Email this article Non-helical exact solutions to the Euler equations for swirling axisymmetric fluid flows
- Authors: Prosviryakov E.Y.1,2
-
Affiliations:
- Institute of Engineering Science, Urals Branch, Russian Academy of Sciences
- Ural Federal University named after the First President of Russia B. N. Yeltsin
- Issue: Vol 23, No 4 (2019)
- Pages: 764-770
- Section: Articles
- URL: https://journals.rcsi.science/1991-8615/article/view/34672
- ID: 34672
Cite item
Full Text
Abstract
Swirling axisymmetric stationary flows of an ideal incompressible fluid are considered within the framework of the Euler equations. A number of new exact solutions to the Euler equations are presented, where, as distinct from the known Gromeka–Beltrami solutions, vorticity is noncollinear with velocity. One of the obtained solutions corresponds to the flow inside a closed volume, with the nonpermeability condition fulfilled at its boundary, the vector lines of vorticity being coiled on revolution surfaces homeomorphic to a torus.
Full Text
##article.viewOnOriginalSite##About the authors
Eugenii Yurevich Prosviryakov
Institute of Engineering Science, Urals Branch, Russian Academy of Sciences; Ural Federal University named after the First President of Russia B. N. Yeltsin
Email: evgen_pros@mail.ru
Doctor of physico-mathematical sciences, no status
References
- Arnold V. I., "Sur la topologie des ecoulements stationnaires des fluides parfaits", Vladimir I. Arnold - Collected Works, v. 2, A. Givental, et all. , Springer, Berlin, Heidelberg, 1965, 15-18
- Kozlov V. V., "Notes on steady vortex motions of continuous medium", J. Appl. Math. Mech., 47:2 (1983), 288-289
- Kozlov V. V., General Vortex Theory, Udmurtia Univ., Izhevsk, 1998, 238 pp. (In Russian)
- Sizykh G. B., "Helical vortex lines in axisymmetric viscous incompressible fluid flow", Fluid Dyn., 54:8 (2019), 1038-1042
- Gromeka I. S., Collected works, Acad. Sci. USSR, Moscow, 1952, 296 pp. (In Russian)
- Beltrami E., "Considerazioni idrodinamiche", Rend. Inst. Lombardo Acad. Sci. Lett., 22 (1889), 122-131
- Sizykh G. B., "Axisymmetric Helical Flows of Viscous Fluid", Russian Mathematics, 63:2 (2019), 44-50
- Meissel E., "Über den Ausfluss des Wassers aus Gefässen in zwei besonderen Fällen nach Eintritt des Beharrungszustandes", Grunert Arch., 55 (1873), 241-252 (In German)
- Batchelor G. K., An Introduction to Fluid Dynamics, Cambridge Univ. Press, Cambridge, 1999, xvii+615 pp
- Loitsyanskii L. G., Mechanics of Liquids and Gases, Pergamon Press, Oxford, 1972, xii+802 pp.
Supplementary files
