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

TL;DR

The paper tackles how an oscillatory boundary layer interacts with a mobile sediment bed, addressing the two-way coupling between flow and bed dynamics. It employs Euler–Lagrange simulations with volume-filtered Navier–Stokes and Maxey–Riley particle dynamics, including drag, added mass, lift, and soft-sphere collisions, under harmonic forcing with $KC$ in the hundreds and $Ga$ fixed, across $Re_\delta=200$–800. The main findings show that bed permeability alone thickens the boundary layer and induces interfacial slip at all $Re_\delta$, while increasing $Re_\delta$ transitions the bed from static to rolling ripples at 400 and to a suspended layer at 800, with substantial enhancements in velocity fluctuations and reductions in bed-shear stress compared to single-phase estimates. The results illuminate bedform development and sediment transport under oscillatory forcing, offering a computationally efficient framework that aligns with PR–DNS and experiments and is suitable for exploring coastal sediment dynamics at large scales.

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 $\mathrm{Re}_δ= 200$, 400, and 800, density ratio $ρ_p/ρ_f = 2.65$, 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 $\mathrm{Re}_δ= 400$ and $\mathrm{Re}_δ= 800$. While at $\mathrm{Re}_δ= 200$ 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 $\mathrm{Re}_δ$, the particles become mobile, which leads to rolling-grain ripples at $\mathrm{Re}_δ= 400$ and suspended sediment at $\mathrm{Re}_δ= 800$. 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.

Figures (19)

• Figure 1: Schematic of the configuration with a bottom sediment bed. The latter is generated in precursor runs where the particles are seeded towards the middle of the domain and allowed to settle on the bottom boundary.
• Figure 2: The particle bed is initialized by letting particles settle onto the bottom wall. (a) This procedure results in a volume fraction profile that is consistent with that of a poured bed. (b,c) The isosurface $\alpha_p=0.2$ represents a good indicator of the location of the bed-fluid interface.
• Figure 3: Zoomed-in view of the instantaneous spanwise vorticity and bed-fluid interface (solid line) at $\Rey_{\delta}=200$. Small ripples in the bedform cause flow disturbances and fluctuations associated with the disturbed laminar regime.
• Figure 4: Zoomed-in view of the instantaneous spanwise vorticity and bed-fluid interface (solid line) at $\Rey_{\delta}=400$. Increasing Reynolds number leads to greater flow disturbances and dynamically-evolving bed-fluid interface.
• Figure 5: Zoomed-in view of the instantaneous spanwise vorticity and bed-fluid interface (solid line) at $\Rey_{\delta}=800$. The bedform shifts into ripples at various phases. The shedding vortices create a large range of scales. The eddies penetrate the bed interface.