Estimates of Lagrangian transport by surface gravity wave groups: The effects of finite depth and directionality

Two physical phenomena drive the Lagrangian trajectories of neutrally buoyant particles underneath surface gravity wave groups: the Stokes drift results in a net displacement of particles in the direction of propagation of the group, whereas the Eulerian return flow transports such particles in the opposite direction. Generally, the Stokes drift is the larger of the two near the surface, whereas the effects of the return flow dominate at depth. A transition depth can be defined that separates the two regimes. Using a multiple-scales expansion, we provide leading-order estimates of the forward transport, the backward transport, and the transition depth for realistic sea states. We consider the effects of both finite depth and the directionally spread nature of the waves on our estimates. We show that from the perspective of the return flow, almost all seas are of finite depth. In fact, many seas can be shown to be "shallow" from the perspective of the return flow with little variation of this flow with depth. Furthermore, even small degrees of directional spreading can considerably reduce the magnitude of the return flow and its transport.