KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Embargo End Date2021-10-30
Permanent link to this recordhttp://hdl.handle.net/10754/659993
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AbstractWe 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.
CitationQuezada de Luna, M., & Ketcheson, D. I. (2021). Solitary water waves created by variations in bathymetry. Journal of Fluid Mechanics, 917. doi:10.1017/jfm.2021.267
SponsorsWe 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.
This work was funded by King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia.
PublisherCambridge University Press (CUP)
JournalJournal of Fluid Mechanics
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