Amplified Erosion above Waterfalls and Oversteepened Bedrock Reaches

Although waterfalls are abundant along steep bedrock channels, none of the conventional erosion laws can predict incision at the lip of a waterfall where flow is non-uniform and bed slope can be vertical. Considering the expected increase in flow velocity and shear stress at the lip of a vertical waterfall we determine erosion amplification at a waterfall lip as: Elip/Enormal= (1+0.4/Fr2)3n, where Fr is the Froude number and n ranges between 0.5-1.7. This amplification expression suggests that erosion at the lip could be as much as 2-5 times higher than normally expected in a setting with identical hydraulic geometry. It also demonstrates that a freefall is expected to amplify upstream incision rates even when the flow approaching the waterfall is highly supercritical. Utilizing this erosion amplification expression in numerical simulations in conjunction with a standard detachment-limited incision model we demonstrate its impact on reach-scale morphology above waterfalls. These simulations indicate that amplified erosion at the lip of a waterfall can trigger the formation of an oversteepened reach whose length is longer than the flow acceleration zone, provided incision velocity (Vi) at the edge of the flow acceleration zone is higher than the retreat velocity of the waterfall face. Such an oversteepened reach is expected to be more pronounced when Vi increases with increasing slope. The simulations also suggest that oversteepening can eventually lead to quasi steady-state gradients upstream from a waterfall provided Vi decreases with increasing slope. Flow acceleration above waterfalls can thus account, at least partially, for oversteepened bedrock reaches that are prevalent above waterfalls. Such reaches have been reported for the escarpments of southeast Australia, western Dead Sea, and at Niagara Falls. Using the cosmogenic isotope 36Cl we demonstrate that Vi upstream of a waterfall at the Dead Sea western escarpment is high enough for freefall-induced oversteepening to be feasible.