Super-Speeding Jets in MHD Couette Flow

Abstract

A magnetohydrodynamic flow of a viscous and conducting fluid confined between two parallel differentially moving boundaries is considered. The whole system is in a strong magnetic field chosen in such a way that the Hartmann boundary layers which form in this problem become singular at the points where the magnetic field becomes tangent to the boundary. Two geometriesaretaken into account: plane and spherical . Withinthe classof such configurations, the velocity field of the fluid and the influence of the conductivity of the boundaries on the fluid ’ s motion are reviewed here. In the region of singularity, where the magnetic field is tangent to the boundary, the fluid ’ s velocity exceeds that of the moving boundary. The effect of nonzero conductivity of the boundaries on the super-speeding jets is vital and has been enlightened in a series of papers, including experimental and theoretical findings.The mechanism of the formation of super-speeding jets in the consideredconfigura- tions has been explained, which is based on strong Hartmann currents allowed to enter the boundarylayerduetothesingularity.Inthecaseofbothperfectlyconductingboundaries,the super velocity wasshown to beasstrong asto scale with theHartmannnumberas O M 1 = 2 (cid:1) (cid:3) .