The Maxey-Riley-Gatignol equations for macroplastics in the North West European Shelf region

Abstract. Floating macroplastics in the ocean have a finite size and density lower than the water in which they are drifting. Due to their inertia, they do not perfectly follow the ocean currents, and their motion might be better described by the Maxey-Riley-Gatignol equations. In this work, we tailor these equations to simulate fully submerged buoyant macroplastics moving in 2D in the North West European shelf Region, where the flow is highly variable in space and time. We implement the Maxey-Riley-Gatignol equations in the Lagrangian simulation framework Parcels. For macroplastics in the North West European shelf we need a particle Reynolds number dependent drag force as we find particle Reynolds numbers of order 100 and thus beyond the Stokes regime. We show that for these higher particle Reynolds numbers, we can ignore the history force and use the slow manifold Maxey-Riley-Gatignol equations. Using these equations to study the trajectories of buoyant macroplastics in the North West European shelf, we find that higher particle Reynolds numbers make the macroplastic trajectories more similar to tracer particles. The difference between tracer particles and macroplastic particles advected with the Maxey-Riley-Gatignol equations is mainly caused by the forcing associated with the Coriolis effect, whereas the forcing associated with the gradients in the velocity field has only a minor effect. This work is a first step towards including inertial effects in Lagrangian simulations of macroplastics in coastal regions with highly varying velocity fields.