Abstract
Particulate matter in the environment, such as sediment, marine debris and plankton, is transported by surface waves. The transport of these inertial particles is different from that of fluid parcels described by Stokes drift. In this study, we consider the transport of negatively buoyant particles that settle in flow induced by surface waves as described by linear wave theory in arbitrary depth. We consider particles that fall under both a linear drag regime in the low Reynolds number limit and in a nonlinear drag regime in the transitional Reynolds number range. Based on an analysis of typical applications, we find that the nonlinear regime is the most widely applicable. From an expansion in the particle Stokes number, we find kinematic expressions for inertial particle motion in waves, and from a multiscale expansion in the dimensionless wave amplitude, we find expressions for the wave-averaged drift velocities. These drift velocities are analogous to Stokes drift and can be used in large-scale models that do not resolve surface waves. We find that the horizontal drift velocity is reduced relative to the Stokes drift of fluid parcels and that the vertical drift velocity is enhanced relative to the particle terminal settling velocity. We also demonstrate that a cloud of settling particles released simultaneously will disperse in the horizontal direction. Finally, we discuss the accuracy of our expressions by comparing against numerical simulations, which show excellent agreement, and against experimental data, which show the same trends.
Highlights
The dynamics of particulate matter in surface gravity waves determine the transport and dispersion of natural particles, such as sediment, ice crystals and plankton, as well as synthetic particles, such as microplastics
From the dynamical equation of inertial spheres in surface waves, we have found a kinematic solution that gives the particle velocity as a function of its position within the background flow field (2.10) and a solution for the particle drift velocity that gives the horizontal and vertical particle motion in the wave-averaged sense (2.12)
Comparisons with numerical simulations of the full dynamical equation show that the solutions accurately predict particle motion up to St = O(1) and ε = O(10−1), suggesting that they are applicable within the confines of linear wave theory even when the particle inertia is significant
Summary
The dynamics of particulate matter in surface gravity waves determine the transport and dispersion of natural particles, such as sediment, ice crystals and plankton, as well as synthetic particles, such as microplastics. The dynamics of most particles in the environment deviate from the tracer limit because of their inertia, stemming from finite size and density difference with the fluid These deviations alter particle transport in surface waves from the classical Stokes drift. If the assumption of small particle Reynolds number is relaxed, the drag force deviates from the Stokes drag law and becomes a nonlinear function of the slip velocity The effects of this nonlinear drag on particle settling have been explored in vertically oscillating fluid columns, which partially mimic the oscillatory flow of surface waves. We find that such particles experience an enhancement in the settling velocity, which stems from a dynamical part related to particle inertia and a kinematic part related to how the particles sample the flow field, akin to a vertical Stokes drift.
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