A generic framework for extending Miles' approach to wind-wave interactions

Abstract

Understanding the energy transfer from wind to waves is an important but complex topic, typically based on phenomenology, on pure numerics, or on technically challenging analysis, carried out on a case by case basis. Here we show that the approach by Miles, initially proposed for a still and infinitely deep ocean of inviscid water, is in fact generic: it can easily be adapted, as we demonstrate directly from the mathematical structure of the arguments put forward by Miles. We establish simple transformations, which infer wave growth rates in complex hydrodynamic situations directly from those in Miles' conditions, without any adjustable parameters. The corresponding conversion factors are determined from the hydrodynamic water pressure produced by a propagating surface wave, and can be determined without requiring to further analyse wind and air flow. We reproduce a variety of results for different hydrodynamic situations to show how such generalisations can be achieved with surprisingly simple calculations and without any additional numerical effort, which should make the approach interesting for real-life applications.