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A first integral of Navier–Stokes equations and its applications

Title data

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. Vol. 467 (2011) Issue 2125 . - pp. 127-143.
ISSN 1364-5021
DOI: https://doi.org/10.1098/rspa.2010.0157

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties > Faculty of Engineering Science > Chair Applied Mechanis and Fluid Dynamics
Faculties > Faculty of Engineering Science
Result of work at the UBT: Yes
DDC Subjects: 600 Technology, medicine, applied sciences > 620 Engineering
Date Deposited: 18 Nov 2015 14:17
Last Modified: 18 Nov 2015 14:17
URI: https://eref.uni-bayreuth.de/id/eprint/22632