Skip to Main content Skip to Navigation
New interface
Preprints, Working Papers, ...

Onset of intermittent octahedral patterns in spherical Bénard convection

Philippe Beltrame 1, * Pascal Chossat 2 
* Corresponding author
2 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : The onset of convection for spherically invariant Rayleigh-Bénard fluid flow is driven by marginal modes associated with spherical harmonics of a certain degree $\ell$, which depends upon the aspect ratio of the spherical shell. At certain critical values of the aspect ratio, marginal modes of degrees $\ell$ and $\ell+1$ coexist. Initially motivated by an experiment of electrophoretic convection between two concentric spheres carried in the International Space Station (GeoFlow project), we analyze the occurrence of intermittent dynamics near bifurcation in the case when marginal modes with $\ell=3, 4$ interact. The situation is by far more complex than in the well studied $\ell=1, 2$ mode interaction, however we show that heteroclinic cycles connecting equilibria with octahedral as well as axial symmetry can exist near bifurcation under certain conditions. Numerical simulations and continuation (using the software AUTO) on the center manifold help understanding these scenarios and show that the dynamics in these cases exhibit intermittent behaviour, even though the heteroclinic cycles may not be asymptotically stable in the usual sense.
Complete list of metadata

Cited literature [26 references]  Display  Hide  Download
Contributor : Philippe Beltrame Connect in order to contact the contributor
Submitted on : Wednesday, February 12, 2014 - 3:41:44 PM
Last modification on : Thursday, August 4, 2022 - 4:58:16 PM
Long-term archiving on: : Tuesday, May 13, 2014 - 11:20:44 AM


Files produced by the author(s)


  • HAL Id : hal-00945597, version 1


Philippe Beltrame, Pascal Chossat. Onset of intermittent octahedral patterns in spherical Bénard convection. 2014. ⟨hal-00945597⟩



Record views


Files downloads