Effects of time-variant wind input on nonlinear broadband wave field

The wind field in the marine atmospheric boundary layer is turbulent and intermittent, resulting in a fluctuation in the wave energy growth. Due to the complexity of the wind turbulence, the time variations in the wind input were often neglected in previous studies. In this study, we evaluate the time-variant wind input effect on the nonlinear broadband wave field. We first conduct a spectral analysis on the turbulent pressure field at the wave surface, where the data is calculated using large-eddy simulation of wind and phase-resolved simulation of nonlinear waves. The space-time characteristics of the pressure field are revealed from the joint probability distribution with the vertical surface velocity, and the wavenumber-frequency spectrum. We then apply the time-variant wind forcing to wave evolution by incorporating the fluctuations of the wave energy growth rate obtained from the coupled wind-wave simulation. The effect of the time-variations is assessed by calculating the gradient of a cost function with respect to the initial surface elevation based on the adjoint model.