Please use this identifier to cite or link to this item: doi:10.22028/D291-36767
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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:
Link to this record: urn:nbn:de:bsz:291--ds-367671
ISSN: 1471-2946
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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