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The onset of convection for spherically invariant Rayleigh-B\'enard fluidflow is driven by marginal modes associated with spherical harmonics of acertain degree $\ell$, which depends upon the aspect ratio of the sphericalshell. At certain critical values of the aspect ratio, marginal modes ofdegrees $\ell$ and $\ell+1$ coexist. Initially motivated by an experiment ofelectrophoretic convection between two concentric spheres carried in theInternational Space Station (GeoFlow project), we analyze the occurrence ofintermittent dynamics near bifurcation in the case when marginal modes with$\ell=3, 4$ interact. The situation is by far more complex than in the wellstudied $\ell=1, 2$ mode interaction, however we show that heteroclinic cyclesconnecting equilibria with octahedral as well as axial symmetry can exist nearbifurcation under certain conditions. Numerical simulations and continuation(using the software AUTO) on the center manifold help understanding thesescenarios and show that the dynamics in these cases exhibits intermittentbehaviour, even though the heteroclinic cycles may not be asymptotically stablein the usual sense.

Onset of intermittent octahedral patterns in spherical B\'enard convection