The divergence-free condition in axisymmetric magnetohydrodynamic models

Axisymmetric magnetohydrodynamic (MHD) models are useful in studies of magnetized winds and non-linear Alfvén waves in solar and stellar atmospheres. We demonstrate that a condition often used in these models for the determination of a nearly vertical magnetic field is applicable to a radial field instead. A general divergence-free condition in curvilinear coordinates is self-consistently derived and used to obtain the correct condition for the variation of a nearly vertical magnetic field. The obtained general divergence-free condition along with the transfield equation completes the set of MHD equations in curvilinear coordinates for axisymmetric motions and could be useful in studies of magnetized stellar winds and non-linear Alfvén waves.