The increased Stokes drift of inertial, finite-size floating plastic

Ross Calvert1, Colin Whittaker2, Alison Raby3, Alistair G. L. Borthwick4, Mark L McAllister1 and Ton van den Bremer5, (1)University of Oxford, Oxford, United Kingdom, (2)University of Auckland, Civil and Environmental Engineering, Auckland, New Zealand, (3)Plymouth University, School of Engineering, Computing and Mathematics, Plymouth, United Kingdom, (4)University of Edinburgh, Edinburgh, United Kingdom, (5)University of Edinburgh, School of Engineering, Edinburgh, United Kingdom
This theoretical and experimental study examines the transport of inertial, finite-size floating plastic under the influence of waves. Periodic water waves generate Stokes drift, as manifested by the Lagrangian orbits under the surface not fully closing. Stokes drift can contribute to the transport of floating pollutants in the ocean, including plastic. Floating plastics have a large range of sizes and densities, which potentially results in different rates of transport by the waves. Previously, all pollutants have been considered to be perfect Lagrangian tracers, thus having the same transport as the Stokes drift of the waves. However, when particle inertia and variable submergence is taken into account, we show that different particles are transported at different rates depending on their size and density. The study is in four parts. First, we report on new laboratory wave flume experiments with floating plastic spheres in periodic waves, which generally show enhanced transport for finite-size particles. Second, we show that numerical solutions of the relevant equation of motion can replicate these experimental results. Third, we use a perturbation expansion in wave steepness to derive a simple equation for the transport of inertial, finite-size floating plastic as a function of non-dimensional numbers dependent on particle dimension and density and the properties of the wave. Finally, we estimate the change in wave-induced transport due to including inertial effects for realistic sizes and densities of plastic found in the ocean and realistic sea states.