An investigation of the stability of a magnetohydrodynamic shear layer

Abstract

This paper presents an experimental investigation of the conditions of instability and post-critical flow in an electrically driven shear layer which has been previously studied both theoretically and experimentally. The shear layer forms as a primarily azimuthal flow in an electrically conducting fluid between the edges of two parallel and coaxial circular electrodes, mounted in insulating planes, when a current is passed between them in the presence of a strong, axially applied magnetic field. The aximuthal velocity at any radial position in the layer is maximum near the electrode planes and decreases to zero at the centreplane between the electrodes. Radial and axial secondary velocity components apparently exist, though smaller in magnitude than the azimuthal velocity throughout most of the layer.

The experiments employ a miniature hot-film sensor as an instantaneous velocity indicator in mercury. The following experimental results are reported. \begin{eqnarray*} & R_c = 2420,\quad 150 \leqslant M \leqslant 350,\\ & R_c = 345\,M^{\frac{1}{3}},\quad 350\leqslant M \leqslant 650, \end{eqnarray*} where R_c is the critical Reynolds number of the shear layer, based upon the maximum velocity in the layer and the layer thickness, and M is the Hartmann number based upon the distance from the electrodes to the centreplane. For values of M below about 300, oscillograms of the hot-film signal show that the layer goes unstable in a chaotic fashion. For M ≥ 300, however, the instabilities grow to produce a wave-like post-critical flow of steady amplitude. The waves are apparently parallel to the applied magnetic field and drift in the azimuthal direction at a constant proportion (10–15%) of the critical velocity. The maximum intensity of the peak to peak fluctuations from the measured mean azimuthal velocity appears to be about 0·05. These fluctuations decrease to zero at the centreplane. By an approximate measurement of wavelength it is determined that the integral number of waves in the post-critical flow increases with M.

The physical mechanism governing the onset of instability has not been established. The manner in which hydrodynamic and electromagnetic forces interact with the destabilizing disturbances cannot be fully understood without further theoretical analysis.