Two-dimensional interactions of solitons in a two-layer fluid of finite depth

Hidekazu Tsuji, Masayuki Oikawa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Two-dimensional (2D) interactions of two interfacial solitons in a two-layer fluid of finite depth are investigated under the assumption of a small but finite amplitude. When the angle v between the wave normals of two solitons is not small, it is shown by a perturbation method that in the lowest order of approximation the solution is a superposition of two intermediate long wave (ILW) solitons and in the next order of approximation the effect of the interaction appears as position phase shifts and as an increase in amplitude at the interaction center of two solitons. When v is small, it is shown that the interaction is described approximately by a nonlinear integro-partial differential equation that we call the two-dimensional ILW (2DILW) equation. By solving it numerically for a V-shaped initial wave that is an appropriate initial value for the oblique reflection of a soliton due to a rigid wall, it is shown that for a relatively large angle of incidence vi the reflection is regular, but for a relatively small vi the reflection is not regular and a new wave called stem is generated. The results are also compared with those of the Kadomtsev-Petviashvili (KP) equation and of the two-dimensional Benjamin-Ono (2DBO) equation.

Original languageEnglish
Article number065506
JournalFluid Dynamics Research
Volume42
Issue number6
DOIs
Publication statusPublished - Dec 1 2010

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Solitons
solitary waves
Fluids
fluids
planetary waves
interactions
Wave equations
approximation
stems
Phase shift
partial differential equations
wave equations
Partial differential equations
phase shift
incidence
perturbation

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes

Cite this

Two-dimensional interactions of solitons in a two-layer fluid of finite depth. / Tsuji, Hidekazu; Oikawa, Masayuki.

In: Fluid Dynamics Research, Vol. 42, No. 6, 065506, 01.12.2010.

Research output: Contribution to journalArticle

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