Onset of Langmuir circulation when shear flow and Stokes drift are not parallel

The linear stability problem for Langmuir circulation in the mixed layer of the ocean is investigated according to the Craik-Leibovich theory, whereby motion is generated through an interaction between a shear flow and the Stokes drift due to the surface gravity waves. This paper, unlike most previous analyses, allows the shear flow and the Stokes drift to be in different directions. Such misalignment provides a simple physical mechanism for the observed lateral drifting of Langmuir circulations. A long-wave asymptotic expansion is used to investigate the orientation of the fastest growing modes of Langmuir circulation: in general they are predicted to take the form of long counter-rotating rolls, whose axes lie parallel to a direction between that of the shear flow and that of the Stokes drift. For a given shear flow, the mixed layer is most unstable when the shear flow and the Stokes drift are parallel to one another.