  Protoplanetary disks are prone to several hydrodynamic instabilities. One
candidate, Convective Overstability (COS), can drive radial semi-convection
that may influence dust dynamics and planetesimal formation. However, the COS
has primarily been studied in local models. This paper investigates the COS
near the mid-plane of radially global disk models. We first conduct a global
linear stability analysis, which shows that linear COS modes exist only
radially inward of their Lindblad resonance (LR). The fastest-growing modes
have LRs near the inner radial domain boundary with effective radial
wavelengths that can be a substantial fraction of the disk radius. We then
perform axisymmetric global simulations and find that the COS's nonlinear
saturation is similar to previous incompressible shearing box simulations. In
particular, we observe the onset of persistent zonal and elevator flows for
sufficiently steep radial entropy gradients. In full 3D, non-axisymmetric
global simulations, we find the COS produces large-scale, long-lived vortices,
which induce outward radial transport of angular momentum via the excitation of
spiral density waves. The corresponding $\alpha$-viscosity values of order
$10^{-3}$ agree well with those found in previous 3D compressible shearing box
simulations. However, in global disks, significant modifications to their
radial structure are found, including the formation of pressure bumps.
Interestingly, the COS typically generates an outward radial mass transport,
i.e. decretion. We briefly discuss the possible implications of our results for
planetesimal formation and for interpreting dust rings and asymmetries observed
in protoplanetary disks.
