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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2013, Volume 54, Issue 4, Pages 33–44 (Mi pmtf1155)  

Stationary cylindrical vortex in a viscous electrically conducting fluid

A. N. Baikina, S. V. Golovinb

a Novosibirsk State University, Novosibirsk, 630090, Russia
b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia
Abstract: An exact solution of the magnetohydrodynamic equations is constructed which describes steady vortex flow in a stationary cylinder on the axis of which a conductor carrying a known current is located. The solution is obtained under the assumption that the fluid is viscous and has finite electrical conductivity and that the magnetic field has only the axial and azimuthal components in a cylindrical coordinate system. It is found that the action of the Lorentz force is compensated by changing the pressure. Fluid flow occurs from the periphery to the axis of the cylinder under a pressure gradient, with flow rotation and swirling. The fluid flow causes a concentration of the magnetic lines near the axis of the cylinder, providing an exponential decrease in the magnetic field strength with distance from the axis. This flow can be considered as a model of a local increase in the magnetic field strength due to the transfer of its force lines by the flow of the electrically conducting fluid.
Keywords: cylindrical vortex, electrically conducting fluid, magnetic hydrodynamics, exact solutions.
Received: 26.12.2012
English version:
Journal of Applied Mechanics and Technical Physics, 2013, Volume 54, Issue 4, Pages 541–551
DOI: https://doi.org/10.1134/S0021894413040044
Bibliographic databases:
Document Type: Article
UDC: 533
Language: Russian
Citation: A. N. Baikin, S. V. Golovin, “Stationary cylindrical vortex in a viscous electrically conducting fluid”, Prikl. Mekh. Tekh. Fiz., 54:4 (2013), 33–44; J. Appl. Mech. Tech. Phys., 54:4 (2013), 541–551
Citation in format AMSBIB
\Bibitem{BaiGol13}
\by A.~N.~Baikin, S.~V.~Golovin
\paper Stationary cylindrical vortex in a viscous electrically conducting fluid
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2013
\vol 54
\issue 4
\pages 33--44
\mathnet{http://mi.mathnet.ru/pmtf1155}
\elib{https://elibrary.ru/item.asp?id=20181187}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2013
\vol 54
\issue 4
\pages 541--551
\crossref{https://doi.org/10.1134/S0021894413040044}
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