Inhibition of Hydrodynamic Instability by an Electric Current

Abstract

The inhibition of instability of a viscous fluid contained in a circular cylinder and heated from below by an electric current is investigated. Previous results indicate that, for a thermally nonconducting wall, the critical Rayleigh number is 452.1 for symmetric convection, and 67.9 for the first (and critical) mode of unsymmetric convection. It has been found in this investigation that unsymmetric convections can be delayed or completely inhibited by an electric current, whereas symmetric convection is not at all affected. This indicates a very interesting physical situation at Rayleigh number 452.1, for an electric current just strong enough to inhibit unsymmetric convection. If the current is slightly increased, only symmetric motion will occur. If it is slightly decreased, unsymmetric convection, being more unstable, will prevail. Thus the physically significant solution of a differential system may have a sudden change of behavior at certain critical values of its parameters.