Parameterizing Particle Dispersion in a Granular Bed Mobilized by Oscillatory Flow

Oscillatory bottom flows induced by surface waves produce a time-dependent transport of bottom sediments that consists of two main phases. As sediments are mobilized by the accelerating flow, grain-grain interactions result in an upward dispersion of the surface sediments. When fluid velocity slows, collisions become more infrequent and the particles fall back to the bed as a result of settling. At any given time, the net vertical flux of sediment is a combination of the collision-driven vertical flux and the settling flux of the particles. While the process of settling is well studied and modeled by empirical relationships, there has been significantly less attention to modeling the dispersion process. Here we use discrete element method (DEM) simulations of unimodal sediments in oscillating sawtooth waves to develop an empirical model of the dispersive flux. We posit that the dispersive flux can be modeled using Fick’s Law with a diffusivity that will scale with the energy of the particles and by extension the free stream velocity. The time-dependent diffusivity is determined by regressing the flux against the concentration gradient in the DEM simulations and expressed as a function of the freestream velocity. The Fick’s law diffusivities are then compared to particle dispersion rates using analysis of Lagrangian particle motion through all phases of the oscillating waves which are used to both validate the diffusion term model and to characterize the horizontal and vertical spread of particles under different forcing conditions. This vertical diffusive flux model is then used to reproduce the DEM simulations, showing that the parameterization of the diffusion accurately predicts the changes in concentration through the wave cycle. The diffusive rates are compared with known empirical sediment transport predictions.