An asymptotic model for the Kelvin-Helmholtz and Miles mechanisms of water wave generation by wind

TL;DR

This paper develops an asymptotic model to distinguish the Kelvin-Helmholtz and Miles mechanisms of water wave generation by wind, revealing their operation at different wind strengths and scales.

Contribution

It introduces an asymptotic approach to analyze the two mechanisms within a two-layer wind profile model, highlighting their distinct roles in wave formation.

Findings

Miles' regime generates short waves at weak winds

Kelvin-Helmholtz mechanism dominates at strong winds

Different scales govern the two instability mechanisms

Abstract

The generalized Kelvin-Helmholtz (KH) and Miles mechanisms of the water wave generation by wind are investigated for two-layer piece-wise linear model of the wind profile. It is shown by asymptotic expansions in small air-to-water density ratio that two mechanisms of the instability operate in quite different scales. Miles' short waves are generated by weak winds, in particular, Miles' regime is responsible for initiation of the instability at the minimum wind speed, while the generalized KH regime dominates at strong winds and raises moderately-short waves.