Direct numerical evidence of the Phillips initial stage and its antecedent during wind-wave generation

How wind generates ocean surface waves is a classic fluid mechanics problem, and it is commonly believed that the resonance mechanism between wind and surface waves, first proposed by Phillips in 1957, is responsible for the early stages of wind-wave generation. However, there has not been any conclusive study to fully validate this theory. We present the results of a combined theoretical and computational study of the initial response of a calm water surface to turbulent wind and an analysis in terms of the Phillips theory on wind-wave generation. We address a nascent stage of wind-wave generation after the sudden impact of a turbulent wind on a calm water surface but before the initial stage described by Phillips. We show that in such nascent stage, the wave energy grows over time following a quartic law. We provide direct numerical evidence of the resonance mechanism during the initial stage and clarify its role in the formation of the heterogeneous wave energy distribution in the spectral space. While Phillips' theory states that the early stages of wind-wave generation are governed by a resonance mechanism, the majority of studies focussed on the situation where surface waves have already been generated by the wind. The authors fill this gap and address the problem of surface wave generation when calm water is exposed to turbulent wind.

Automated summary

This study combines theoretical and computational methods to investigate the initial impact of turbulent wind on a calm water surface and analyzes the process of wind-wave generation based on Phillips theory. The study reveals that the wave energy grows following a quartic law during the early stages of wave generation and provides numerical evidence of the resonance mechanism, which plays a crucial role in the heterogeneous distribution of wave energy in the spectral space.