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.