Dynamics of an oscillatory boundary layer over a sediment bed

Abstract: 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 $2.79 \times 10^{-2}$ to $4.40 \times 10^{-2}$, 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 sheet flow at $\mathrm{Re}\delta = 800$. 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 and reduction of the bed shear stress by 38%. 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. In addition, greater flow intrusion causes the bed shear stress to decrease by 54% at $\mathrm{Re}\delta = 400$and 79% at $\mathrm{Re}_\delta = 800$, compared to the flow over a smooth and impermeable wall.