A turbulent curvilinear model for wave-induced airflow perturbations for marine atmospheric boundary layer

Progressive waves on the ocean surface influence the structure and turbulence characteristics of the marine atmospheric boundary layer (MABL) flow through wave-induced momentum transfer. This study develops a novel model to predict wave-induced airflow perturbations above surface waves. We extend the linearized viscous curvilinear model from Cao, Deng & Shen (J. Fluid Mech., vol. 901, 2020, A27) by incorporating turbulent stress terms modeled using the Boussinesq eddy viscosity hypothesis. The resulting model equation resembles an Orr-Sommerfeld-like ordinary differential equation with additional eddy viscosity and forcing terms. We conduct large-eddy simulations of wind over progressive waves for various wind-following and wind-opposing wave scenarios, considering different wave ages. These simulations reveal that eddy viscosity in the turbulence-dominated region within the wave boundary layer can be parameterized as a linear function of the vertical distance from the water surface in a wave-fitted curvilinear coordinate system. Our findings demonstrate that solving the turbulent curvilinear model equations enhances predictions of wave-induced fluctuations compared to the linearized viscous curvilinear model, across different wave scenarios.