The role of wave-induced Coriolis-Stokes forcing on the wind-driven mixed layer

The interaction between the Coriolis force and the Stokes drift associated with ocean surface waves leads to a vertical transport of momentum, which can be expressed as a force on the mean momentum equation in the direction along wave crests. How this Coriolis-Stokes forcing affects the mean current profile in a wind-driven mixed layer is investigated using simple models, results from large-eddy simulations, and observational data. The effects of the Coriolis-Stokes forcing on the mean current profile are examined by reappraising analytical solutions to the Ekman model that include the Coriolis-Stokes forcing. Turbulent momentum transfer is modeled using an eddy-viscosity model, first with a constant viscosity and second with a linearly varying eddy viscosity. Although the Coriolis-Stokes forcing penetrates only a small fraction of the depth of the wind-driven layer for parameter values typical of the ocean, the analytical solutions show how the current profile is substantially changed through the whole depth of the wind-driven layer. It is shown how, for this oceanic regime, the Coriolis-Stokes forcing supports a fraction of the applied wind stress, changing the boundary condition on the wind-driven component of the flow and hence changing the current profile through all depths. The analytical solution with the linearly varying eddy viscosity is shown to reproduce reasonably well the effects of the Coriolis-Stokes forcing on the current profile computed from large-eddy simulations, which resolve the three-dimensional overturning motions associated with the turbulent Langmuir circulations in the wind-driven layer. Last, the analytical solution with the Coriolis-Stokes forcing is shown to agree reasonably well with current profiles from previously published observational data and certainly agrees better than the standard Ekman model. This finding provides evidence that the Coriolis-Stokes forcing is an important mechanism in controlling the dynamics of the upper ocean