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 ${\textit{Re}}_\delta = 200$ , 400 and 800, density ratio $\rho _{\!p}/\rho _{\!f} = 2.65$ , Galileo number ${\textit{Ga}} = 51.9$ , 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 ${\textit{Re}}_\delta = 400$ and ${\textit{Re}}_\delta = 800$ . While at ${\textit{Re}}_\delta = 200$ 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 ${\textit{Re}}_\delta$ , the particles become mobile, which leads to rolling-grain ripples at ${\textit{Re}}_\delta = 400$ and suspended sediment at ${\textit{Re}}_\delta = 800$ . 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.