Breaking Solutions of the Variable Coefficient Korteweg-deVries Equation.

Abstract

Strongly shoaling solutions to the variable coefficient Korteweg-deVries equation have been obtained for arbitrary initial or off-shore waveforms and depth variations. These solutions are valid when eta << delta << 1, where eta is the ratio of the initial wave amplitude to the depth and delta is the ratio of the initial length of the wave to the length scale associated with the depth variation. The conditions at breaking are given in terms of the initial shape of the wave and the depth variation. An equation for the actual wave amplitude at breaking was found. Numerical solutions of the equation were obtained and were in excellent agreement with the asymptotic results.

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Document Details

Document Type
Technical Report
Publication Date
Feb 23, 1981
Accession Number
ADA095247

Entities

People

  • B. Mccown
  • M. E. Bowman
  • M. S. Cramer

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Agreements
  • Amplitude
  • Asymptotic Series
  • Coefficients
  • Computational Science
  • Coordinate Systems
  • Differential Equations
  • Electrical Solitons
  • Equations
  • Fluid Mechanics
  • Method Of Characteristics
  • Military Research
  • Shallow Water
  • Solitons
  • Water
  • Water Waves
  • Waves

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.