Scholle, Markus and Marner, Florian and Gaskell, Philip (2020) 'Potential fields in fluid mechanics : a review of two classical approaches and related recent advances.', Water., 12 (5). p. 1241.
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.
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|Publisher Web site:||https://doi.org/10.3390/w12051241|
|Publisher 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.|
|Date accepted:||24 April 2020|
|Date deposited:||28 April 2020|
|Date of first online publication:||27 April 2020|
|Date first made open access:||28 April 2020|
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