Numerical bifurcation analysis of a voltage-driven electrically conducting fluid

We study numerically the bifurcation from the quiescent ground state of an incompressible, viscous, electrically conducting fluid confined between stress-free plane boundaries at x 1 = 0,1 and driven by an ezternal electric field in the x 3 direction. If the electrical conductivity is uniform and thus the magnetic field profile across the sheet linear, the ground state remains stable, no matter how strong the driving electric field and irrespective of the values of other system parameters. If, however, the conductivity profile is chosen such that the ground state is the Harris sheet with the magnetic field profile B 2 (x 1 ) ∼ tanh(x 1 - 0.5)/a), instability is found for a? 0.4. The bifurcating new time-asymptotic states calculated for a two-dimensional special case are of the tearing-mode type, characterized by a chain of magnetic islands and fluid motion in convection rolls.