  We perform local numerical experiments to investigate the nonlinear stability
of thin, radially-stratified disks. We demonstrate the presence of radial
convective instability when the disk is nearly in uniform rotation, and show
that the net angular momentum transport is slightly inwards, consistent with
previous investigations of vertical convection. We then show that a
convectively-unstable equilibrium is stabilized by differential rotation.
Convective instability is determined by the Richardson number Ri =
N_r^2/(q\Omega)^2, where N_r is the radial Brunt-Vaisala frequency and q\Omega
is the shear rate. Classical convective instability in a nonshearing medium (Ri
-> -infinity) is suppressed when Ri > -1, i.e. when the shear rate becomes
greater than the growth rate. Disks with a nearly-Keplerian rotation profile
and radial gradients on the order of the disk radius have Ri > -0.01 and are
therefore stable to local nonaxisymmetric disturbances. One implication of our
results is that the ``baroclinic'' instability recently claimed by Klahr &
Bodenheimer is either global or nonexistent. We estimate that our simulations
would detect any genuine growth rate > 0.0025\Omega.
