Understanding gravel beach formation: Tracking waves and wave-bed dynamics through experiments and simulations

Coasts all over the globe are subjected to enhanced erosion as a result of rising sea levels and negative effects of engineering work. In an effort to further understand the processes and timescales of the underlying mechanisms that drive beach formation and erosion, a vertical Hele-Shaw cell, representing a `slice' of gravel beach, was introduced [90]. Within this set-up, wave-sloshing and beach formation can be observed in a matter of seconds to minutes rather than months to decades. An image-analysis algorithm was developed with the aim of translating images from the experiment into useful data. Its core operation is based on a colour-channel-detection method that can detect and export the depth and area occupied by the water and the moving bottom topography in the tank over time. The simple and easy-to-use algorithm has been tested successfully against a variety of experiments involving water and water-beds, with its novelty being the precise tracking of water infiltrating the moving bed. The acquired wave-only data were imposed as the boundary conditions during the validation process of a shallow-water and a potential-flow shallow-water model, discretised using a one-dimensional finite-volume/Godunov method and a second-order finite-element method respectively [47, 42]. It was found that the finite-volume method handles steep waves of higher amplitudes better than the finite-element method. The tracking results were further analysed with plunging, collapsing and surging breakers present in the examined water-bed cases. It was also found that lower wave frequency cases lead to faster beach formation, with the angles of repose of the corresponding final bed profiles being in the same range as those for real-life gravel beaches [4], confirming the gravel-like nature of the beach present in the Hele-Shaw cell.