Gnanadesikan, A., and R. A. Weller, 1995: Structure and instability of the Ekman spiral in the presence of surface gravity waves. Journal of Physical Oceanography, 25(12), 3148-3171.

Abstract: The physical processes responsible for maintaining the mixed layer are examined by considering the velocity structure. The low-frequency Ekman response in the interior of unstratified mixed layers is much less sheared than is predicted using eddy viscosity models that reproduce the temperature structure. However, the response is more sheared than predicted by models that parameterize the mixed layer as a slab. An explanation is sought by considering the effect of an infinite train of surface gravity waves on the mean Ekman spiral. For some realistic conditions, the Ekman spiral predicted by assuming small-scale diffusion alone is strongly unstable to Langmuir cells driven by wave-current interaction. In the Northern Hemisphere, these cells are oriented to the right of the wind, the result of a balance between maximizing the wave- current forcing, maximizing the efficiency of this forcing in producing cells, and minimizing the crosscell shear. The cells are capable of replacing small-scale turbulent diffusion as the principal transport mechanism within the mixed layer. Finite-difference code runs that include infinite-length trains of surface gravity waves qualitatively explain the reduction in shear within the mixed layer relative to that predicted by small-scale mixing. However, the theory also predicts an Eulerian return flow balancing the Stokes drift that has not been observed.