[1] Large eddy simulations of the Craik-Leibovich equations are used to assess the effect of misaligned Stokes drift and wind direction on Langmuir cells in the ocean mixed layer. Misalignments from 0 to 135 are examined and Langmuir turbulence structures are evident in all cases. The Stokes drift is modeled using a broadband empirical spectrum, and cases with and without the Coriolis effect, wind waves, and an initial mixed layer are examined. The expected scaling for the vertical velocity variance is recovered in the aligned simulations and is adapted here to the misaligned cases. The adjusted scaling projects the friction velocity (aligned with the wind stress) into the dominant axial direction of the Langmuir cells. The turbulent Langmuir number is generalized through a similar projection into the axial direction of the Langmuir cells, which reduces its value in realistic conditions. For known Langmuir cell orientations, the strength of Langmuir turbulence for misaligned cases can be estimated using the projected Langmuir number. A prediction for the angle between the wind stress and cell direction is obtained using the law of the wall; this prediction only requires the wind stress, Stokes drift, and boundary layer depth. Conditional analyses show that, with increasing misalignment, the typically antisymmetric Langmuir cell pairs become asymmetric. This asymmetry is due, in part, to the advection by cross cell flow of vorticity from one vortex tube onto the other, and in part due to an asymmetry induced by the stretching of vertical vorticity into cross cell vorticity.

Here, the effects of surface waves on submesoscale instabilities are studied through analytical and linear analyses as well as nonlinear large-eddy simulations of the wave-averaged Boussinesq equations. The wave averaging yields a surface-intensified current (Stokes drift) that advects momentum, adds to the total Coriolis force, and induces a Stokes shear force. The Stokes–Coriolis force alters the geostrophically balanced flow by reducing the burden on the Eulerian–Coriolis force to prop up the front, thereby potentially inciting an anti-Stokes Eulerian shear, while maintaining the Lagrangian (Eulerian plus Stokes) shear. Since the Lagrangian shear is maintained, the Charney–Stern–Pedlosky criteria for quasigeostrophic (QG) baroclinic instability are unchanged with the appropriate Lagrangian interpretation of the shear and QG potential vorticity. While the Stokes drift does not directly affect vorticity, the anti-Stokes Eulerian shear contributes to the Ertel potential vorticity (PV). When the Stokes shear and geostrophic shear are aligned (antialigned), the PV is more (less) cyclonic. If the Stokes-modified PV is anticyclonic, the flow is unstable to symmetric instabilities (SI). Stokes drift also weakly impacts SI through the Stokes shear force. When the Stokes and Eulerian shears are the same (opposite) sign, the Stokes shear force does positive (negative) work on the flow associated with SI. Stokes drift also allows SI to extract more potential energy from the front, providing an indirect mechanism for Stokes-induced restratification.

The restratification of the cold wakes of Tropical Cyclones Fanapi, Frances, Igor and Katrina are examined based on derived scalings for processes that can restore the hurricane wake toward the precyclone conditions. The different restoration processes depend on the parameters of the wake: depth, width, buoyancy anomaly and wind stress. The parameters needed are derived for each wake from satellite and climatological data. The scalings are based on model results and existing parameterizations, including air-sea heat fluxes (one-dimensional) Ekman buoyancy fluxes (two-dimensional) and mixed layer eddies (three-dimensional). The dominant surface restoration occurs by a combination of surface fluxes and Ekman buoyancy fluxes, while the submesoscale mixed layer eddy bolus fluxes are the dominant subsurface effect.

Groups of surface gravity waves induce horizontally varying Stokes drift that drives convergence of water ahead of the group and divergence behind. The mass flux divergence associated with spatially variable Stokes drift pumps water downwards in front of the group and upwards in the rear. This ‘Stokes pumping’ creates a deep Eulerian return flow that sets the isopycnals below the wave group in motion and generates a trailing wake of internal gravity waves. We compute the energy flux from surface to internal waves by finding solutions of the wave-averaged Boussinesq equations in two and three dimensions forced by Stokes pumping at the surface. The two-dimensional (2-D) case is distinct from the 3-D case in that the stratification must be very strong, or the surface waves very slow for any internal wave (IW) radiation at all. On the other hand, in three dimensions, IW radiation always occurs, but with a larger energy flux as the stratification and surface wave (SW) amplitude increase or as the SW period is shorter. Specifically, the energy flux from SWs to IWs varies as the fourth power of the SW amplitude and of the buoyancy frequency, and is inversely proportional to the fifth power of the SW period. Using parameters typical of short period swell (e.g. 8 s SW period with 1 m amplitude) we find that the energy flux is small compared to both the total energy in a typical SW group and compared to the total IW energy. Therefore this coupling between SWs and IWs is not a significant sink of energy for the SWs nor a source for IWs. In an extreme case (e.g. 4 m amplitude 20 s period SWs) this coupling is a significant source of energy for IWs with frequency close to the buoyancy frequency.