Geometric approaches to Lagrangian averaging
dc.contributor.author | Gilbert, AD | |
dc.contributor.author | Vanneste, J | |
dc.date.accessioned | 2024-06-26T12:07:44Z | |
dc.date.issued | 2024 | |
dc.date.updated | 2024-06-26T11:08:41Z | |
dc.description.abstract | Lagrangian averaging theories, most notably the Generalised Lagrangian Mean (GLM) theory of Andrews & McIntyre (1978a), have been primarily developed in Euclidean space and Cartesian coordinates. We re-interpret these theories using a geometric, coordinate-free formulation. This gives central roles to the flow map, its decomposition into mean and perturbation maps, and the momentum 1-form dual to the velocity vector. In this interpretation, the Lagrangian mean of any tensorial quantity is obtained by averaging its pull back to the mean configuration. Crucially, the mean velocity is not a Lagrangian mean in this sense. It can be defined in a variety of ways, leading to alternative Lagrangian mean formulations that include GLM and Soward & Roberts’s (2010) glm. These formulations share key features which the geometric approach uncovers. We derive governing equations both for the mean flow and for wave activities constraining the dynamics of the pertubations. The presentation focusses on the Boussinesq model for inviscid rotating stratified flows and reviews the necessary tools of differential geometry. | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
dc.description.sponsorship | Natural Environment Research Council (NERC) | en_GB |
dc.identifier.citation | Awaiting citation and DOI | en_GB |
dc.identifier.grantnumber | EP/T023139/1 | en_GB |
dc.identifier.grantnumber | NE/W002876/1 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/136448 | |
dc.identifier | ORCID: 0000-0002-6940-1801 (Gilbert, Andrew) | |
dc.language.iso | en | en_GB |
dc.publisher | Annual Reviews | en_GB |
dc.rights.embargoreason | Under temporary indefinite embargo pending publication by Annual Reviews. No embargo required on publication | en_GB |
dc.rights | © 2024 by the author(s). For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising | |
dc.subject | wave–mean flow interactions | en_GB |
dc.subject | generalised Lagrangian mean | en_GB |
dc.subject | flow map | en_GB |
dc.subject | pseudomomentum | en_GB |
dc.subject | wave activity | en_GB |
dc.title | Geometric approaches to Lagrangian averaging | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2024-06-26T12:07:44Z | |
dc.identifier.issn | 0066-4189 | |
dc.description | This is the author accepted manuscript | en_GB |
dc.description | Data access statement: No data was produced or analysed in this article. | en_GB |
dc.identifier.eissn | 1545-4479 | |
dc.identifier.journal | Annual Review of Fluid Mechanics | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0 | en_GB |
dcterms.dateAccepted | 2024-04-22 | |
dcterms.dateSubmitted | 2024-03-05 | |
rioxxterms.version | AM | en_GB |
rioxxterms.licenseref.startdate | 2024-04-22 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2024-06-26T11:08:49Z | |
refterms.versionFCD | AM | |
refterms.panel | B | en_GB |
exeter.rights-retention-statement | Yes |
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Except where otherwise noted, this item's licence is described as © 2024 by the author(s). For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising