Stratified equatorial flows in cylindrical coordinates

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dc.contributor.authorHenry, David
dc.contributor.authorMartin, Calin I.
dc.contributor.funderScience Foundation Irelanden
dc.contributor.funderAustrian Science Funden
dc.date.accessioned2021-05-25T15:07:44Z
dc.date.available2021-05-25T15:07:44Z
dc.date.issued2020-06-05
dc.date.updated2021-05-20T12:22:08Z
dc.description.abstractWe construct an exact solution modelling the geophysical dynamics of an inviscid and incompressible fluid which possesses a variable density stratification, where the fluid density may vary with both the depth and latitude. Our solution pertains to the large-scale equatorial dynamics of a fluid body with a free surface propagating steadily in a purely azimuthal direction, and is expressed in terms of cylindrical coordinates. Allowing for general fluid stratification greatly complicates the Bernoulli relation—which relates the imposed pressure to the reciprocal fluid distortion at the free-surface—thereby acting as a constraint on the existence of a solution. Employing the implicit function theorem, we establish the existence of solutions and determine that the requisite monotonicity properties hold for the flow solutions we found. Furthermore, since the fluid velocity and pressure are prescribed by explicit formulae in the framework of cylindrical coordinates, our solution is amenable to analysis by the short-wavelength stability approach, which we investigate.en
dc.description.sponsorshipAustrian Science Fund ((FWF) under the research grant P 30878-N32).en
dc.description.statusPeer revieweden
dc.description.versionPublished Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationHenry, D. and Martin, C. I. (2020) 'Stratified equatorial flows in cylindrical coordinates', Nonlinearity, 33(8), pp. 3889-3904. doi: 10.1088/1361-6544/ab801fen
dc.identifier.doi10.1088/1361-6544/ab801fen
dc.identifier.endpage3904en
dc.identifier.issn0951-7715
dc.identifier.journaltitleNonlinearityen
dc.identifier.startpage3889en
dc.identifier.urihttps://hdl.handle.net/10468/11384
dc.identifier.volume33en
dc.language.isoenen
dc.publisherIOP Publishingen
dc.relation.projectinfo:eu-repo/grantAgreement/SFI/SFI Career Development Award/13/CDA/2117/IE/Nonlinear wave-current interactions in the nearshore: addressing the role of vorticity and nonlinearity in the modelling of ocean energy/en
dc.relation.urihttps://iopscience.iop.org/article/10.1088/1361-6544/ab801f
dc.rights© 2020 The Author(s). IOP Publishing Ltd & London Mathematical Society Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.en
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/en
dc.subjectAzimuthal flowsen
dc.subjectGeneral densityen
dc.subjectCylindrical coordinatesen
dc.subjectCoriolis forceen
dc.subjectShort-wavelength perturbationsen
dc.subjectFree surfaceen
dc.subjectGeophysical wavesen
dc.subjectWater wavesen
dc.subjectInstabilityen
dc.subjectExistenceen
dc.subjectCurrentsen
dc.subjectSteadyen
dc.titleStratified equatorial flows in cylindrical coordinatesen
dc.typeArticle (peer-reviewed)en
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