Pulsating and traveling wave modes of natural convection in spherical shells

A numerical study is made of the natural convective fluid motion in the spherical shell geometry, i e, the gap between two concentric spheres The case of homogeneously heated inner sphere and cooled outer sphere is considered for the radius ratio eta=0 714 and Prandtl number Pr=0 7 Patterns of fluid flow are established by the variation of the Rayleigh number Ra and its heat transfer is characterized by the Nusselt number Nu For small values of the Rayleigh number, a crescent shaped axisymmetric vortex is formed and is regarded as the basic flow By increasing the Rayleigh number, two transitions occur to a fully developed three-dimensional irregular flow On the first bifurcation branch, a pulsating wave flow was found with petal-like formations pulsating in meridional direction On the second branch, a traveling wave flow exists with an azimuthal rotation of the spirally distributed petal patterns Various characteristics of the flow patterns are investigated as well as their transition to chaos Both branches conjoin in the very supercritical domain, where the traveling wave dominates (C) 2010 American Institute of Physics [dot 10 1063/1 3507886]