Generation of Langmuir circulation for nonaligned wind stress and the Stokes drift

The growth rate of Langmuir cells is calculated from a linear stability analysis for different orientations of wind, waves, and cells as well as for various values of the dimensionless parameters describing wave‐current interaction. These parameters could be the Stokes drift/friction velocity ratio and the shear ratio Sr which describes the relative strength of the Stokes drift shear and mean Eulerian shear. The growth rate is maximal overall when wind and waves are aligned. For a given angle between the Stokes drift and the wind (the misalignment angle), the direction of the cell axis for maximal growth lies between wind and waves and is mainly determined by (1) the misalignment angle and (2) the shear ratio. For a fixed value of the latter, the orientation of the fastest growing cells (the preferential cell direction) is nearly independent of the one other dimensionless parameter which could be the Stokes drift/friction velocity ratio or the Langmuir number. The direction of the fastest growing cells shifts closer toward the wave direction as the Stokes drift shear increases relative to the mean shear and vice versa. However, while the preferential cell direction lies close to the wind for small Sr, it does not align with the waves for reasonably large Sr. When wind and waves are not aligned and the Stokes drift shear and the mean shear are of the same order, the cells drift sideways at an angle to the cell axes, with a speed which is comparable with the magnitude of the mean Eulerian current at a depth of approximately 0.7 times the cell depth. The drift amplitude increases as the misalignment angle increases and is larger for larger values of the shear ratio. When wind and waves are oriented in the opposite directions, there is no source of instability, and the cells are damped.