Efficient numerical model for vortex and sediment motions above ripples beneath wave and current

Vortex structure development and sediment motion above ripples play an important role in coastal landforms under the coupled action of waves and currents. An efficient single-phase model for sediment transport is developed to study the vortex and suspended sediment motions above ripples under the combined wave-current conditions. To minimize computational cost while ensuring accuracy, the model incorporates (1) the effects of acceleration and asymmetric boundary layer from nonlinear waves in the bottom sediment boundary condition, as well as mass conservation and phase-lag of sediment, (2) sediment inertia and wake flow around sediment in the suspended sediment motion equation. Results quantify periodic variations in flow velocity, vortex structure (center, size, and strength), and sediment motion, illustrating inherent differences among current-only, wave-only, and wave-current conditions. The results perform (1) an increase in turbulent viscosity and apparent roughness, along with alterations to the logarithmic profile of current velocity induced by the waves' momentum transfer mechanism, (2) promotion/inhibition of vortex development and generation of net wave boundary layer flow and sediment transport induced by currents, and (3) sediment concentration distribution and peak value within a wave period. This model provides an efficient numerical tool for simulating ripple dynamics under wave and current conditions, providing scientific guidance for coastal and ocean engineering projects.