This paper deals with the linear instability analysis of the spherical Couette flow of an electrically conducting fluid in the presence of an axial magnetic field. The numerical investigations are performed for different ratios, η = 0.5 and η = 0.6, and compared with Hollerbach's work for η = 0.33 (Hollerbach in Proc R Soc 465:2003, 2009). The corresponding instability diagrams, i.e., the critical values of the Reynolds number Re, the wave number, and the frequency on the Hartmann number Ha, are presented and accompanied by simulation of the transition between three-dimensional flow states of different symmetries. The characteristic subdivision of the linear stability curves into anti-symmetric modes, which is responsible for the instability at small Ha, and symmetric modes occurring at higher Ha is found for larger η, too. However, the extension of the stability corridor between the anti-symmetric and the symmetric modes increases nonlinearly with η. This offers the possibility to stabilize the basic flow up to high Re by appropriately increasing Ha.
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机译：本文研究了在存在轴向磁场的情况下导电流体的球形库埃特流的线性不稳定性分析。对不同的比率η= 0.5和η= 0.6进行了数值研究，并将其与η= 0.33的Hollerbach的工作进行了比较（Hollerbach，Proc R Soc 465：2003，2009）。给出了相应的不稳定性图，即雷诺数Re，波数和Hartmann数Ha上的频率的临界值，并模拟了不同对称的三维流动状态之间的过渡。线性稳定性曲线的特征细分为反对称模式，这是造成小Ha处的不稳定性的原因，而对于高η而言，在高Ha处也会出现对称模式。但是，反对称和对称模式之间的稳定通道的扩展随η非线性增加。这提供了通过适当增加Ha来将基本流量稳定到高Re的可能性。
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