Surface gravity waves are one of the hydrodynamic processes in the nearshore area that play a key role in the transport of plastic, plankton, sediment and other particles. Previous research has studied the combined effect of the Earth's rotation and turbulent mixing on the wave-driven cross-shore velocity profile in both the surf zone and on the inner continental shelf. However, these studies either used eddy viscosity profiles typical for wind-driven currents or determined the turbulence characteristics based on the amount of energy dissipated by wave breaking. This research aims to unravel the connection between the Coriolis force and momentum diffusion in the absence of wave breaking by using a turbulence model that is based exclusively on wave-driven flow dynamics. To this end, the existing one-dimensional wave-averaged model of Lentz et al. (2008) was improved by incorporating a low-Re one-equation turbulence model to determine the eddy viscosity generated by the Eulerian-mean flow. Furthermore, a complementary three-dimensional RANS model was constructed in SWASH.

In an inertial frame of reference, the models predict velocity profiles that are similar to the theoretical inviscid depth-uniform return flow in the inner part of the water column, while in a rotating frame of reference, the results approach the anti-Stokes drift profile based on the theory of Hasselmann (1970). Deviations are observed near the bed, caused by vertical radiation shear stresses, especially in relatively shallow water. The inverse wave Ekman number is shown to be a key indicator of the relative importance of the Coriolis force with respect to turbulent mixing. The results emphasize the importance of including the Coriolis force in nearshore wave-driven flow models. Compared with laboratory measurements, the theoretical model accurately predicts the near-bed velocity profile, indicating that a turbulence model that is based on wave-driven flow dynamics is essential to properly model wave-induced currents. ... Read more