Experiments and simulations on the magnetized spherical Couette problem

Experiments on the magnetized spherical Couette system are presently being carried out at Helmholtz-Zentrum Dresden-Rossendorf (HZDR). A liquid metal (GaInSn) is confined within two differentially rotating spheres and exposed to a magnetic field parallel to the axis of rotation. Bifurcation diagrams for rotating waves, obtained with continuation methods when only the magnetic field is increased, are presented. Bifurcation diagrams for modulated rotating waves and chaotic flows, obtained by means of DNS, are presented as well. This allows us to carefully investigate the nonlinear saturation of the radial jet, return flow, and shear layer instabilities, as found in previous studies. The main focus is on studing their spatio-temporal symmetries. We find that at moderate differential rotation the modulated rotating waves give rise to several types of chaotic flows, but only for the radial jet instability. With this study we reveal how the flow patterns and time-scales depend on the magnetic field, reproducing thus different physical situations of the HZDR experiments.