Reduced Equations for Langmuir Turbulence

Langmuir circulation (LC) is a wind and surface-wave driven convective flow that dominates vertical transport within the ocean surface mixed layer under wind-forced seas. When the forcing is sufficiently strong, LC exhibits a range of length and times scales, from centimeters to hundreds of meters and seconds to hours. The emergence of a broad spectrum of scales prompted McWilliams, Sullivan and Moeng (JFM 1997) to re-dub this phenomenon "Langmuir turbulence" both to emphasize that LC is properly viewed as part of the upper ocean turbulence and to distinguish it from wall-bounded shear flow turbulence. Even under uncontrolled, strongly supercritical environmental conditions, however, LC is dominated by energetic counter-rotating vortical structures that are elongated in the wind direction (assuming the wind-driven shear and surface-wave Stokes drift are themselves aligned with the wind).
In this study, we exploit this anisotropic flow structure by carrying out a multiple-scale asymptotic analysis of the Craik-Leibovich (CL) equations -a surface-wave filtered version of the Navier-Stokes equations frequently used to investigate LC - to derive a reduced set of PDEs governing quasi-3D Langmuir turbulence. Results of linear and secondary (i.e. nonlinear) stability analyses will be reported, which suggest that the reduced equations economically capture the key 3D instabilities. The derivation of this reduced model is a first step in an effort to investigate the interaction of mesoscale eddies with mixed-layer turbulence.