Influence of an axial magnetic field on the stability of spherical Couette flows with different gap widths

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 .