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

• Autores: Christoph Geiger, Gerhard Dangelmayr
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 254, Nº 1, 2013 (Ejemplar dedicado a: Nonlinear Elliptic Differential Equations, Bifurcation, Local Dynamics of Parabolic Systems and Numerical Methods), págs. 154-174
• Idioma: inglés
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• Resumen

  • 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.