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

Abstract

Wave abrasion is a major erosional process shaping shallow-water coastal bedrock morphologies. In spite of various erosion studies having been conducted on underwater bedrock features, modelling research for wave-induced abrasion is limited.Based on an existing formula for bedrock abrasion by fluid flows, this study obtains a predictive equation for the rate of wave abrasion, which is given by a function of a shear stress of wave-induced, oscillatory bottom flow and the resistivity of bedrock. A model is derived from this equation to describe temporal change in abrasion depth of subaqueous bedrock. The model is applied to rapidly abrading summits of two submarine tephra cones, J olnir and Syrtlingur, both residing adjacent to the Surtsey volcanic island in Iceland. Nearly horizontal platforms develop as a result of abrasion. J olnir is a site exposed to storm-wave attack, while Syrtlingur is a sheltered site. The modelling based on design storm waves is found to well describe temporal change in erosion depth in the middle to late stage of the platform evolution at the two sites. The result of model calculations indicates that: (1) deep-water wave energy of waves causing abrasion at Syrtlingur is 33% that of waves responsible for abrasion at J olnir; (2) the efficacy of abrasion occurring at Syrtlingur is about four times higher than that at J olnir; and (3) the wave base (i.e. the maximum water depth for bedrock erosion) is 51.5 m for J olnir and 34.4 m for Syrtlingur.

Initial shape reconstruction of a volcanic island as a tool for quantifying long-term coastal erosion: the case of Corvo Island (Azores)

“…As they approach the coast, the waves conserve their energy until they break. From this point on, the energy of the swell is dissipated: one aspect of this dissipation is erosion of the bedrock to about 10 m below sea level (Dietz and Menard, 1951;Trenhaile, 2000Trenhaile, , 2001Sunamura, 2021). The erosional feature formed during the present-day sea level by wave action therefore has a theoretical depth ranging from around 0 m at the coast to about 10 m at the edge, and it is called a shore platform.…”

Testing the equations for wave attenuation over shore platforms

“…Numerical modelling has been used to study how coastal cliffs comprising rock or consolidated sediment evolve over geological timescales (Trenhaile, 2002;Walkden and Hall, 2005;Castedo et al, 2012;Matsumoto et al, 2022). The heights of waves as they approach sea cliffs dictate the forces that they exert at the base of each cliff and thus long-term erosion rates (Trenhaile, 2009), as well as abrasion of the rock platform surface created by cliff retreat (Sunamura, 2021). Although complicated by effects of glacial-interglacial sea-level variation, these models typically show that a negative feedback develops, in which coastline retreat leads to a wider shallow rock platform, which attenuates waves and thus slows down further retreat (Sunamura, 1978;Trenhaile, 2000Trenhaile, , 2001Quartau et al, 2010).…”