A generalized kdv type equation for uneven depths

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Abstract

A Korteweg & de Vries type equation with improved dispersion characteristics for uneven water depths is presented. The new KdV type equation contains mixed dispersion and shoaling terms, which extend its applicable range of relative depths to virtually deep waters. The wave equation also satisfies an important consistency condition that there is an exact agreement between the shoaling rate of the equation itself and the rate obtained from the constancy of energy flux. A finite-difference scheme is devised for simulating several linear and nonlinear cases over varying bathymetry. The performance the new KdV type equation is observed to be quite satisfactory.

Original languageEnglish
Title of host publicationProceedings of the 35th International Conference on Coastal Engineering, ICCE 2016
EditorsPatrick Lynett
PublisherAmerican Society of Civil Engineers (ASCE)
ISBN (Electronic)9780989661133
Publication statusPublished - 2016
Event35th International Conference on Coastal Engineering, ICCE 2016 - Antalya, Turkey
Duration: 17 Nov 201620 Nov 2016

Publication series

NameProceedings of the Coastal Engineering Conference
Volume35
ISSN (Print)0161-3782

Conference

Conference35th International Conference on Coastal Engineering, ICCE 2016
Country/TerritoryTurkey
CityAntalya
Period17/11/1620/11/16

Keywords

  • Improved linear dispersion
  • Improved linear shoaling
  • KdV type equation

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