Models for very wide-angle water waves and wave diffraction

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40 Scopus citations

Abstract

For a bathymetry consisting of parallel bottom contours, wide-angle parabolic models are developed to describe the diffraction of linear water waves. The first model, developed by operator correspondence, extends the validity of conventional forms of the parabolic model for wave angles up to 70° from the assumed wave direction. Through the use of Fourier decomposition, wave models valid to 90° are developed for three different lateral boundary conditions. By application, it is shown that the diffraction of waves through gaps or around structures is governed by the initial wave condition at the structure, which can be expanded into progressive and evanescent wave modes. Away from the structure, the wave field consists of only the progressive wave modes, which disperse according to their direction of propagation, the water depth and Snell’s Law. Examples are shown for oblique waves through a gap, directional seas past a breakwater, a plane wave with varying crest amplitude, and finally for the diffraction of waves into a channel.

Original languageEnglish (US)
Pages (from-to)33-50
Number of pages18
JournalJournal of fluid Mechanics
Volume192
DOIs
StatePublished - Jan 1 1988

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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