Modulated rotating waves and triadic resonances in spherical fluid systems: The case of magnetized spherical Couette flow

The existence of triadic resonances in the magnetized spherical Couette system is related to the development of modulated rotating waves, which are quasiperiodic flows understood in terms of bifurcation theory in systems with symmetry. In contrast to previous studies in spherical geometry, the resonant modes are not inertial waves but related to the radial jet instability, which is strongly equatorially antisymmetric. We propose a general framework in which triadic resonances are generated through successive Hopf bifurcations from the base state. The study relies on an accurate frequency analysis of different modes of the flow, for solutions belonging to two different bifurcation scenarios. The azimuthal and latitudinal nonlinear coupling among the resonant modes is analyzed and interpreted using spherical harmonics, and the results are compared with previous studies in spherical geometry.