The Lagrangian mass transport in the Stokes progressive edge wave is obtained from the vertically integrated equations of momentum and mass, correct to second order in wave steepness. The cross-shore momentum balance is between the mean pressure at the sloping bottom, the radiation stress, and the pressure gradient due to the mean surface slope. In the alongshore direction, the effect of viscosity leads to a wave attenuation, and hence a radiation stress component. The frictional effect on the mean Eulerian motion is modeled through a turbulent bottom drag. The alongshore momentum balance is between the mean pressure gradient due to the surface slope, the radiation stress, and the turbulent drag on the mean Eulerian flow. It is shown that −∂E/∂y, where E is the total mean energy density for waves along the y-axis, is the wave-forcing term for the total mean Lagrangian momentum in the trapping region. This result is independent of the bottom slope angle. Vertically-averaged drift velocity components are obtained from the fluxes, divided by the local depth. Utilizing physical parameters relevant for field conditions, it appears the traditional Stokes drift in the Stokes edge wave is negligible compared to the mean Eulerian velocity component. The importance of this drift for the near-shore transport of effluents and suspended light sediments is discussed.
Weber, Jan Erik H., and Peygham Ghaffari. 2009. "Mass transport in the Stokes edge wave." Journal of Marine Research 67, (2). https://elischolar.library.yale.edu/journal_of_marine_research/229