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 metadatas

Cited literature [26 references]  Display  Hide  Download

https://hal-univ-avignon.archives-ouvertes.fr/hal-00945597
Contributor : Philippe Beltrame <>
Submitted on : Wednesday, February 12, 2014 - 3:41:44 PM
Last modification on : Friday, March 22, 2019 - 11:34:04 AM
Long-term archiving on: Tuesday, May 13, 2014 - 11:20:44 AM

File

ChBe13v14.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00945597, version 1

Citation

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

Share

Metrics

Record views

995

Files downloads

310