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doi:10.22028/D291-36767
Title: | A variational formulation for steady surface water waves on a Beltrami flow |
Author(s): | Groves, Mark Horn, Jens |
Language: | English |
Title: | Proceedings of the Royal Society of London, Series A: Mathematical, physical and engineering sciences |
Volume: | 476 |
Issue: | 2234 |
Publisher/Platform: | Royal Society |
Year of Publication: | 2020 |
Free key words: | calculus of variations Beltrami flows water waves |
DDC notations: | 510 Mathematics 530 Physics |
Publikation type: | Journal Article |
Abstract: | This paper considers steady surface waves ‘riding’ a Beltrami flow (a three-dimensional flow with parallel velocity and vorticity fields). It is demonstrated that the hydrodynamic problem can be formulated as two equations for two scalar functions of the horizontal spatial coordinates, namely the elevation η of the free surface and the potential Φ defining the gradient part (in the sense of the Hodge–Weyl decomposition) of the horizontal component of the tangential fluid velocity there. These equations are written in terms of a non-local operator H(η) mapping Φ to the normal fluid velocity at the free surface, and are shown to arise from a variational principle. In the irrotational limit, the equations reduce to the Zakharov–Craig–Sulem formulation of the classical three-dimensional steady water-wave problem, while H(η) reduces to the familiar Dirichlet–Neumann operator. |
DOI of the first publication: | 10.1098/rspa.2019.0495 |
URL of the first publication: | https://royalsocietypublishing.org/doi/10.1098/rspa.2019.0495 |
Link to this record: | urn:nbn:de:bsz:291--ds-367671 hdl:20.500.11880/33409 http://dx.doi.org/10.22028/D291-36767 |
ISSN: | 1471-2946 1364-5021 |
Date of registration: | 12-Jul-2022 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Professorship: | MI - Prof. Dr. Mark Groves |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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