Numerical investigation on the principal stage of wind-wave generation

We use a combined numerical and theoretical approach to study the dynamics of wind-generated water waves in the principal stage of the Phillips theory (Phillips, J. Fluid Mech., 1957). Using a wave-surface-fitted grid, we perform direct numerical simulation of turbulent wind over initially calm water to capture the multistage generation of water waves. Detailed analyses are conducted to evaluate the Phillips theory in both physical space and wavenumber space. We obtain numerical evidence on the existence of the principal stage when the surface elevation variance grows linearly with time. The wavenumber spectrum of surface wave elevations is further analyzed using a time-dependent norm to elucidate the role of the resonance mechanism in wave generation. In the physical space, we propose an improved model to obtain a quantitative prediction of the growth rate of surface elevation variance in the principal stage, which agrees with the direct numerical simulation results better than the Phillips theory.