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dc.contributor.authorOwen, A
dc.contributor.authorGrimshaw, R
dc.contributor.authorWingate, B
dc.date.accessioned2018-07-31T08:07:00Z
dc.date.issued2018-07-02
dc.description.abstractIn this paper we examine triad resonances in a rotating shallow water system when there are two free interfaces. This allows for an examination in a relatively simple model of the interplay between baroclinic and barotropic dynamics in a context where there is also a geostrophic mode. In contrast to the much-studied one-layer rotating shallow water system, we find that as well as the usual slow geostrophic mode, there are now two fast waves, a barotropic mode and a baroclinic mode. This feature permits triad resonances to occur between three fast waves, with a mixture of barotropic and baroclinic modes, an aspect which cannot occur in the one-layer system. There are now also two branches of the slow geostrophic mode with a repeated branch of the dispersion relation. The consequences are explored in a derivation of the full set of triad interaction equations, using a multi-scale asymptotic expansion based on a small amplitude parameter. The derived nonlinear interaction coefficients are confirmed using energy and enstrophy conservation. These triad interaction equations are explored with an emphasis on the parameter regime with small Rossby and Froude numbers.en_GB
dc.description.sponsorshipThe authors would like to acknowledge funding received from the EPSRC DTP PhD studentship EPSRC-1636446, as well as support received from the University of Exeter.en_GB
dc.identifier.citationPublished online: 02 July 2018en_GB
dc.identifier.doi10.1017/jfm.2018.468
dc.identifier.urihttp://hdl.handle.net/10871/33598
dc.language.isoenen_GB
dc.publisherCambridge University Press (CUP)en_GB
dc.rights.embargoreasonUnder embargo until 3 January 2019 in compliance with publisher policy.en_GB
dc.rights© 2018 Cambridge University Pressen_GB
dc.subjectphysics.flu-dynen_GB
dc.subjectphysics.flu-dynen_GB
dc.titleFast and slow resonant triads in the two layer rotating shallow water equationsen_GB
dc.typeArticleen_GB
dc.identifier.issn0022-1120
dc.descriptionThis is the author accepted manuscript. The final version is available from Cambridge University Press via the DOI in this record.en_GB
dc.identifier.journalJournal of Fluid Mechanicsen_GB


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