| Abstract: | The analog of Orr's problem is formulated for MHD flows. Arbitrary three-dimensional disturbances satisfying the continuity equations are considered. It is established that direct interaction of the disturbances of the magnetic field and the velocity field cannot increase the energy estimate of the critical Reynolds number. Numerical calculations for Hartmann flow and modified Couette flows are made for the particular case of small magnetic Reynolds numbers, The minimum value of R is attained for disturbances with a wave vector perpendicular to the velocity vector of the main flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–9, July–August, 1971.The authors thank M. A. Gol'dshtik for his interest in their work. |
