Memory effects in wave-induced microplastic transport

Abstract

Microplastics are transported by ocean surface waves in ways that depart significantly from the Stokes drift of fluid parcels, and accurate modeling of this transport requires accounting for forces beyond linear drag. Existing modeling of microplastic transport often neglect the Basset-Boussinesq history force, effectively limiting their use to the smallest particle sizes. Here, we extend the applicability of these models by implementing the history term with a multistep integration scheme, allowing us to capture the transport of larger microplastics in linear surface waves of arbitrary depth. We quantify when the Basset-Boussinesq history force significantly affects microplastic transport by surface gravity waves. We show that memory effects become the leading-order horizontal drag once $S=St/\gamma^2$ exceeds a critical value $S\approx 0.25$, where $St$ is the Stokes number and $\gamma$ is the density ratio of the particle and the fluid. The corresponding critical $St$ number is found to be a factor of about three smaller than that given by classical inertial estimates that neglect history effects. These results help provide regime maps that can be used to indicate when history effects can be safely neglected. Our simulations also reveal that history effects significantly increase horizontal transport distances and enhance orbit shearing of particle ensembles.