The understanding of thermal convection in fluid spheres and spherical shells is fundamental for improving the knowledge of many astrophysical and geophysical phenomena. Bifurcation diagrams and flow patterns of rotating (RW) and modulated rotating waves (MRW) up to the appearance of chaos are presented in terms of their physical properties. They are obtained from direct numerical simulations of Boussinesq thermal convection in rotating spherical shells with constrained azimuthal symmetry. The parameters are taken so close as possible to those of the Earth's outer core. The periodicity and quasiperiodicity of the solutions is quantified by means of an accurate analysis of their frequency spectrum, together with the Poincaré sections. In addition an heuristic five degree model, based on the symmetries of the solutions, that reproduces with significative agreement the sequence of bifurcations and the type of solutions of the simulations is derived and explored.

Author Institutional Affiliation | Universitat Politècnica de Catalunya and Ecole Normale Supérieure Paris |

Author Email | |

Author Postal Mail | Campus Nord, Mòdul B4, Jordi Girona Salgado 1--3, 08034 Barcelona, Spain. |

Notes | This media entry is based on the paper SIAM Journal on Applied Dynamical Systems 2015 14:4, 1787--1807. |

Keywords | thermal convection, rotating spherical geometry, modulated waves, period doubling, reduced model |