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dc.contributor.authorDritschel, David Gerard
dc.contributor.authorJalali, Mohammad Reza
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 .
dc.identifier.otherPURE: 268469171
dc.identifier.otherPURE UUID: 2947fc33-1ea9-4d04-a760-c3d19390a5da
dc.identifier.otherORCID: /0000-0001-6489-3395/work/79917920
dc.identifier.otherScopus: 85090011171
dc.identifier.otherWOS: 000558733100001
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.relation.ispartofJournal of Fluid Mechanicsen
dc.rightsCopyright © The Author(s), 2020. Published by Cambridge University Press. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectShallow water flowsen
dc.subjectGeneral fluid mechanicsen
dc.subjectVortex dynamicsen
dc.subjectQA Mathematicsen
dc.subjectQC Physicsen
dc.titleThe validity of two-dimensional models of a rotating shallow fluid layeren
dc.typeJournal articleen
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.description.statusPeer revieweden

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