Abstract
Under consideration is the MHD problem of oscillations of a heavy conductive liquid inside a channel with vertical walls in presence of an external horizontal electromagnetic field. We show that the standing surface waves are not damped in the case of symmetric position (with respect to the mid-channel) of the segment affected by a magnetic force. In the case of nonsymmetric position of the active segment, the magnetic force acts selectively on different standing waves. The selectivity condition for each standing wave depends on the width and position of the active segment. We obtain the general conditions for the absence of electromagnetic influence and inspect various special cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. A. Glukhikh, A. V. Tananaev, and I. R. Kirillov, Magnetic Hydrodynamics in Nuclear Power (Energoatomizdat, Moscow, 1987) [in Russian].
K. D. Danov and M. S. Ruderman, “Nonlinear Waves on Shallow Water in the Presence of a Horizontal Magnetic Field,” Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza No. 5, 110–115 (1983) [Fluid Dynamics 18 (5), 751–756 (1983)].
M. Hofman, “Nonlinear Waves on Free Surface of an Electrically Conducting Liquid,” Wave Motion 5 (2), 115–124 (1983).
Yu. N. Gordeev and V. V. Murzenko, “Wave Flows of a Conductive Viscous Fluid Film in a Transverse Magnetic Field,” Prikl. Mat. Tekhn. Fiz. No. 3, 96–100 (1990) [J. Appl. Mech. Techn. Phys. 31 (3), 431–435 (1990)].
A. I. Zadorozhnyi and R. A. Gruntfest, “Natural Oscillations of a Liquid of Finite Electrical Conductivity in the Presence of an External Magnetic Field,” Prikl. Mat. Tekhn. Fiz. 41 (2), 3–10 (2000) [J. Appl. Mech. Techn. Phys. 41 (2), 205–211 (2000)].
A. K. Tomilin, Oscillations of Electromechanical Systems with Distributed Parameters (Vost.-Kazakh. Tekhn. Univ. (VKGTU), Ust’-Kamenogorsk, 2004) [in Russian].
A. K. Tomilin and N. F. Kurilskaya, “Vibrations of a Conductive String in a Nonstationary Magnetic Field under Presence of Two Nonlinear Factors,” Sibir. Zh. Industr. Mat. 20 (4), 61–66 (2017) [J. Appl. Indust. Math. 11 (4), 600–604 (2017)].
N. N. Moiseev and V. V. Rumyantsev, Dynamics of a Body with Cavities Containing a Liquid (Nauka, Moscow, 1965) [in Russian].
G. G. Branover and A. B. Tsinober, Magnetic Hydrodynamics of Incompressible Media (Nauka, Moscow, 1970) [in Russian].
I. I. Novikov, Applied Magnetic Hydrodynamics (Atomizdat, Moscow, 1969) [in Russian].
Author information
Authors and Affiliations
Corresponding authors
Additional information
Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2019, Vol. XXII, No. 2, pp. 94–104.
Rights and permissions
About this article
Cite this article
Tomilin, A.K., Kurilskaya, N.F. Selectivity of Electromagnetic Influence on the Oscillations of a Heavy Conductive Liquid in a Channel. J. Appl. Ind. Math. 13, 363–371 (2019). https://doi.org/10.1134/S1990478919020170
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1990478919020170