Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2015-6pp.566-571

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V.N. Golubkin, V.V. Markov, and G.B. Sizykh, "The integral invariant of the equations of motion of a viscous gas," J. Appl. Math. Mech. 79 (6), 566-571 (2015)
Year 2015 Volume 79 Issue 6 Pages 566-571
DOI 10.1016/j.jappmathmech.2016.04.002
Title The integral invariant of the equations of motion of a viscous gas
Author(s) V.N. Golubkin (Central Aerohydrodynamic Institute, Zhukovskii, Russia, vgolubkin@ou-link.ru)
V.V. Markov (V.A. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia, markov@mi.ras.ru)
G.B. Sizykh (Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia, o1o2o3@yandex.ru)
Abstract An expression for the velocity of motion of a simple vortex contour for which the circulation of the fluid velocity is preserved in it is obtained in the general three-dimensional case for the flow of a viscous gas or liquid. The velocity of motion of the contour at each point is calculated from the values of the flow parameters and their derivatives at the same point. This result extends Thomson's theorem, which is well known for an ideal barotropic fluid. A previously unknown conservation property is found, which consists of the fact that the circumferential circulation of the swirling axisymmetric flow in the potential field of mass forces is the first integral of the equations of unsteady flow of a non-barotropic ideal gas.
Received 22 April 2015
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