An Assessment of Dynamic Subgrid-Scale Sea-Surface Roughness Models

Abstract

Covered by waves with various lengths, the mobile sea surface represents a great challenge to the large-eddy simulation (LES) of atmospheric boundary layer flow over the ocean surface. In this study, we report recent developments and tests of dynamic modeling approaches for the subgrid-scale (SGS) sea-surface roughness for LES. In the model, introduced originally in Yang et al. (J. Fluid Mech., in press, 2013), the SGS roughness is quantified by an integral of the SGS wave spectrum, \(\sigma_{\eta}^{\Delta}\), weighted based on the wind-wave kinematics, with an unknown model coefficient αw as pre-factor. The coefficient αw is determined dynamically based on the basic constraint that the total surface drag force must be independent of the LES filter scale. The weighted integral \(\sigma_{\eta}^{\Delta}\) represents the effective amplitude of the SGS waves, for which five candidate models are reviewed. Following the computational tests presented in Yang et al. (J. Fluid Mech., in press, 2013), in this study the performance of the dynamic SGS sea-surface roughness models is assessed by a theoretical approach, in which the roughness model is coupled with the critical-layer theory of wind–wave interaction. This theoretical approach mimics the averaged behavior of the LES. Meanwhile, its low computation cost allows the assessment of the model performance over a wide range of parameters. The test results indicate that the dynamic modeling approach can reliably model the roughness length of the SGS waves without ad-hoc prescription of the model parameter αw. Also, we confirm that to model \(\sigma_{\eta}^{\Delta}\), an expression based on the kinematics of wind–wave relative motion achieves the best performance among the five candidate models considered.