Cell merging and the jet/downwelling ratio in
Langmuir circulation
J. Mar. Res., 51, 737-769, 1993.
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 0.01 U_w
(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 La^1/2, the downwelling velocity as La^-1/3 and
the pitch as La^1/6. These predictions are supported by numerical results.
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