Simulation-based study of surface wave dynamics at the initial stage of wind-wave generation process

How wind generates waves is of great interest over decades, while the mechanism of wave development at the initial stage still lacks detailed study. We performed direct numerical simulation (DNS) of turbulent wind over calm water. Navier-Stokes equations are solved on a curvilinear wave surface fitted grid, where fully-nonlinear kinematic and dynamic boundary conditions at the free surface are implemented. We focus on the initial development of wave patterns, which refers to the Phillips’ theory (1957). Results show that the temporal behaviors of surface wave fluctuations transit from power law growth ⟨η² ⟩~t⁴ to linear growth ⟨η² ⟩~t, and the corresponding mechanism is proposed based on the modification of Phillips’ framework. Contributions of both turbulent air pressure and turbulent air shear stress, acting on the water surface, to the wave temporal growth behavior are quantified. Detailed analysis of the feedback of surface deformation to the turbulent airflow is also presented. It is found that the space-time correlation of turbulent air pressure on the water surface also characterizes the linear growth rate of wave fluctuations.