Kadomtsev-Petviashvili type equation for entire range of relative water depths


Beji S.

COASTAL ENGINEERING JOURNAL, vol.60, no.1, pp.60-68, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1080/21664250.2018.1436241
  • Title of Journal : COASTAL ENGINEERING JOURNAL
  • Page Numbers: pp.60-68

Abstract

A Kadomtsev-Petviashvili type equation valid for the entire range of relative water depths; namely, shallow, intermediate, and deep, is derived. The new equation is capable of simulating the shallow water cnoidal waves and the deep water second-order Stokes waves equally well besides accounting for wave shoaling due to varying water depths. Linear shoaling properties of the equation for unidirectional sinusoidal waves are in complete agreement with the energy flux concept. A finite-difference scheme is adopted for numerical solution of the equation to demonstrate its performance against test cases and its wide range of possible applications.