Unsteady Ekman-Stokes Dynamics: Implications for Surface Wave-Induced Drift of Floating Marine Litter

We examine Stokes drift and wave-induced transport of floating marine litter on the surface of a rotating ocean with a turbulent mixed layer. Due to Coriolis-Stokes forcing and surface wave stress, a second-order Eulerian-mean flow forms, which must be added to the Stokes drift to obtain the correct wave-induced Lagrangian velocity. We show that this wave-driven Eulerian-mean flow can be expressed as a convolution between the unsteady Stokes drift and an "Ekman-Stokes kernel." Using this convolution, we calculate the unsteady wave-driven contribution to particle transport. We report significant differences in both direction and magnitude of transport when the Eulerian-mean Ekman-Stokes velocity is included.