Computation of bifurcation coefficients in a spherically symmetric convection problem
Abstract
Convection in spherical shells is investigated analytically. The equation of bifurcation in a spherically invariant system is derived and subjected to a LiapunovSchmidt decomposition in order to calculate the bifurcation coefficients near the transition. The method developed is applied to several cases of the spherical Benard problem, and the results are presented in graphs and tables. The calculation of the sign of the coefficients permits the identification of the physically observable solutions and the quantitative description of their development as functions of the Rayleigh number. Complete theoretical results are obtained for systems in which the ratio of the innersphere radius to that of the outer sphere is about 0.3.
 Publication:

Journal de Mecanique Theorique et Appliquee
 Pub Date:
 1983
 Bibcode:
 1983JMecT...2..799C
 Keywords:

 Branching (Mathematics);
 Convective Flow;
 RayleighBenard Convection;
 Spherical Shells;
 Coefficients;
 Numerical Stability;
 Fluid Mechanics and Heat Transfer