On the Wind Generation of Water Waves

In this work, we consider the mathematical theory of wind generatedwater waves. This entails determining the stability properties ofthe family of laminar flow solutions to the two-phase interfaceEuler equation. We present a rigorous derivation of the linearizedevolution equations about an arbitrary steady solution, and, usingthis, we give a complete proof of the instability criterion of Miles [16]. Our analysis is valid even in thepresence of surface tension and a vortex sheet (discontinuity in thetangential velocity across the air–sea interface). We are thusable to give a unified equation connecting the Kelvin–Helmholtz andquasi-laminar models of wave generation.