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.
