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Scholle, Markus ; Haas, André ; Gaskell, Philip H.:
A first integral of Navier–Stokes equations and its applications.
In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
Bd. 467
(2011)
Heft 2125
.
- S. 127-143.
ISSN 1364-5021
DOI: https://doi.org/10.1098/rspa.2010.0157
Abstract
Although it is well known that Bernoulli’s equation is obtained as the first integral of Euler’s equations in the absence of vorticity and that in the case of non-vanishing vorticity a first integral of them can be found using the Clebsch transformation for inviscid flow, generalization of the procedure for viscous flow has remained elusive. Accordingly, in this paper, a first integral of the Navier–Stokes equations for steady flow is constructed. In the case of a two-dimensional flow, this is made possible by formulating the governing equations in terms of complex variables and introducing a new scalar potential. Associated boundary conditions are considered, and an extension of the theory to three dimensions is proposed. The capabilities of the new approach are demonstrated by calculating a Reynolds number correction to the laminar shear flow generated in the narrow gap between a flat moving and a stationary wavy wall, as is often encountered in lubrication problems. It highlights the first integral as a suitable tool for the development of new analytical and numerical methods in fluid dynamics.
Weitere Angaben
| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Institutionen der Universität: | Fakultäten > Fakultät für Ingenieurwissenschaften > Lehrstuhl Technische Mechanik und Strömungsmechanik Fakultäten Fakultäten > Fakultät für Ingenieurwissenschaften |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften |
| Eingestellt am: | 18 Nov 2015 14:17 |
| Letzte Änderung: | 18 Nov 2015 14:17 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/22632 |