A parabolic equation for the combined refraction diffraction of Stokes waves by mildly varying topography

James T. Kirby, Robert A. Dalrymple

Research output: Contribution to journalArticlepeer-review

143 Scopus citations

Abstract

A parabolic equation governing the leading order amplitude for a forward scattered Stokes wave is derived using a multiple scale perturbation method, and the connection between the linearized version and a previously derived approximation of the linear mild slope equation is investigated. Two examples are studied numerically for the situation where linear refraction theory leads to caustics, and the nonlinear model is shown to predict the development of wave jump conditions and significant reductions in amplitude in the vicinity of caustics.

Original languageEnglish (US)
Pages (from-to)453-466
Number of pages14
JournalJournal of fluid Mechanics
Volume136
DOIs
StatePublished - Nov 1983

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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