Axially symmetric and latitudinally propagating nonlinear patterns in rotating spherical convection

Abstract

We report a nonlinear phenomenon discovered in the classical problem of thermal convection in rapidly rotating, self-gravitating, internally heated Boussinesq fluid spheres. When linear convective instability (the most unstable mode of convection) is in the form of an axially symmetric, equatorially antisymmetric torsional oscillation, its equatorial symmetry must be broken by nonlinear effects and, consequently, the key properties of the primary solution bifurcating from the instability cannot be predicted on the basis of linear solutions at the onset of convection. We reveal that, when the supercritical Rayleigh number is in the vicinity of its critical value, the primary nonlinear solution is in the form of an axially symmetric, equatorially nonsymmetric, latitudinally propagating spatiotemporal pattern whose amplitude varies periodically, representing an unusual nonlinear phenomenon of thermal convection in rotating fluid spheres.