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, Delta, 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 alpha(w)sigma(Delta)(eta). Here, sigma(Delta)(eta) 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, alpha(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 Delta. 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 alpha(w). Also, for sigma(Delta)(eta), a model based on the kinematics of wind-wave relative motion achieves the best performance among the five candidate models.