We investigated quasi-2D sand ripple geometry (i.e., ripple height, ripple wavelength, and ripple asymmetry) on a mound subject to the influence of waves, currents, and combined wave-current flows. The results of this study quantify how ripple geometry is influenced by bed slope and combined wave-current flows. The geometry of the ripples is shown to depend on the combined wave-current flow ratio and the local bed slope. Under wave-only conditions, the wave-driven ripple length and height decreased as a function of depth and local slope. Under combined wave-current conditions, the ripples increased in height and wavelength on the stoss slope of the mound, and decreased on the lee slope of the mound. Existing ripple geometry predictors, developed for combined flows on flat sand beds, were unable to predict ripple geometry on the sloped bed accurately. We propose correction factors for ripple geometry predictors to account for slope effects and combined wave-current flow conditions. Applying the correction factors significantly improves the predictor performance for predicting ripple height, wavelength, and asymmetry on sloping beds.

We investigate pathways of sediment diffusion for a Gaussian-shaped sand mound subjected to monochromatic waves. Our unique results nearly close the sediment budget by quantifying each of the sediment transport processes responsible for mound diffusion associated with sediment flux due to slope driven transport and ripple migration. Downslope ripple progression was observed as ripples formed at the mound top advanced down the side slopes in a direction perpendicular to wave propagation. Once ripples formed on the sides of the mounds the ripples became pathways for sediment flux from the top to the bottom of the mound, persisting even after ripples reached the base of the mound as sediment avalanching due to gravity and mound slope. Lateral ripple migration caused ripples to migrate along the sides of the sand mound in a direction parallel to wave propagation. Once ripples reached the base of the mound, lateral migration of ripples caused spreading of sand around the sides of the mound. Lateral ripple migration was largely driven by ripple splitting caused by a large downslope sediment flux from the center of the mound that generated ripples with longer wavelengths than wave orbital hydrodynamics could support. To restore equilibrium between sediment and flow conditions, ripples with longer wavelengths continuously split and migrated laterally around the mound. Our results reflect the importance of slope driven transport, bed fluidization, and ripple dynamics on the larger scale diffusivity and suggest that slope driven and ripple driven sediment fluxes should be more explicitly included in sediment transport formulations.