Article ID Journal Published Year Pages File Type
650219 European Journal of Mechanics - B/Fluids 2015 19 Pages PDF
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 ℓℓ, which depends upon the aspect ratio of the spherical shell. At certain critical values of the aspect ratio, marginal modes of degrees ℓℓ and ℓ+1ℓ+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 ℓ=3,4ℓ=3,4 interact. The situation is by far more complex than in the well studied ℓ=1,2ℓ=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 behavior, even though the heteroclinic cycles may not be asymptotically stable in the usual sense.

Related Topics
Physical Sciences and Engineering Chemical Engineering Fluid Flow and Transfer Processes
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