Incisional cyclic steps of permanent form in mixed bedrock‐alluvial rivers

Abstract

Most bedrock river channels have a relatively thin, discontinuous cover of alluvium and are thus termed mixed bedrock‐alluvial channels. Such channels often show a series of steps formed at relatively regular intervals. This bed form is the bedrock equivalent of cyclic steps formed on beds composed of cohesive soil in gullies. In this paper, we perform a full nonlinear analysis for the case of cyclic steps in mixed bedrock‐alluvial channels to explain the formation of these steps. We employ the shallow water equations in conjunction with equations describing the process of bedrock incision. As a model of bedrock incision, we employ the recently introduced Macro‐Roughness Saltation Abrasion Alluviation model, which allows direct interaction between alluvial and bedrock morphodynamics. The analysis is greatly simplified by making the quasi‐steady assumption that alluvial processes occur much faster than bedrock erosional processes. From our analysis, we obtain the conditions for the formation of cyclic steps in bedrock, as well as the longitudinal profiles of bed elevation, water surface elevation, and areal fraction of alluvial cover. It is found from the analysis that when the sediment supply is small relative to the transport capacity, cyclic steps form only on slopes with very high gradients. The analysis indicates that the shape of a step formed on bedrock is characterized by a relatively short upstream portion with an adverse slope and a long, almost planar downstream portion with a constant slope.

A Mechanistic Model of Waterfall Plunge Pool Erosion into Bedrock

“…While this process has not been investigated in detail, new waterfalls may be created by instabilities such as cyclic steps that can form in the high Froude‐number drawdown zone upstream of waterfall escarpments (Haviv et al, ; Scheingross, ; Yokokawa et al, ). Because cyclic step wavelength is predicted to decrease with reach‐averaged bed slope (Brooks, ; Izumi et al, ), an increase in knickzone relief may also result in knickzones with more closely spaced waterfalls. We explore this scenario by varying knickzone relief while holding knickzone length, waterfall drop height, and all else constant.…”

“…Our results highlight the importance of waterfall internal dynamics (i.e., waterfall spacing, height, and number) in setting knickzone retreat rates by successive, vertically drilling waterfalls (Figure ) and points to a need to develop new theory capable of predicting waterfall formation, spacing, and number (e.g., Izumi et al, ) over landscape evolution timescales. Waterfall spacing and number have the same order of magnitude effect on knickpoint retreat rates within our model as changes in external forcing.…”

Self‐formed waterfall plunge pools in homogeneous rock

“…Keyholes provide a path to flush sediment out of pools enabling continued vertical incision of the pool floor. In turn, new pools might be generated through cyclic-step or steppool morphodynamics in the supercritical drawdown region upstream of the waterfall brink (Figure 2a) [Johnson and Whipple, 2007;Yokokawa et al, 2013;Scheingross, 2016;Izumi et al, 2016].…”

“…Thus, the mechanism of upstream waterfall retreat (i.e., headwall undercutting versus vertical drilling) should depend on the relative rates of lateral and vertical plunge pool erosion, as well as whether lateral erosion is focused on the upstream pool wall leading to headwall retreat or the downstream pool wall leading to sediment evacuation that allows continued vertical incision. Retreat via drilling also requires a mechanism to continually generate new waterfalls in the high Froude number, drawdown region at the upstream end of the escarpment [ Lamb et al ., ] (Figure a), which might occur by morphodynamic instabilities similar to cyclic steps [ Brooks , ; Johnson and Whipple , ; Yokokawa et al ., ; Izumi et al , ].…”

Alluvial cover on bedrock channels: applicability of existing models

“…As sediment availability increases, the sediment starts settling down on the river bed providing a cover for the bed underneath from further erosion, which is known as the cover effect. In the last 20 yr, various field-scale (Turowski et al, 2008b;Turowski and Rickenmann, 2009;Jansen et al, 2011;Hobley et al, 2011;Cook et al, 2013;Inoue et al, 2014;Beer and Turowski, 2015;Beer et al, 2017), laboratory-scale (Sklar and Dietrich, 2001;Chatanantavet and Parker, 2008;Finnegan et al, 2007;Johnson andWhipple, 2007, 2010;Hodge and Hoey, 2016a, b;Hodge et al, 2016;Turowski and Bloem, 2016;Inoue et al, 2017b, Mishra et al, 2018Fernandez et al, 2019;Inoue and Nelson, 2020), and theoretical and numerical studies (Hancock and Anderson, 2002;Dietrich, 2004, 2006;Lague, 2010;Seminara, 2011, 2012;Johnson, 2014;Nelson et al, 2014;Zhang et al, 2015;Inoue et al, 2016Inoue et al, , 2017aTurowski and Hodge, 2017;Turowski, 2018) have been performed to reveal the effects of tools and cover on bedrock erosion and erosional morphology.…”