Wind-stratification controls on energy pathways to mixed layer deepening by Langmuir circulation

The present study examines the influence of the interaction between Langmuir cells and preexisting stratification on mixed-layer deepening using a quasi–two-dimensional model in the vertical and crosswind directions. We estimate the mixed-layer depth in terms of the depth of the maximum temperature gradient, which deepens with time and eventually stabilizes at a quasi–steady state. After an initial period, Langmuir cells emerge, grow, intensify, and penetrate deeper as time progresses, while simultaneously distorting the isotherms and producing buoyancy torque. We investigate the response of mixed-layer deepening to different wind speeds and stratification profiles through a series of sensitivity experiments. We further analyze the resulting isotherm distortions in detail under varying wind and stratification conditions. To identify the specific energy pathways associated with mixed-layer deepening, we examine both the temporal evolution of total kinetic energy and the time-averaged depth profile of the turbulent kinetic energy budget. While stronger winds increase the total kinetic energy, stronger stratification reduces it. Furthermore, variations in wind speed significantly modify the Stokes production of turbulent kinetic energy, whereas changes in stratification primarily affect buoyancy loss. These results provide key insights into the mechanisms governing energy transfer during mixed-layer deepening under different scenarios.