Abstract
The subject considered is a homogeneous electrically conducting incompressible medium with a current in a homogeneous external magnetic field and bounded by parallel insulating planes normal to the induction vector. When the current is fed by means of a system of coaxial electrodes located on one or both of the insulating planes, regions arise in which the medium is in rotational motion. If the lateral wall is at a sufficient distance from the electrodes, the rotating layer which forms as a result of the interaction of the axial magnetic field and the radial component of the electric current has free lateral boundaries. A study is made of the way in which the Reynolds number for the loss of stability in such a layer depends on the Hartmann number and on the geometric parameter for high values of the Hartmann number and low values of the magnetic Reynolds number.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
T. G. Cowling, Magnetohydrodynamics, New York (1957).
S. I. Braginskii, “On the magnetohydrodynamics of weakly conducting fluids,” Zh. Eksp. Teor. Fiz.,37, 1417 (1959).
J. C. R. Hunt and W. E. Williams, “Some electrically driven flows in magnetohydrodynamics. Pt. 1. Theory,” J. Fluid Mech.,31, 705 (1968).
J. C. R. Hunt and D. G. Malcolm, “Some electrically driven flows in magnetohydrodynamics. Pt. 2. Theory and experiment,” J. Fluid Mech.,33, 775 (1968).
J. C. R. Hunt and J. A. Shercliff, “Magnetohydrodynamics at high Hartmann number,” Ann. Rev. Fluid Mech.,3, 37 (1971).
B. Lehnert, “An instability of laminar flow of mercury caused by an external magnetic field,” Proc. R. Soc. London Ser. A,233, 299 (1955).
D. G. Malcolm, “An investigation of the stability of a magnetohydrodynamic shear layer,” J. Fluid Mech.,41, 531 (1970).
A. Brahme, “On the hydromagnetic stability of a nonuniformly rotating fluid,” Phys. Scr.,2, 108 (1970).
V. B. Levin, “A free rotating layer of an electrically conducting fluid in an axial magnetic field,” Magn. Gidrodin., No. 1, 86 (1980).
A. A. Klyukin, Yu. B. Kolesnikov, and V. B. Levin, “Experimental investigation of a free rotating layer in an axial magnetic field. 2. The stability boundary and the structure of the perturbations,” Magn. Gidrodin., No. 1, 140 (1980).
A. A. Klyukin, Yu. B. Kolesnikov, and V. B. Levin, “Experimental investigation of a free rotating layer in an axial magnetic field. 1. Stable working,” Magn. Gidrodin., No. 1, 93 (1980).
A. S. Monin and A. M. Yaglom, Statistical Hydromechanics, Pt. 1 [in Russian], Nauka, Moscow (1965).
V. M. Ievlev, The Turbulent Motion of High Temperature Continuous Media [in Russian], Nauka, Moscow (1975).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 166–173, September–October, 1984.
Rights and permissions
About this article
Cite this article
Klyukin, A.A., Levin, V.B. The stability of a free rotating layer in an electrically conducting fluid in an axial field. Fluid Dyn 19, 815–822 (1984). https://doi.org/10.1007/BF01093554
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01093554