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A first Integral of NavierStokes equations for two‐dimensional flows
Author(s) -
Scholle M.,
Haas A.
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010234
Subject(s) - inviscid flow , bernoulli's principle , euler equations , vorticity , mathematics , mathematical analysis , integral equation , euler's formula , flow (mathematics) , representation (politics) , boundary (topology) , vortex , classical mechanics , physics , geometry , mechanics , politics , political science , law , thermodynamics
As wellknown, Bernoulli's equation is obtained as the first integral of Euler's equations in the absence of vorticity. Even in case of non‐vanishing vorticity, a first integral from Euler's equations is obtained by using the so called Clebsch transformation [1] for inviscid flows. In contrast to this, a generalisation of this procedure towards viscous flows has not been established so far. In the present paper a first integral of Navier‐Stokes equations is constructed in the case of two‐dimensional flow by making use of an alternative representation of the fields in terms of complex coordinates and introducing a potential representation for the pressure. The associated boundary conditions are also considered. The first integral is a suitable tool for the development of new analytical methods and numerical codes in fluid dynamics. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)