The present paper investigates numerically the hydrodynamic instabilities occurring in a cylindrical container filled with a conducting viscous fluid and submitted to an axial magnetic field. The axisymmetric swirling flow produced by rotation of the bottom disk, in which a vortex breakdown bubble occurred on the axis of symmetry. This flow structure represents one of the most important instabilities. The governing Navier–Stokes and potential equations are solved by using the finite-volume method. For both steady-state and oscillatory regimes, various combinations of the top, bottom, and side walls conductivity are considered. The effects of the magnetic field and wall electrical conductivities on the position of vortex breakdown and his disappearance is developed. The results obtained showed that the vortex breakdown is suppressed beyond the magnitude of the magnetic field exceeds a critical value. The stability diagram (Ha${}_{cr}$–Re) corresponding to the vortex breakdown disappearance for electrically conducting and insulating walls is obtained.

本文从数值上研究了在装有导电粘性流体并受到轴向磁场作用的圆柱形容器中发生的水动力不稳定性。由底盘旋转产生的轴对称旋流，其中在对称轴上出现了涡旋破裂气泡。这种流动结构代表了最重要的不稳定性之一。使用有限体积方法可以解决控制Navier–Stokes和势能方程。对于稳态和振荡状态，都应考虑顶，底和侧壁电导率的各种组合。研究了磁场和壁电导率对涡旋击穿位置及其消失的影响。所获得的结果表明，在超过磁场强度超过临界值的情况下，涡旋破坏得到了抑制。稳定性图（哈${}_{C\mathrm{[R}}$-Re）对应于导电壁和绝缘壁的涡旋击穿消失。