Spiral Roll State in Heat Convection between Nonrotating Concentric Double Spherical Boundaries

We studied the single-arm spiral roll state in the system of Boussinesq fluid confined between nonrotating double concentric spherical boundaries with an opposing temperature gradient previously reported by Zhang et al. [Phys. Rev. E 66, 055203(R) (2002)]. It was found that the state exists even in a gap thicker than that used in this previous study, as an autonomously rotating wave solution with a finite constant angular velocity in a nonrotating geometry. We further confirmed that individual spiral roll states bifurcate directly from the static state at a number of intersections of the marginal stability curves. The double convective timescales peculiar to the state may involve global mixing through the entire domain albeit at the onset of convection, where a passive tracer geometrically explores through the entire spherical domain for sufficient time beyond a cell that would be formed by the other highly-symmetric steady states bifurcating at the onset.