Similarity theory in the surface layer of large-eddy simulations of the wind-, wave-, and buoyancy-forced southern ocean

Monin–Obukhov similarity theory is applied to the surface layer of large-eddy simulations (LES) of deep Southern Ocean boundary layers. Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes drift) forcing. Two No-Stokes LES are used to determine the extent of the ocean surface layer and to adapt the nondimensional momentum and buoyancy gradients, as functions of the stability parameter. Stokes-forced LES are used to modify this parameter for wave effects, then to formulate dependencies of Stokes similarity functions on a Stokes parameter ξ. To account for wind-wave misalignment, the dimensional analysis is extended with two independent variables, namely, the production of turbulent kinetic energy in the surface layer due to Stokes shear and the total production, so that their ratio gives ξ. Stokes forcing is shown to reduce vertical shear more than stratification, and to enhance viscosity and diffusivity by factors up to 5.8 and 4.0, respectively, such that the Prandtl number can exceed unity. A practical parameterization is developed for ξ in terms of the meteorological forcing plus a Stokes drift profile, so that the Stokes and stability similarity functions can be combined to give turbulent velocity scales. These scales for both viscosity and diffusivity are evaluated against the LES, and the correlations are nearly 0.97. The benefit of calculating Stokes drift profiles from directional wave spectra is demonstrated by similarly evaluating three alternatives.