Abstract
This paper considers wave processes in a centrifuged layer of an incompressible viscous conducting fluid in an axial magnetic field in the cavity of a rapidly rotating infinite cylinder with insulating walls. Inertial modes (solutions of the linearized boundary-value problem of magnetohydrodynamics) are represented as a superposition of helical fields. Expressions for the vorticity parameters of the helical flows forming the inertial mode at a small Stewart number are given. Dispersion curves of inertial waves are constructed, and the influence of the magnetic field on the flow field is analyzed. The critical frequencies at which the lowest (surface) mode arises are determined. The spatial and temporal stability of the modes are investigated.
Similar content being viewed by others
References
N. N. Moiseev and V. V. Rumyantsev, Dynamics of a Body with Cavities Containing a Fluid (Nauka, Moscow, 1965) [in Russian].
N. V. Derendyaev and V. M. Sandalov, “Stability of Stationary Rotation of a Rotor Filled with a Stratified Viscous Incompressible Fluid,” Mashinovedenie, No. 1, 19–26 (1986).
L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Nauka, Moscow, 1986; London, Pergamon Press, 1959).
H. P. Greenspan, The Theory of Rotating Fluids (Cambridge Univ. Press, 1968).
N. D. Kopachevsky, S. G. Krein, and Ngo Zuy Can, Operator Methods in Linear Hydrodynamics: Evolutionary and Spectral Problems (Nauka, Moscow, 1989) [in Russian].
S. V. Alekseenko, P. A. Kuibin, and V. L. Okulov, Introduction to the Theory of Concentrated Vortices (Institute of Computer Studies, Izhevsk, 2005) [in Russian].
S. D. Nigam and P. D. Nigam, “Magnetohydrodynamic Waves in Rotating Fluids,” Proc. Roy. Soc. London, Ser. A. 272, 529–541 (1963).
N. V. Saltanov, “Generalized Potential in the Theory of Homogeneous Helical Incompressible Fluid Flows,” Dokl. Akad. Nauk SSSR 305 (6), 1325–1327 (1989).
I. N. Soldatov, “Gyroscopic Waves in a Rotating Liquid Layer,” Prikl. Mech. Tech. Fiz. 49 (2), 15–20 (2008) [Appl. Mech. Tech. Phys. 49 (2), 161–171 (2008)].
O. F. Vasil’ev, Fundamentals of Mechanics of Helical and Circulation Flows (Gosenergoizdat, Moscow–Leningrad, 1958) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.V. Klueva, V.M. Sandalov, M.E. Tkach, I.N. Soldatov.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 3, pp. 30–38, May–June, 2015.
Rights and permissions
About this article
Cite this article
Klueva, N.V., Sandalov, V.M., Tkach, M.E. et al. Magnetic field effect on waves in a centrifuged layer of a rotating conducting viscous fluid. J Appl Mech Tech Phy 56, 369–376 (2015). https://doi.org/10.1134/S0021894415030049
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894415030049