Near-onset convection patterns in the spherical Bénard problem with l=2 critical

摘要

Bifurcation of convective patterns in a spherical shell of Boussinesq fluid is investigated using center manifold reduction at the onset of the instability of the l=2 spherical harmonics. The existence and stability of patterns with D(2) and O(2) symmetry are determined using results from singularity theory and a complete classification is given as a function of aspect ratio and Prandtl number for both the degenerate self-adjoint case and for small non-self-adjoint perturbations. The results are compared to those of a previous study for l=4 critical.