The form and orientation of Langmuir cells for misaligned winds and waves

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.