Mixture theory simulation of vortex sand ripple dynamics

The presence of ripples on the seabed affects the turbulent dynamics of the wave bottom boundary layer (WBBL). The difference in the roughness length scales between a planar and rippled sand beds produces quantifiable differences in the turbulent WBBL that affect wave energy dissipation, coastal circulation, and sediment transport. A complete understanding of the effects of sediment and fluid properties on the turbulent wave bottom boundary layer and small-scale bedform evolution are currently unknown. We implement a three-dimensional bottom boundary layer model (SedMix3D) using mixture theory for highly resolved simulations of the coupled interactions between fluid and sediment in domains up to 32 cm x 24 cm x 16 cm. Mixture theory treats the fluid-sediment mixture as a single continuum with effective properties that parameterize the fluid-sediment and sediment-sediment interactions. The grid spacing is on the order of a sediment grain diameter and simulated flows have maximum free stream velocities between 10 and 120 cm/s and periods between 2 and 4 s. Modeled ripple geometries range from a single ripple to multiple ripples with varying heights, lengths, and steepness. Only non-cohesive sediments (0.02 < d < 0.054 cm) are considered. The model predicts ripple heights and lengths that compare reasonably to an existing ripple predictor formula. SedMix3D also predicts the merging and separation of ripples as they transition from an initial state to an equilibrium state. Comparisons of SedMix3D to laboratory measurements of fluid velocity and sediment concentration over rippled sand beds are in excellent agreement. We compare two-dimensional to three-dimensional simulations to find that the vortex dynamics over sand ripples are highly three-dimensional. Two-dimensional flow simulations are inadequate for the numerical modeling of turbulent flow in the WBBL. We also test the model sensitivity to the parameterizations for effective viscosity, particle pressure, and bulk hindered settling velocity. Finally, we demonstrate the capability of SedMix3D to provide detailed information on the dynamics of complex three-dimensional ripple geometry evolution.