Nonlinear Stability of Thin, Radially Stratified Disks

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 inward, 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/(Ω)², where N_r is the radial Brunt-Väisälä frequency and Ω is the shear rate. Classical convective instability in a nonshearing medium (Ri → -∞) 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 ≳0.0025Ω.