A fundamental equation for describing the rate of bedrock erosion by sediment‐laden fluid flows in fluvial, coastal, and aeolian environments

Abstract

A major physical process shaping bedrock landforms in fluvial, coastal, and aeolian environments is abrasion by sediment‐carrying fluid flows. A unifying formula to describe the rate of abrasion occurring in these environments has not been presented, the exploration of which is the purpose of this study. Considering the threshold concept the formulation is made including erosivity of fluid flows and erodibility of bedrock. The formula is described as dΓ/dt = C [(FA/FR) – 1], where Γ is the amount of erosion, i.e. eroded length (distance), volume, mass, or weight, t is the time, dΓ/dt is the erosion rate, FA (= A x [fluid force]) is the assailing force of sediment‐laden fluid flows used as an index of the flow erosivity, FR (= B x [bedrock strength]) is the resisting force representing the bedrock erodibility, C is a coefficient with the same unit as that of dΓ/dt, and A and B are dimensionless coefficients. The equation is confirmed by existing laboratory abrasion data and its applicability is examined using existing laboratory data of fluvial and aeolian abrasion experiments and field data from a coastal area. Examinations applying fluvial and aeolian abrasion data indicate that the coefficient C is found to represent the amount of sediment working as abrasives in fluid flows and the hardness of sediment relative to bedrock; and A is presented to reflect the particle size of the sediment. The coefficient B is a conversion factor from conventional mechanical strength of rocks to the resisting force. Selecting appropriate physical quantities for FA and FR enables the application of this equation to abrasion studies on various landforms in these environments. © 2018 John Wiley & Sons, Ltd.

Seeking the Shore: Evidence for Active Submarine Canyon Head Incision Due to Coarse Sediment Supply and Focusing of Wave Energy

“…Findings from Delgada Canyon may help explain these phenomena by showing that coarse sediment supply and wave focusing by submarine bathymetry work in concert to promote canyon incision and maintain littoral connectivity. The effectiveness of this mechanism is likely strongly modulated by the grain size and supply of clastic detritus in the system Lamb et al, 2015;Sunamura, 2018), which is ultimately related to tectonic uplift and the presence of durable bedrock lithologies (Smith et al, 2017). We propose that high littoral sediment supply and canyon focusing of waves make canyons seek the shore (Figure 3b).…”

“…Shepard and Emery (1941) noted that the largest submarine canyons offshore California are clustered around three mountainous coastal promontories (cf. The effectiveness of this mechanism is likely strongly modulated by the grain size and supply of clastic detritus in the system Lamb et al, 2015;Sunamura, 2018), which is ultimately related to tectonic uplift and the presence of durable bedrock lithologies (Smith et al, 2017). Several classifications have been proposed for submarine canyon littoral connectivity (Romans et al, 2016;Sweet & Blum, 2016); however, no single mechanism has been identified to explain why a select group have avoided being disconnected during post-LGM sea level rise.…”

A model for wave abrasion on underwater bedrock, with an application to rapidly downwearing tephra cones adjacent to Surtsey Island in Iceland

“…(4) the relative hardness of sediment to bedrock. Sunamura (2018) examined quantitative relationships between abrasion rate and these factors using existing data (mostly laboratory-based). Robinson (1977) had already appreciated from his field study on the northeast Yorkshire coast that sediment grain size and the thickness of a sediment layer on bedrock are key determinants for the rate of abrasion.…”

Wave-driven geomorphology of Pacific carbonate coastlines: from landscape to wavelength scale

“…Despite the prevalence of wave-driven abrasion along coasts worldwide, few studies have measured the dependence of the erosional process on wave characteristics and sediment availability. Wave tank experiments have shown that abrasion of coastal cliff faces, which can produce cliff retreat rates of up to 1 m yr −1 (Sunamura, 2018), is modulated by the presence and width of a beach at the base of the cliff (Sunamura, 1976). Numerical modeling suggests that beach sediment can also induce morphological feedbacks responsible for the evolution of headlands and embayments on rocky coastlines (Limber and Murray, 2014).…”