## 1. Introduction

[2] Waves are a ubiquitous feature of the surface ocean that combined with even a light surface wind stress can produce upper ocean quasi two-dimensional instabilities known as Langmuir circulations. These features were reported by *Langmuir* [1938] following an Atlantic crossing where he observed Sargassum weed arranging into linear bands aligned with the wind direction. These flotsam streaks are the surface signature of counter rotating Langmuir circulation vortices. These features have been observed to penetrate deeply [*Pollard and Thomas*, 1989] and subsequent observational campaigns have led to the documentation of their structure and variability [e.g., *Plueddemann et al.*, 1996]. It is widely accepted that the Langmuir circulations are generated through an instability which arises through an interaction between the Stokes drift of the waves and the local vorticity. The effect can be incorporated into the Navier-Stokes equations by a process called wave filtering, giving rise to the wave-filtered equations [*Craik and Leibovich*, 1976].

[3] Large eddy simulation (LES) of these equations was pioneered by *Skyllingstad and Denbo* [1995] and *McWilliams et al.* [1997]. More recent contributions have further developed the field addressing higher complexity problems, for example notable studies include effects of wave breaking [*Noh et al.*, 2004; *Sullivan et al.*, 2004] (see also P. P. Sullivan et al., Surface gravity wave effects in the oceanic boundary layer: Large-eddy simulation with vortex force and stochastic breakers, submitted to *Journal of Fluid Mechanics*, 2007), buoyancy forcing [*Li et al.*, 2005], biology [*Lewis*, 2005] and a modified K-profile parameterization [*Smyth et al.*, 2002]. For a comprehensive review on Langmuir circulations, refer to *Thorpe* [2004]. In particular, *Sullivan et al.* [2004] describe a downward turbulent kinetic energy flux that is a product of a stochastic parameterization for the effect of wave breaking at the surface. However, a similar transport effect can also be seen without wave breaking, that is in less extreme weather conditions. *McWilliams et al.* [1997] demonstrate evidence of enhanced downwelling in their simulations without recourse to wave breaking parameterizations. We investigate how this process varies with the external wave parameters. Additionally of particular interest to this study, *Li et al.* [2005] vary the size of the surface Stokes drift and use the relative magnitudes of depth averaged velocity variances to classify turbulence regimes in wave forced simulations of the ocean mixed layer. They demonstrate, for strong enough Stokes drift, a transition occurs in the nature of the mixed layer turbulence from a shear-driven turbulence to a Langmuir turbulence. By retaining depth-dependent information in our diagnostics, we investigate further how this transition varies as a function of the wave forcing depth scale.

[4] Non parallel wind and wave forcing [*Gnanadesikan and Weller*, 1995; *Polonichko*, 1997]; density structure [*Li and Garrett*, 1997] and time-dependent forcing [*Skyllingstad et al.*, 2000] will doubtless have an effect on the surface layer dynamics as modeled in eddy viscosity models, however since much less is known about the influence of the wave forcing in a fully 3D turbulent flow this study's objective is to investigate as clean an experiment as usefully possible. There still much to be gained by investigating the simplest LES scenarios to highlight clearly the role of the wave induced processes. We consider the case with a constant density, steady wind forcing, and monochromatic wave forcing (as parameterized through the Craik-Leibovich equations) that is in a direction parallel to the wind. Parallel and steady wind and wave forcing are chosen for this study of Langmuir turbulence since this configuration has the fastest growing linear instabilities [*Polonichko*, 1997]. This investigation is into the nature of the vertical structure of a mixed layer where wave induced downwelling jets are capable of being the principle transport mechanism [*Gnanadesikan and Weller*, 1995]. To this end we analyze data from an ensemble of LES runs to investigate how the wave parameters control the statistically steady state dynamics of the mixed layer.

[5] In section 2 the LES model formulation and parameter ranges are presented. In section 3 the complex three dimensional structure of the flow field is dissected using trajectories, instantaneous velocity sections and turbulent kinetic energy budgets. These analyses motivate diagnostics, presented in section 4, that compare Stokes shear to mean shear and that quantify anisotropy in the turbulence in order to describe the vertical structure of the Langmuir turbulence. We conclude with a discussion in Section 5.