Show simple item record

Files in this item


Item metadata

dc.contributor.authorDritschel, Heidi Jessica
dc.contributor.authorDritschel, David Gerard
dc.contributor.authorCarr, Magda
dc.identifier.citationDritschel , H J , Dritschel , D G & Carr , M 2023 , ' A conformal mapping approach to modelling two-dimensional stratified flow ' , Journal of Computational Physics: X , vol. 17 , 100129 .
dc.identifier.otherPURE: 286643445
dc.identifier.otherPURE UUID: c45384af-d3ff-4433-b85c-221586f86a08
dc.identifier.otherORCID: /0000-0001-6489-3395/work/137088891
dc.identifier.otherScopus: 85161697732
dc.descriptionFunding: This research received support from the UK Engineering and Physical Sciences Research Council (Impact Acceleration Account, both at the University of St Andrews and Newcastle University). This research received support from the UK Engineering and Physical Sciences Research Council (grants EP/R511778/1 and EP/R511584/1).en
dc.description.abstractHerein we describe a new approach to modelling inviscid two-dimensional stratified flows in a general domain. The approach makes use of a conformal map of the domain to a rectangle. In this transformed domain, the equations of motion are largely unaltered, and in particular Laplace's equation remains unchanged. This enables one to construct exact solutions to Laplace's equation and thereby enforce all boundary conditions. An example is provided for two-dimensional flow under the Boussinesq approximation, though the approach is much more general (albeit restricted to two-dimensions). This example is motivated by flow under a weir in a tidal estuary. Here, we discuss how to use a dynamically-evolving conformal map to model changes in the water height on either side of the weir, though the example presented keeps these heights fixed due to limitations in the computational speed to generate the conformal map. The numerical approach makes use of contour advection, wherein material buoyancy contours are advected conservatively by the local fluid velocity, while a dual contour-grid representation is used for the vorticity in order to account for vorticity generation from horizontal buoyancy gradients. This generation is accurately estimated by using the buoyancy contours directly, rather than a gridded version of the buoyancy field. The result is a highly-accurate, efficient numerical method with extremely low levels of numerical damping.
dc.relation.ispartofJournal of Computational Physics: Xen
dc.rightsCopyright © 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (
dc.subjectContour advectionen
dc.subjectConformal transformationen
dc.subjectLagrangian methodsen
dc.subjectDensity stratified flowsen
dc.subjectTurbulent flowsen
dc.subjectQA Mathematicsen
dc.subjectQC Physicsen
dc.titleA conformal mapping approach to modelling two-dimensional stratified flowen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
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

This item appears in the following Collection(s)

Show simple item record