Taylor instability in an electromagnetic field

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 R_m is assumed to be finite. It is shown that for all R_m, 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 P_m 1 [1].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.