  The spherical Couette system consists of two differentially rotating
concentric spheres with a fluid filled in between. We study a regime where the
outer sphere is rotating rapidly enough so that the Coriolis force is important
and the inner sphere is rotating either slower or in the opposite direction
with respect to the outer sphere. We numerically study the sudden transition to
turbulence at a critical differential rotation seen in experiments at BTU
Cottbus - Senftenberg, Germany and investigate its cause. We find that the
source of turbulence is the boundary layer on the inner sphere, which becomes
centrifugally unstable. We show that this instability leads to generation of
small scale structures which lead to turbulence in the bulk, dominated by
inertial waves, a change in the force balance near the inner boundary, the
formation of a mean flow through Reynolds stresses, and consequently, to an
efficient angular momentum transport. We compare our findings with axisymmetric
simulations and show that there are significant similarities in the nature of
the flow in the turbulent regimes of full 3D and axisymmetric simulations but
differences in the evolution of the instability that leads to this transition.
We find that a heuristic argument based on a Reynolds number defined using the
thickness of the boundary layer as a length scale helps explain the scaling law
of the variation of critical differential rotation for transition to turbulence
with rotation rate observed in the experiments.
