Abstract
The linear stability of the periodic and axisymmetric solutions of the convection in rotating, internally heated, and self-gravitating fluid spheres is presented. The transition to quasiperiodic flows via Neimark–Sacker bifurcations of different azimuthal wave numbers, m, is studied using matrix-free continuation and Floquet theory. Several pairs of Ekman and Prandtl numbers are considered in the region where the first bifurcation from the conduction state gives rise to the axisymmetric solutions. It is shown that the azimuthal wave numbers m = 1 and m = 2 are preferred and that, for small Ekman and Prandtl numbers, the secondary bifurcations to different m accumulate close to the onset of convection. This study confirms some results previously found just by direct simulations. The methods presented can be applied to systems of parabolic partial differential equations with O(2) or SO(2) symmetry group, when a periodic orbit, invariant under the group, loses stability through a Neimark–Sacker bifurcation.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
