Abstract In this paper, we derive new shallow asymptotic models for the free boundary plasma-vacuum problem governed by magnetohydrodynamic equations which are vital when describing large-scale processes in flows of astrophysical plasma. More precisely, present magnetic analogue 2D Green–Naghdi water waves under a weak pressure assumption presence weakly sheared vorticity and currents. Our meth...

A flow of electrically conducting fluid in the presence of a steady magnetic field has a tendency to become quasi two-dimensional, i.e. uniform in the direction of the magnetic field, except in thin so-called Hartmann boundary layers. The condition for this tendency is that of a strong magnetic field, corresponding to large values of the dimensionless Hartmann number (Ha >> 1). This is analogou...