Exploring shoreface dynamics and a mechanistic explanation for a morphodynamic depth of closure

Using energetics-based formulations for wave-driven sediment transport, we develop a robust methodology for estimating the morphodynamic evolution of a cross-shore sandy coastal profile. In our approach, wave-driven cross-shore sediment flux depends on three components: two onshore-directed terms (wave asymmetry and wave streaming) and an offshore-directed slope term. In contrast with previous work, which applies shallow water wave assumptions across the transitional zone of the lower shoreface, we use linear Airy wave theory. The cross-shore sediment transport formulation defines a dynamic equilibrium profile and, by perturbing about this steady state profile, we present an advection-diffusion formula for profile evolution. Morphodynamic Peclet analysis suggests that the shoreface is diffusionally dominated. Using this depth-dependent characteristic diffusivity timescale, we distinguish a morphodynamic depth of closure for a given time envelope. Even though wave-driven sediment transport can (and will) occur at depths deeper than this morphodynamic closure depth, the rate of morphologic bed changes in response to shoreline change becomes asymptotically slow. Linear wave theory suggests a shallower shoreface depth of closure and much sharper break in processes than shallow water wave assumptions. Analyzing hindcasted wave data using a weighted frequency-magnitude approach, we determine representative wave conditions for selected sites along the U.S. coastline. Computed equilibrium profiles and depths of closure demonstrate reasonable similarities, except where inheritance is strong. The methodology espoused in this paper can be used to better understand the morphodynamics at the lower shoreface transition with relative ease across a variety of sites and with varied sediment transport equations.