摘要：

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 windu2013wave 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} hspace{0.167em} { sigma }_{eta }^{Delta } $ . Here, ${ sigma }_{eta }^{Delta } $ 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 }_{eta }^{Delta } $ , a model based on the kinematics of windu2013wave relative motion achieves the best performance among the five candidate models.

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