Evolution of ocean surface waves in the early stage of wind-wave generation

How the ocean surface waves respond to the turbulent wind in the early stage of the wind-wave generation process has been a fascinating research topic for several decades. In this study, we conduct high-fidelity numerical simulations to reveal the multi-stage wave evolution. We have discovered a nascent stage in wind-wave generation, which occurs immediately after a turbulent wind impacts a calm water surface. This nascent stage precedes the initial stage described by Phillips' resonance theory and exhibits a new quartic law of growth over time. Our study offers direct numerical evidence supporting the existence of the resonance mechanism in the initial stage of Phillips' theory. The results shed light on the resonance mechanism's role in shaping the distribution of wave energy in the spectral space. Based on numerical observations, we further investigate surface wave energy growth in the initial stage, for which a quantitative analysis was challenging. We develop a novel complex analysis approach to quantify the temporal evolution of wave energy in Phillips' initial stage. Our study presents a quantitative analysis of surface wave energy growth, revealing the significant influence of surface tension on both the resonance curve and wave energy amplification.

* This work was supported by Office of Naval Research. Tianyi Li’s work after August 28, 2023 was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.