Modeling Wind–Wave Interactions with a Machine Learning-Augmented Turbulence Curvilinear Model

Progressive ocean waves induce wave-coherent disturbances and turbulence in the overlying wind field. The turbulence curvilinear model, which extends the viscous curvilinear model of Cao et al. (J. Fluid Mech., vol. 901, 2020) by incorporating wave-induced turbulence stresses, provides an efficient framework for predicting airflow disturbances and form drag resulting from wind–wave interactions. To develop a fully predictive and self-consistent wind–wave interaction computational framework, accurate modeling of the wave-induced Reynolds stresses is crucial. Unlike traditional eddy viscosity models, which are suitable for representing shear-driven turbulence, these stresses exhibit a strong wave-phase dependence and require nonlinear modeling. In this study, we employ Pope’s nonlinear eddy viscosity model, with tensorial model coefficients learned using a Tensor-Based Neural Network (TBNN) as introduced by Ling et al. (J. Fluid Mech., vol. 807, 2016). The TBNN is trained on large-eddy simulation (LES) data of wind over progressive waves spanning a range of wave ages. Integrating this TBNN-based closure into the turbulence curvilinear model alongside standard k–ω type turbulence models yields a fully predictive framework for modeling wind–wave interactions. We assess the performance of this hybrid model by comparing its predictions with LES data for wave-induced stresses, airflow disturbances, and form drag across multiple wind-over-wave conditions. This hybrid model approach provides a computationally efficient and physics-based framework for modeling offshore wind fields.