Controls on Erosion and Cyclic Step-Formation Upstream of Waterfalls

Abstract

Waterfall retreat transmits base-level perturbations upstream, thereby providing markers of changing climate and tectonics. In homogeneous rock, waterfalls often retreat either by direct waterfall-face erosion or incision from repeating ('cyclic') steps formed above waterfalls. We lack knowledge on the conditions driving these different erosion styles, limiting our ability to predict waterfall retreat. We address this knowledge gap through flume experiments assessing how changing flow hydraulics modulates bedrock erosion. We show that, under large discharges, changes in flow hydraulics cause spatial variability in particle impact velocity, leading to cyclic step formation. As discharge decreases, both the magnitude and spatial variability of particle impact velocity decreases, causing more uniform erosion, limiting cyclic step development and potentially allowing direct erosion of the waterfall face to become the dominant retreat mechanism. These results suggest climate change and water-resource management can alter the rate and style of waterfall retreat.

Keywords: bedrock; cyclic steps; erosion; waterfall.

Figure 1

Run A1 (a) side view and (b) bedrock‐bed longitudinal profiles.

Figure 2

Run B1 flow hydraulics. (a) Horizontal component of time‐averaged flow velocity, white lines represent the water and fixed‐bed surface, white dots are resin particles. The pink circle shows a local reduction in near‐surface flow velocity relative to deeper flow. (b) Water surface profile (measured from 20 images showing temporal variability). (c) Vertical component of flow velocity. Top plot shows all data and bottom plot shows zoom in; the dashed line is the mean vertical component of flow velocity (2.0 mm/s) measured from 10 to 120 mm.

Figure 3

Run B1 particle impacts. (a) Mean impact rate ($I_r$) averaged over 1,518 impacts, (b) mean vertical particle‐impact velocity ($w_i$), (c) the product $I_r{w}_i^2$ and (d) the quantity $I_r{(w}_i^2-w_{ic}^2)$ where $w_{ic}$ is the estimated threshold impact velocity for bedrock erosion. Dashed lines in (a), (b) and (c) are spatial means measured in (a) from 0 to 120 mm (1.01 impacts per second), and in (b) and (c) measured from 10 to 120 mm (mean impact velocity of 29.9 mm/s and mean I _r w _i ² of 902.6 mm²/s³ in b and c, respectively). Panels (b), (c), and (d) show all data (top plots) and zoom in (bottom plots).

Figure 4

Particle impacts in Runs B1–B3. (a) Spatial distribution of the vertical particle impact velocity, w _i , with arrows denoting the spatial location of maximum impact velocity for each Run. Arrows denote the maximum impact velocity between 20 and 120 mm upstream of the waterfall. (b) The effective impact velocity ${(w}_i^2-w_{ic}^2)$. In both panels top plots show all data, bottom plots show zoom in. Dashed lines in bottom plot of panel (a) are the mean impact velocity from 10 to 120 mm for Runs B1–B3.