ABSENCE OF MAGNETOHYDRODYNAMIC ACTIVITY IN THE VOLTAGE-DRIVEN SHEET PINCH

We have numerically studied the bifurcation properties of a sheet pinc h with impenetrable stress-free boundaries. An incompressible, electri cally conducting fluid with spatially and temporally uniform kinematic viscosity and magnetic diffusivity is confined between planes at x(1) =0 and 1. Periodic boundary conditions are assumed in the x(2) and x(3 ) directions and the magnetofluid is driven by an electric field in th e x(3) direction, prescribed on the boundary planes. There is a statio nary basic state with the fluid at rest and a uniform current J=(0,0,J (3)). Surprisingly, this basic state proves to be stable and apparentl y to be the only time-asymptotic state, no matter how strong the appli ed electric field and irrespective of the other control parameters of the system, namely, the magnetic Prandtl number, the spatial periods L (2) and L(3) in the x(2) and x(3) directions, and the mean values <(B) over bar (2)> and <(B)over bar (3)> of the magnetic-field components i n these directions.