over geological time, deepening the canyon. Niagara Falls has retreated ~11 km (7 miles) in 12,500 years.
In hydraulics engineering, "brink" also refers to the control section of a weir or spillway where flow passes through critical depth. In river morphology, a nickpoint or knickpoint is a sudden change in channel gradient—the brink is the most dramatic expression of this.