Damping rate of magnetohydrodynamic vortices at low magnetic Reynolds number

Abstract

The damping rate of vortices in an electrically conducting fluid submitted to a uniform magnetic field is analyzed for a large Hartmann number Ha. The fluid is contained in a layer of constant thickness h, bounded by two insulating walls that are perpendicular to the magnetic field. The damping times and the eigenfunctions along the magnetic field are obtained from a linear eigenvalue problem. According to the damping times and these eigenfunctions, vortices are classified into several classes by the range of combinations of the mode number m in the magnetic field direction and the wave number k2D in the plane perpendicular to the magnetic field. It is found that the damping rate of vortices in the range of k2D∼[(m+12)πHa]1∕2h−1 and m=0,1,2 is of the same order as that of large-scale two-dimensional vortices. This fact suggests that actual quasi-two-dimensional magnetohydrodynamic turbulent flows include not only m=0 but also higher-mode (m⩾1) eigenfunctions of this wave-number range, although the eigenfunction of m=0 has a 30% variation and the higher-mode eigenfunctions change their sign along the magnetic field.