Wave-induced drift and mixing

Over the past 10 years, several investigations have revealed that waves dramatically enhance the turbulent mixing near the surface (e.g. Agrawal et al., 1992). Besides, waves are known to have a non-zero mean motion in the direction of propagation: the Stokes drift. In a rotating frame, waves also induce a stress to the right of the direction of propagation: the Hasselmann force or "Stokes-Coriolis" effect. This effect is believed to compensate the Stokes drift by driving the mean flow in the opposite direction, and recent studies have proposed that it significantly modifies the profile of the Eulerian current near the surface (Lewis and Belcher, 2004). To embrace all these effects, a model of the ocean mixed layer is proposed. The motion is separated into a quasi-Eulerian mean flow and the wave-induced Stokes drift. Sigma coordinates are used to follow the surface motion (Mellor, 2003). This yields equations for the mean flow that are compatible to those of ocean-circulation models, with the wave part acting as a supplementary forcing. A 2.5 level turbulence closure scheme is used, in which dissipation of waves enhances turbulent kinetic energy near the surface. The different effects are investigated and the model is validated with measured profiles of turbulent kinetic energy (Terray et al., 1996), shear of Eulerian currents (Santala and Terray, 1992) and Lagrangian surface drifts. The model is generally consistent with all these observation, and suggests that surface drift observations, of the order of 3% of the wind speed, must be related to a strong surface shear that mainly comes from the shear of the Stokes drift. Essentially, a strong surface mixing is incompatible with large surface shears of the quasi-Eulerian velocity. Still, the model mean water velocities are only about 60% of observed drift velocities. The model also suggests a dependence of surface mixing and drift on the state of development of the waves that can be represented by a wave age parameter. It raises the question of the adequacy of parameterisations based on the wind only, as usual in ocean circulation models. We argue for a coupled wave-circulation model, particularly for fetch limited conditions often met in coastal areas, and estimate the likely impact on upwelling-type circulations.