  We present a study devoted to a detailed description of modulated rotating
waves (MRW) in the magnetized spherical Couette system. The set-up consists of
a liquid metal confined between two differentially rotating spheres and
subjected to an axially applied magnetic field. When the magnetic field
strength is varied, several branches of MRW are obtained by means of three
dimensional direct numerical simulations (DNS). The MRW originate from parent
branches of rotating waves (RW) and are classified according to Rand's (Arch.
Ration. Mech. Anal 79:1-37, 182) and Coughling & Marcus (J. Fluid Mech.
234:1-18,1992) theoretical description. We have found relatively large
intervals of multistability of MRW at low magnetic field, corresponding to the
radial jet instability known from previous studies. However, at larger magnetic
field, corresponding to the return flow regime, the stability intervals of MRW
are very narrow and thus they are unlikely to be found without detailed
knowledge of their bifurcation point. A careful analysis of the spatio-temporal
symmetries of the most energetic modes involved in the different classes of MRW
will allow in the future a comparison with the HEDGEHOG experiment, a
magnetized spherical Couette device hosted at the Helmholtz-Zentrum
Dresden-Rossendorf.
