Inertial modes, turbulence and magnetic effects in a differentially rotating spherical shell

The study of a fluid trapped inside a spherical shell is of fundamental interest in fluid mechanics, having given rise to numerous theoretical and experimental studies. This is also a geometric feature shared by geo- and astrophysical objects such as the interior and atmosphere of the Earth, the interiors of stars, gas giants, exoplanets and so on. Driven by these motivations, the present work builds over past studies of the spherical Couette system - two concentric differentially rotating spheres with the space in between filled with a fluid. Despite the numerous theoretical and experimental investigations, several aspects of this system still remain elusive. Examples are the origin of special instabilities called ‘inertial modes’, transition to turbulence and the effect of magnetic fields on inertial modes. In the first part of this work, numerical simulations are compared with experiments. The focus is mainly on the origin of inertial modes in the system which are global oscillatory modes of a rotating fluid restored by the Coriolis force. Continuing this comparison, the work then focuses on the transition to turbulence and features of the turbulent regime. Lastly, an external axial magnetic field is applied to the setup with a conducting fluid and its effect on the flow is studied with special emphasis on the effect on inertial modes and rise of a class of magneto-Coriolis modes where the restoring forces consist of the Lorentz and Coriolis forces. Some aspects are compared to observations in magnetohydrodynamic experiments.