  We study the formation, longevity and breakdown of convective rings during
impulsive spin-up in square and cylindrical containers using direct numerical
simulations. The rings, which are axisymmetric alternating regions of up- and
down-welling flow that can last for O (100) rotation times, were first
demonstrated experimentally and arise due to a balance between Coriolis and
viscous effects. We study the formation of these rings in the context of the
Greenspan-Howard spin-up process, the disruption of which modifies ring
formation and evolution. We show that, unless imprinted by boundary geometry,
convective rings can only form when the surface providing buoyancy forcing is a
free-slip surface, thereby explaining an apparent disagreement between
experimental results in the literature. For Prandtl numbers from 1--5 we find
that the longest-lived rings occur for intermediate Prandtl numbers, with a
Rossby number dependence. Finally, we find that the constant evaporative
heat-flux conditions imposed in the experiments are essential in sustaining the
rings and in maintaining the vortices that form in consequence of the ring
breakdown.
