Dynamics of an oscillatory boundary layer over a sediment bed in Euler-Lagrange simulations

We investigate the dynamics of an oscillatory boundary layer developing over a bed of collisional and freely evolving sediment grains. We perform Euler-Lagrange simulations at Reynolds numbers $\mathrm{Re}_\delta= 200$, 400, and 800, density ratio $\rho_p/\rho_f = 2.65$, Galileo number $\mathrm{Ga} = 51.9$, maximum Shields numbers from $5.60 \times 10^{-2}$ to $2.43 \times 10^{-1}$, based on smooth wall configuration, and Keulegan-Carpenter number from $134.5$ to $538.0$. We show that the dynamics of the oscillatory boundary layer and sediment bed are strongly coupled due to two mechanisms: (I) bed permeability, which leads to flow penetration deep inside the sediment layer, a slip velocity at the bed-fluid interface, and the expansion of the boundary layer, and (II) particle motion, which leads to rolling-grain ripples at $\mathrm{Re}_\delta = 400$ and $\mathrm{Re}_\delta = 800$. While at $\mathrm{Re}_\delta = 200$ the sediment bed remains static during the entire cycle, the permeability of the bed-fluid interface causes a thickening of the boundary layer. With increasing $\mathrm{Re}_\delta$, the particles become mobile, which leads to rolling-grain ripples at $\mathrm{Re}_\delta = 400$ and suspended sediment at $\mathrm{Re}_\delta = 800$. Due to their feedback force on the fluid, the mobile sediment particles cause greater velocity fluctuations in the fluid. Flow penetration causes a progressive alteration of the fluid velocity gradient near the bed interface, which reduces the Shields number based upon bed shear stress.