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

Abstract

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.