Direct numerical simulations of wind wave growth of a broad banded wave spectrum.*

We perform Direct Numerical Simulations (DNS) of a broad-banded wave spectrum forced by turbulent wind. Utilizing the open-source solver Basilisk, we solve the full two-phase air-water Navier-Stokes equations with adaptive mesh refinement, including surface tension and geometric volume of fluid interface reconstruction. Our simulations cover a spectrum from millimeter-sized capillary waves to meter-scale waves forced by a turbulent boundary layer.

We employ space-time Fourier analysis to investigate the propagation, growth, and decay of the full wave spectrum under various wind-wave parameters, including changes in wind forcing intensity and initial wave conditions. We discuss the angular energy distribution and development of bound waves near the peak frequency and at higher frequencies, providing insights into their propagation speeds, growth, and decay rates in a fully coupled systems. These findings are compared with theoretical models based on linear stability and critical layer theory.