  We consider a classical problem about dynamic instability that leads to the
Langmuir circulation. The problem statement assumes that there is initially a
wind-driven shear flow and a plane surface wave propagating in the direction of
the flow. The unstable mode is a superposition of i) shear flow and ii) surface
waves both modulated in the horizontal spanwise direction and iii) circulation
that is made up with vortices forming near-surface rolls whose axis are
coaligned along the shear flow streamlines and whose transverse size
corresponds to the modulation period. Usually, the Langmuir circulation is
understood as the vortical part of the mode slowly varying in time, which is
the combination of the first and the last flows. The novelty of our approach is
that we, firstly, take into account the scattering of the initial surface wave
on the slow current. Second, we find the interference of the scattered and the
initial waves generating a Stokes drift modulated in the same direction. Third,
we establish the subsequent affect of the circulation by the vortex force
created by the nonlinear interaction of the initial shear flow and the
modulated part of the Stokes drift. S. Leibovich & A.D.D. Craik previously
showed that the third part of the mechanism could maintain the Langmuir
circulation. We calculate the growth rate which is approximately twice smaller
than that obtained by A.D.D. Craik. The vertical structure of the circulation
in the mode consists of two vortices, that corresponds to the next mode in
Craik's model. Considering the wave scattering, we describe the fast-wave
motion as a potential flow with relatively weak vortical correction.
Application of the technique can be expanded on other flows where fast
oscillating surface waves coexist with a slow current.
