Solitary water waves created by variations in bathymetry

Manuel Quezada de Luna, David I. Ketcheson

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study the flow of water waves over bathymetry that varies periodically along one direction. We derive a linearized, homogenized model and show that the periodic bathymetry induces an effective dispersion, distinct from the dispersion inherently present in water waves. We relate this dispersion to the well-known effective dispersion introduced by changes in the bathymetry in non-rectangular channels. Numerical simulations using the (non-dispersive) shallow water equations reveal that a balance between this effective dispersion and nonlinearity can create solitary waves. We derive a Korteweg–de Vries-type equation that approximates the behaviour of these waves in the weakly nonlinear regime. We show that, depending on geometry, dispersion due to bathymetry can be much stronger than traditional water wave dispersion and can prevent wave breaking in strongly nonlinear regimes. Computational experiments using depth-averaged water wave models confirm the analysis and suggest that experimental observation of these solitary waves is possible.
Original languageEnglish (US)
JournalJournal of Fluid Mechanics
StatePublished - Apr 30 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-05-07
Acknowledgements: We thank Professor J. Kirby for bringing to our attention the literature on waves in non-rectangular channels, and the anonymous referees for many suggestions that improved this work. For computer time, this research used the resources of the Supercomputing Laboratory at KAUST.

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Condensed Matter Physics


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