Variational generalization of the Green–Naghdi and Whitham equations for fluid sloshing in three-dimensional rotating and translating coordinates
dc.contributor.author | Alemi Ardakani, H | |
dc.date.accessioned | 2021-04-12T07:46:58Z | |
dc.date.issued | 2021-04-16 | |
dc.description.abstract | This paper derives an averaged Lagrangian functional for dynamic coupling between rigid-body motion and its interior shallow-water sloshing in three-dimensional rotating and translating coordinates; with a time-dependent rotation vector. A new set of variational shallow-water equations (SWEs) and generalized Green–Naghdi equations for the interior fluid sloshing with 3–D rotation vector and translations, and also the equations of motion for the linear momentum and angular momentum of the rigid-body containing shallow water, are derived from the averaged Lagrangian functional, which describes a columnar motion, by using Hamilton’s principle and the Euler–Poincare variational ´ framework. The generalized Green–Naghdi equations have a form of potential vorticity (PV) conservation, which can be obtained from the particle-relabeling symmetry, and is a combination of the PV derived by Miles and Salmon (1985) and the PV derived by Dellar & Salmon (2005) for geophysical fluid dynamics problems, where the rotation vector varies spatially. By applying the assumption of zero-potential-vorticity flow to the averaged Lagrangian functional, a new set of Boussinesq-like evolution equations are derived, which are a generalization of the Whitham equations for fluid sloshing in three-dimensional rotating and translating coordinates. Moreover, the new variational principles are appended to Luke’s variational principle to present a unified variational framework for the hydrodynamic problem of interactions between gravity-driven potential-flow water waves and a freely floating rigid-body, dynamically coupled to its interior weakly dispersive nonlinear shallow-water sloshing in three dimensions. | en_GB |
dc.identifier.citation | Vol. 88, pp. 208-227 | en_GB |
dc.identifier.doi | 10.1016/j.euromechflu.2021.04.004 | |
dc.identifier.uri | http://hdl.handle.net/10871/125328 | |
dc.language.iso | en | en_GB |
dc.publisher | Elsevier / European Mechanics Society (Euromech) | en_GB |
dc.rights.embargoreason | Under embargo until 16 April 2022 in compliance with publisher policy | en_GB |
dc.rights | © 2021. This 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.title | Variational generalization of the Green–Naghdi and Whitham equations for fluid sloshing in three-dimensional rotating and translating coordinates | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2021-04-12T07:46:58Z | |
dc.identifier.issn | 0997-7546 | |
dc.description | This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record | en_GB |
dc.identifier.journal | European Journal of Mechanics B/Fluids | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | en_GB |
dcterms.dateAccepted | 2021-04-10 | |
rioxxterms.version | AM | en_GB |
rioxxterms.licenseref.startdate | 2021-04-10 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2021-04-11T14:17:09Z | |
refterms.versionFCD | AM | |
refterms.panel | B | en_GB |
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Except where otherwise noted, this item's licence is described as © 2021. This version is made available under the CC-BY-NC-ND 4.0 license: https://creativecommons.org/licenses/by-nc-nd/4.0/