On the wind generation of water waves

Abstract

In this work, we consider the mathematical theory of wind generated water waves. This entails determining the stability properties of the family of laminar flow solutions to the two-phase interface Euler equation. We present a rigorous derivation of the linearized evolution equations about an arbitrary steady solution, and, using this, we give a complete proof of the instability criterion of Miles. Our analysis is valid even in the presence of surface tension and a vortex sheet (discontinuity in the tangential velocity across the air--sea interface). We are thus able to give a unified equation connecting the Kelvin--Helmholtz and quasi-laminar models of wave generation.

Cited by in corpus (4)

• Pressure transfer functions for interfacial fluid problems
• Elliptic equations with transmission and Wentzell boundary conditions and an application to steady water waves in the presence of wind
• Modelling of ocean waves with the Alber equation: application to non-parametric spectra and generalization to crossing seas
• Capillary gravity water waves linearized at monotone shear flows: eigenvalues and inviscid damping