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Potential Fields in Fluid Mechanics: A Review of Two Classical Approaches and Related Recent Advances

Scholle, Markus; Marner, Florian; Gaskell, Philip

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Authors

Markus Scholle

Florian Marner



Abstract

The use of potential fields in fluid dynamics is retraced, ranging from classical potential theory to recent developments in this evergreen research field. The focus is centred on two major approaches and their advancements: (i) the Clebsch transformation and (ii) the classical complex variable method utilising Airy’s stress function, which can be generalised to a first integral methodology based on the introduction of a tensor potential and parallels drawn with Maxwell’s theory. Basic questions relating to the existence and gauge freedoms of the potential fields and the satisfaction of the boundary conditions required for closure are addressed; with respect to (i), the properties of self-adjointness and Galilean invariance are of particular interest. The application and use of both approaches is explored through the solution of four purposely selected problems; three of which are tractable analytically, the fourth requiring a numerical solution. In all cases, the results obtained are found to be in excellent agreement with corresponding solutions available in the open literature.

Citation

Scholle, M., Marner, F., & Gaskell, P. (2020). Potential Fields in Fluid Mechanics: A Review of Two Classical Approaches and Related Recent Advances. Water, 12(5), Article 1241. https://doi.org/10.3390/w12051241

Journal Article Type Article
Acceptance Date Apr 24, 2020
Online Publication Date Apr 27, 2020
Publication Date May 31, 2020
Deposit Date Apr 27, 2020
Publicly Available Date Apr 28, 2020
Journal Water
Electronic ISSN 2073-4441
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 12
Issue 5
Article Number 1241
DOI https://doi.org/10.3390/w12051241
Public URL https://durham-repository.worktribe.com/output/1272075

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Published Journal Article (1.8 Mb)
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
© This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.






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