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An extended linear shallow water equation

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)413-427
Number of pages15
JournalJournal of Fluid Mechanics
Early online date1 Aug 2019
DOIs
DateAccepted/In press - 4 Jul 2019
DateE-pub ahead of print (current) - 1 Aug 2019

Abstract

An extension to the classical shallow water equation (SWE) is derived which exactly satisfies the bed condition and can be regarded as an approximation to wave scattering at the next order in the small parameter $(h/\lambda)^2$ (depth to wavelength ratio squared.) In the frequency domain, the extended SWE shares the same simple structure as the standard SWE with coefficients modified by terms relating to the bed variation. In three dimensions the governing equation demonstrates that variable topography gives rise to anisotropic effects on wave scattering not present in the standard SWE with consequences for the design of water wave metamaterials. Numerical examples illustrate that approximations to wave scattering using the extended SWE are significantly improved in comparison with the standard SWE.

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://doi.org/10.1017/jfm.2019.555 . Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 202 KB, PDF document

    Licence: Other

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