Analysis of large eddy simulation data reveals that Langmuir circulation (LC) induces a significant enhancement of the mixed layer deepening, only if the mixed layer depth (MLD) h is shallow and the buoyancy jump across it ΔB is small, when simulations are initiated by applying the wind stress to a motionless mixed layer with stratification. The difference in the entrainment rate between the cases with and without LC decreases with hΔB/υL2, where yL is the velocity scale of LC. The ratio of the mixing length scale l between the cases with and without LC is close to 1 for larger Rt [=(Nl0/q)2; Rt>~1], but it increases to above 10 with the decrease of Rt, where N is the Brunt-Väisälä frequency and q and l0 are the velocity and length scales of turbulence in the homogeneous layer. It is also found that, in the presence of LC, the effect of stratification on vertical mixing should be parameterized in terms of Rt instead of Ri (=(N/S)2), because velocity shear S is no longer a dominant source of turbulence. The parameterization is provided by l/l0=(1+αRt)-1/2 with α~50, regardless of the presence of LC. However, LC makes l0 much larger than conventionally used for the boundary layer.
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