A Study of Langmuir Turbulence based on Statistical State Dynamics

Roll circulations are commonly observed in the ocean surface mixed layer. Traditionally, formation of these rolls has been ascribed to the Langmuir modal instability arising from Stokes drift included by the surface wave field. 

However, it has also been shown that in turbulent wall bounded shear flows rolls also form by direct destabilization of the roll structure by Reynolds stress torque. Understanding roll formation in the turbulent mixed layer under the influence of both Stokes drift and mean Eulerian shear, in which both the Langmuir modal instability and the Reynolds stress torque induced roll instability are supported, remains to be understood. Because both of these roll formation mechanisms are supported by the associated representation of the dynamics using statistical state dynamics (SSD), a comprehensive understanding of

the roll formation mechanism can be obtained by studying the associated SSD. 

By analyzing the SSD we find parameter regimes for which both the Langmuir destabilization mechanism and the Reynolds stress torque mechanism contribute to the formation and maintenance of rolls in mixed layer.