Area waves on a slender vortex revisited
dc.contributor.author | Childress, S | |
dc.contributor.author | Gilbert, AD | |
dc.date.accessioned | 2021-06-07T14:38:18Z | |
dc.date.issued | 2021-06-07 | |
dc.description.abstract | This paper considers the classic problem of the dynamics of axisymmetric waves on a rectilinear vortex, in the absence of viscosity. The waves alter the axial pressure distribution and thus generate axial flows which depend on the radial distribution of vorticity. To simplify this problem, models have been introduced which average over the cross-section and eliminate the radial dependence. One approach, pioneered by Lundgren & Ashurst (1989), J. Fluid Mech. 200, 283–307, averages the momentum equation. Another averaging method, due to Leonard (1994), Phys. Fluids 6, 765– 777, focuses on the vorticity equation. The present paper takes a fresh look at the derivation of these two distinct models, which we refer to as the momentum wave model and vorticity wave model respectively, using the tools of differential geometry to develop a hybrid Eulerian–Lagrangian approach. We compare these models with area waves in the asymptotic limit of a slender vortex, with radial structure retained. Numerical calculations are presented to show the differences between waves in the full slender vortex system and those in the momentum and vorticity wave models. We also discuss modification of the vorticity wave model to allow an external irrotational flow, and simulations are presented where a vortex is subjected to uniform axial stretching. Our approach can also be developed to model more complicated configurations, such as occur during vortex collisions. | en_GB |
dc.description.sponsorship | Leverhulme Trust | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
dc.identifier.citation | Vol. 53 (3), article 03550 | en_GB |
dc.identifier.doi | 10.1088/1873-7005/ac08e2 | |
dc.identifier.grantnumber | EP/T023139/1 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/125973 | |
dc.language.iso | en | en_GB |
dc.publisher | IOP Publishing / Japan Society of Fluid Mechanics | en_GB |
dc.rights.embargoreason | Under embargo until 7 June 2022 in compliance with publisher policy | en_GB |
dc.rights | © 2021 The Japan Society of Fluid Mechanics and IOP Publishing Ltd. his version is made available under the CC-BY-NC-ND 4.0 license: https://creativecommons.org/licenses/by-nc-nd/4.0/ | en_GB |
dc.subject | vortex stretching | en_GB |
dc.subject | area waves | en_GB |
dc.subject | Euler equation | en_GB |
dc.subject | Lagrangian coordinates | en_GB |
dc.subject | vortex collision | en_GB |
dc.title | Area waves on a slender vortex revisited | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2021-06-07T14:38:18Z | |
dc.identifier.issn | 0169-5983 | |
dc.description | This is the author accepted manuscript. The final version is available from IOP Publishing via the DOI in this record | en_GB |
dc.identifier.journal | Fluid Dynamics Research | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | en_GB |
dcterms.dateAccepted | 2021-06-07 | |
exeter.funder | ::Leverhulme Trust | en_GB |
exeter.funder | ::Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
rioxxterms.version | AM | en_GB |
rioxxterms.licenseref.startdate | 2021-06-07 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2021-06-07T13:45:37Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2022-06-20T23:00:00Z | |
refterms.panel | B | en_GB |
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Except where otherwise noted, this item's licence is described as © 2021 The Japan Society of Fluid Mechanics and IOP Publishing Ltd. his version is made available under the CC-BY-NC-ND 4.0 license: https://creativecommons.org/licenses/by-nc-nd/4.0/