The Craik-Leibovich equations for Langmuir circulation have been integrated numerically to investigate the cell merging process as well as the strength and structure of the cells. We find that pairs of counterrotating vortices cancel each other, leading to a growth in scale of the dominant vortices. However, when there is no external forcing, vortices of opposite sign do not merge irrespective of the vortex size and circulation strength. The merging of Langmuir cells, or rather the cancellation of counterrotating vortices, is thus different from the amalgamation of like-signed vortices in two-dimensional turbulence. The forcing due to the Stokes drift plays an important role in the cell-merging process. As the Langmuir number La decreases, the maximum downwelling velocity increases while the pitch (the ratio of surface downwind jet strength to the maximum downwelling velocity) decreases. When La is about 0.01, as for an eddy viscosity in the range of values commonly used for the ocean surface layer, the model predicts a maximum downwelling velocity of 0.006 to 0.01Uw (the wind speed), comparable with the observed magnitude. However, the surface downwind jet is significantly weaker than the observed strength. At small La a simple scale analysis, which couples a surface boundary layer with a narrow downwelling region, suggests that the thickness of these regions should vary as La1/2, the downwelling velocity as La−1/3 and the pitch as La1/6. These predictions are supported by numerical results.
Li, Ming, and Chris Garrett. 1993. "Cell merging and the jet/downwelling ratio in Langmuir circulation." Journal of Marine Research 51, (4). https://elischolar.library.yale.edu/journal_of_marine_research/2079