Title: Subcritical thermal convection of liquid metals in a rapidly rotating sphere,
Abstract: Planetary cores consist of liquid metals (low Prandtl number $Pr$) that
convect as the core cools. Here we study nonlinear convection in a rotating
(low Ekman number $Ek$) planetary core using a fully 3D direct numerical
simulation. Near the critical thermal forcing (Rayleigh number $Ra$),
convection onsets as thermal Rossby waves, but as the $Ra$ increases, this
state is superceded by one dominated by advection. At moderate rotation, these
states (here called the weak branch and strong branch, respectively) are
smoothly connected. As the planetary core rotates faster, the smooth transition
is replaced by hysteresis cycles and subcriticality until the weak branch
disappears entirely and the strong branch onsets in a turbulent state at $Ek <
10^{-6}$. Here the strong branch persists even as the thermal forcing drops
well below the linear onset of convection ($Ra=0.7Ra_{crit}$ in this study). We
highlight the importance of the Reynolds stress, which is required for
convection to subsist below the linear onset. In addition, the Péclet number
is consistently above 10 in the strong branch. We further note the presence of
a strong zonal flow that is nonetheless unimportant to the convective state.
Our study suggests that, in the asymptotic regime of rapid rotation relevant
for planetary interiors, thermal convection of liquid metals in a sphere onsets
through a subcritical bifurcation.