Derivation, Validation, and Numerical Implementation of a Two-Dimensional Boulder Transport Formulation by Coastal Waves

Abstract

Numerical computations for boulder transport have become a state-of-the-art tool for hindcasting the hydraulic processes associated with past storm wave and tsunami events. Since most previously developed two-dimensional formulations cater to boulders with symmetric outlines, they can consequently reproduce the transport distance and the velocity of boulders of cubic shape or similar structured geometries reasonably well. However, the formulations exhibit limitations when applied to rectangular- and flat-shaped boulders. The presently available formulations have difficulties reproducing the variations of frictional drag force due to the changes of the boulders’ contact time with the ground. We have developed an extended boulder transport formulation and derived a new empirical roughness coefficient by considering the shape of boulders that accounts for the changes of the boulders’ contact time with the ground. In comparison to other existing transport formulations, the present method provides superior accuracy of block velocity and transport distance in most cases — especially for boulders of rectangular geometry. Even by neglecting the full three-dimensional processes, numerical computations extended with the proposed boulder transport formulation can help explaining historic wave regimes, which were responsible for the transport of a variety of coastal boulders reported around the world.

A Numerical Modeling Approach for Better Differentiation of Boulders Transported by a Tsunami, Storm, and Storm‐Induced Energetic Infragravity Waves

“…This effect can be considered using the model of Watanabe et al. (2023). The boulder shape controls the boulder transport distance (Oetjen et al., 2020, 2021), and the flatness Index of the boulder is considered a crucial parameter for boulder transport (Oetjen et al., 2021).…”

“…Watanabe et al. (2023) assumed that external forces, including those produced by the current, acting on the boulder are represented by the hydraulic force F m , the frictional force at the bottom F b , and the component of the gravitational force F g along the slope (Noji et al., 1993): $$${\rho }_{\mathrm{s}}V\left({d}^{2}X/d{t}^{2}\right)={F}_{\mathrm{m}}-{F}_{\mathrm{b}}-{F}_{\mathrm{g}},$$$ where ρ s is the density of the boulder, V is the volume of the boulder, and X is the position of the boulder in the x ‐direction. F m represents the sum of the forces of drag and inertia (Noji et al., 1993): $$${F}_{\mathrm{m}}={C}_{\mathrm{d}}\frac{1}{2}{\rho }_{\mathrm{f}}A(U-dX/dt)\vert U-dX/dt\vert +{C}_{\mathrm{m}}{\rho }_{\mathrm{f}}V\left(\frac{dU}{dt}\right)-\left({C}_{\mathrm{m}}-1\right){\rho }_{\mathrm{f}}V\left(\frac{{d}^{2}X}{d{t}^{2}}\right),$$$ where ρ f is the density of the water, U is the flow velocity at the position of the boulder, A is the projected area of the boulder against the current, and C d and C m are coefficients of drag and mass, respectively.…”

“…For boulder transport by tsunami and storm waves, we applied the model developed by Watanabe et al. (2023). Watanabe et al.…”

“…Watanabe et al. (2023) proposed a new empirical friction coefficient μ to represent the decrease in friction force when the boulder velocity increased. In concrete terms, during the sliding phase, a boulder moves, maintaining contact with the bottom.…”

On a ~210 t Caribbean coastal boulder: The huracanolito seaward of the ruins of the Bucanero resort, Juragua, Oriente, Cuba

“…However, even the improved equations have been questioned (e.g., Cox et al, 2018, 2020; Cox et al, 2019; Nandasena et al, 2022; Scicchitano et al, 2020, 2021). More reliable estimates of the wave conditions controlling boulder transport have been proposed, for example, by Imamura et al (2008), Nandasena et al (2013, 2022) and Watanabe et al (2023).…”