On the spiral roll state in thermal convection in spherical shell

It is found that the ``giant'' spiral roll state in thermal convection in non-rotating spherical shell with a finite Pr reported by Zhang and others (Phys.Rev.E, 2002) exists with a subtle modification under conservation of invariance of ${\cal C}_2$ symmetry even at a relatively thicker spherical shell. By means of a detail numerical bifurcation analysis with aid of direct numerical simulation for the time-development of the system, it is elucidated that this state orginates, in the parameter space, at a higher Rayleigh number but a lower azimuthal wavenumber than the set of parameters where the state previously found by Zhang exists.