On the Wind Generation of Water Waves

Oliver Bühler, Jalal Shatah, Samuel Walsh, Chongchun Zeng

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)827-878
Number of pages52
JournalArchive for Rational Mechanics and Analysis
Issue number2
StatePublished - Nov 1 2016

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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