Four-frequency solution in a magnetohydrodynamic Couette flow as a consequence of azimuthal symmetry breaking

Abstract

The occurrence of four-tori in differentially rotating magnetohydrodynamic (MHD) flows in spherical geometry is understood in terms of a sequence of Hopf bifurcations breaking the azimuthal symmetry of the flow as the applied magnetic field strength is varied. These flows originate from unstable rotating waves (RW), and two-tori modulated rotating waves (MRW), with broken equatorial symmetry but having azimuthal symmetry m = 4. A posterior bifurcation gives rise to m = 2 symmetric three-tori MRW and a further bifurcation to a four-tori MRW which has lost all the spatial symmetries. This bifurcation scenario may be favoured when differential rotation is increased and rotating waves with azimuthal symmetry m, product of several prime numbers, emerge at sufficiently large magnetic field.