We investigate and model the initiation of motion of a single particle on a structured substrate within an oscillatory boundary layer flow, following a mechanistic approach. By deterministically relating forces and torques acting on the particle to the instantaneous ambient flow, the effects of flow unsteadiness are captured, revealing rich particle dynamics. Laboratory experiments in an oscillatory flow tunnel characterise the initiation and early stages of motion, with particle imaging velocimetry measurements yielding the flow conditions at the motion threshold. The experiments validate and complement results from particle-resolved direct numerical simulations, combining an immersed boundary method with a discrete element method that incorporates a static friction contact model. Within the parameter range just above the motion threshold, the mobile particle rolls without sliding over the substrate, indicating that motion initiation is governed by an unbalanced torque rather than a force. Both experimental and numerical results show excellent agreement with an analytical torque balance including hydrodynamic torque derived from the theoretical Stokes velocity profile, and contributions of lift, added mass and externally imposed pressure gradient. In addition to static and rolling particle states, we identify a wiggling regime where the particle moves but does not leave its original pocket. Our deterministic approach enables prediction of the phase within the oscillation cycle at which the particle starts moving, without relying on empirical threshold estimates, and can be extended to a wide range of flow and substrate conditions, as long as turbulence is absent and interactions with other mobile particles are negligible.

Waves transport particles in the direction of wave propagation with the Stokes drift. When the Earth’s rotation is accounted for, waves induce an additional (Eulerian-mean) current that reduces drift and is known as the anti-Stokes drift. This effect is often ignored in oceanic particle-tracking simulations, despite being important. Although different theoretical models exist, they have not been validated by experiments. We conduct laboratory experiments studying the surface drift induced by deep-water waves in a purpose-built rotating wave flume. With rotation, the Lagrangian-mean drift deflects to the right (counterclockwise rotation) and reduces in magnitude. Compared with two existing steady theoretical models, measured drift speed follows a similar trend with wave Ekman number but is larger. The difference is largely explained by unsteadiness on inertial time scales. Our results emphasise the importance of considering unsteadiness when predicting and analysing the transport of floating material by waves.

The alignment of a pair of spherical particles perpendicular to a horizontally oscillating flow is attributed to a non-zero residual flow, known as steady streaming. This phenomenon is the basis of complex patterns in denser systems, such as particle chains and the initial stages of rolling-grain ripples. Previous studies on such self-organization processes used two distinct systems: an oscillating box filled with viscous fluid and an oscillating channel flow, where the fluid oscillates relative to the bottom boundary. In this paper, we show that particle pair dynamics in these two systems are fundamentally different, due to the presence of a Stokes boundary layer above the bottom in the oscillating channel flow. The results are obtained from direct numerical simulations in which the dynamics of a pair of particles are simulated using an immersed boundary method. The oscillating box and the oscillating channel flow are only equivalent in a limited region of the parameter space, where both the normalized Stokes boundary layer thickness and the normalized relative particle excursion length are small. Overall, the particle dynamics in the oscillating channel flow, compared to the oscillating box, are governed by an additional dimensionless parameter, that is, the particle–fluid density ratio.

When two spherical particles submerged in a viscous fluid are subjected to an oscillatory flow, they align themselves perpendicular to the direction of the flow leaving a small gap between them. The formation of this compact structure is attributed to a nonzero residual flow known as steady streaming. We have performed direct numerical simulations of a fully resolved, oscillating flow in which the pair of particles is modeled using an immersed boundary method. Our simulations show that the particles oscillate both parallel and perpendicular to the oscillating flow in elongated figure-8 trajectories. In absence of bottom friction, the mean gap between the particles depends only on the normalized Stokes boundary layer thickness δ∗, and on the normalized, streamwise excursion length of the particles relative to the fluid Ar∗ (equivalent to the Keulegan-Carpenter number). For Ar∗≲1, viscous effects dominate and the mean particle separation only depends on δ∗. For larger Ar∗ values, advection becomes important and the gap widens. Overall, the normalized mean gap between the particles scales as L∗≈3.0δ∗1.5+0.03Ar∗3, which also agrees well with previous experimental results. The two regimes are also observed in the magnitude of the oscillations of the gap perpendicular to the flow, which increases in the viscous regime and decreases in the advective regime. When bottom friction is considered, particle rotation increases and the gap widens. Our results stress the importance of simulating the particle motion with all its degrees of freedom to accurately model the system and reproduce experimental results. The insights of the particle pairs provide an important step towards understanding denser and more complex systems.