Dynamic modelling of sea-surface roughness for large-eddy simulation of wind over ocean wavefield

Wind blowing over the ocean surface can be treated as a turbulent boundary layer over a multiscale rough surface with moving roughness elements, the waves. Large-eddy simulation (LES) of such flows is challenging because LES resolves wind-wave interactions only down to the grid scale, Δ, while the effects of subgrid-scale (SGS) waves on the wind need to be modelled. Usually, a surface-layer model based on the law of the wall is used; but the surface roughness has been known to depend on the local wind and wave conditions and is difficult to parameterize. In this study, a dynamic model for the SGS sea-surface roughness is developed, with the roughness corresponding to the SGS waves expressed as α_w σ_η ^Δ. Here, σ_η^Δ is the effective amplitude of the SGS waves, modelled as a weighted integral of the SGS wave spectrum based on the geometric and kinematic properties of the waves for which five candidate expressions are examined. Moreover, α_w is an unknown dimensionless model coefficient determined dynamically based on the first-principles constraint that the total surface drag force or average surface stress must be independent of the LES filter scale Δ. The feasibility and consistency of the dynamic sea-surface roughness models are assessed by a priori tests using data from high-resolution LES with near-surface resolution, appropriately filtered. Also, these data are used for a posteriori tests of the dynamic sea-surface roughness models in LES with near-surface modelling. It is found that the dynamic modelling approach can successfully capture the effects of SGS waves on the wind turbulence without ad hoc prescription of the model parameter α_w. Also, for σ_η ^Δ, a model based on the kinematics of wind-wave relative motion achieves the best performance among the five candidate models.