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dc.contributor.authorDritschel, David Gerard
dc.contributor.authorJalali, Mohammad Reza
dc.date.accessioned2021-02-12T00:39:12Z
dc.date.available2021-02-12T00:39:12Z
dc.date.issued2020-10-10
dc.identifier268469171
dc.identifier2947fc33-1ea9-4d04-a760-c3d19390a5da
dc.identifier85090011171
dc.identifier000558733100001
dc.identifier.citationDritschel , D G & Jalali , M R 2020 , ' The validity of two-dimensional models of a rotating shallow fluid layer ' , Journal of Fluid Mechanics , vol. 900 , A33 . https://doi.org/10.1017/jfm.2020.487en
dc.identifier.issn0022-1120
dc.identifier.otherORCID: /0000-0001-6489-3395/work/79917920
dc.identifier.urihttps://hdl.handle.net/10023/21418
dc.descriptionFunding: Support for this research has come from the UK Engineering and Physical Sciences Research Council (grant no. EP/H001794/1).en
dc.description.abstractWe investigate the validity and accuracy of two commonly used two-dimensional models of a rotating, incompressible, shallow fluid layer: the shallow-water (SW) model and the Serre/Green–Naghdi (GN) model. The models differ in just one respect: the SW model imposes the hydrostatic approximation while the GN model does not. Both models assume the horizontal velocity is independent of height throughout the layer. We compare these models with their parent three-dimensional (3-D) model, initialised with a height-independent horizontal velocity, and with a mean height small compared to the domain width. For small to moderate Rossby and Froude numbers, we verify that both models well approximate the vertically averaged 3-D flow. Overall, the GN model is found to be substantially more accurate than the SW model. However, this accuracy is only achieved using an explicit reformulation of the equations in which the vertically integrated non-hydrostatic pressure is found from a novel linear elliptic equation. This reformulation is shown to extend straightforwardly to multi-layer flows having uniform density layers.
dc.format.extent33
dc.format.extent2039470
dc.language.isoeng
dc.relation.ispartofJournal of Fluid Mechanicsen
dc.subjectShallow water flowsen
dc.subjectGeneral fluid mechanicsen
dc.subjectVortex dynamicsen
dc.subjectQA Mathematicsen
dc.subjectQC Physicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.subject.lccQCen
dc.titleThe validity of two-dimensional models of a rotating shallow fluid layeren
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.institutionUniversity of St Andrews. Marine Alliance for Science & Technology Scotlanden
dc.contributor.institutionUniversity of St Andrews. Scottish Oceans Instituteen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.identifier.doihttps://doi.org/10.1017/jfm.2020.487
dc.description.statusPeer revieweden
dc.date.embargoedUntil2021-02-12
dc.identifier.grantnumberEP/H001794/1en


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