Abstract
A study is made of the gravitational instability of the interface between two incompressible liquids in an electromagnetic field parallel to the interface when one of the liquids has a finite conductivity and the other is nonconducting. The magnetic Reynolds number Rm is assumed to be finite. It is shown that for all Rm, the electromagnetic field cannot stabilize the interface (if both liquids conduct, there is also no stabilization), although there may exist stable directions of propagation of perturbations. The greatest growth rate of perturbations corresponds to waves propagating at right angles to the vector of the initial magnetic field, and the electromagnetic field and conductivity of the walls do not affect these perturbations. The small-parameter method is used to obtain a dispersion relation for the small induced magnetic fields. It is shown that the range of angles between the wave vector and the vector of the initial magnetic field that correspond to unstable perturbations is greater than in the case when Pm ≪ 1 [1].
Similar content being viewed by others
Literature cited
M. V. Shchelkachev, “Taylor instability of the interface between two liquids in an electromagnetic field,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5 (1976).
Dak Nguen, “Study of Rayleigh-Taylpr instability in magnetohydrodynamics,” Pryamoe Preobrazovanie Teplovoi Énergii v Élektricheskuyu, i Toplivnye Élementy, No. 7 (1968).
H. Lamb, Hydrodynamics, Dover (1932).
L. E. Él'sgol'ts, Differential Equations and Variational Calculus [in Russian], Nauka, Moscow (1965).
A. B. Varazhin, G. A. Lyubimov, and S. A. Regirer, Magnetohydrodynamic Flows in Channels [in Russian], Nauka, Moscow (1970).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 118–121, November–December, 1979.
I thank A. A. Barmin and A. G. Kulikovskii for constant interest in the work.
Rights and permissions
About this article
Cite this article
Shchelkachev, M.V. Taylor instability in an electromagnetic field. Fluid Dyn 14, 909–912 (1979). https://doi.org/10.1007/BF01051996
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01051996