Modulated Rotating Waves in the Magnetised Spherical Couette System

We present a study devoted to a detailed description of modulated rotating waves (MRW) in the magnetised 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. The MRW originate from parent branches of rotating waves and are classified according to Rand’s (Arch Ration Mech Anal 79:1–37, 1982) and Coughling and 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 magnetised spherical Couette device hosted at the Helmholtz-Zentrum Dresden-Rossendorf.