TOROIDAL VISCO-RESISTIVE MAGNETOHYDRODYNAMIC STEADY-STATES CONTAIN VORTICES

Poloidal velocity fields seem to be a fundamental feature of resistive toroidal magnetohydrodynamic (MHD) steady states. They are a conseque nce of force balance in toroidal geometry, do not require any kind of instability, and disappear in the ''straight cylinder'' (infinite aspe ct ratio) limit. If a current density j results from an axisymmetric t oroidal electric field that is irrotational inside a torus, it leads t o a magnetic field B such that del x (j x B) is nonvanishing, so that the Lorentz force cannot be balanced by the gradient of any scalar pre ssure in the equation of motion. In a steady state, finite poloidal ve locity fields and toroidal vorticity must exist. Their calculation is difficult, but explicit solutions can be found in the limit of low Rey nolds number. Here, existing calculations are generalized to the more realistic case of no-slip boundary conditions on the velocity field an d a circular toroidal cross section. The results of this paper strongl y suggest that discussions of confined steady states in toroidal MHD m ust include flows from the outset. (C) 1998 American Institute of Phys ics. [S1070-664X(98)02407-0].