Nonlinear Stability of Thin, Radially Stratified Disks

We perform local numerical experiments to investigate the nonlinear stabilityof thin, radially-stratified disks. We demonstrate the presence of radialconvective instability when the disk is nearly in uniform rotation, and showthat the net angular momentum transport is slightly inwards, consistent withprevious investigations of vertical convection. We then show that aconvectively-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\Omegais the shear rate. Classical convective instability in a nonshearing medium (Ri-> -infinity) is suppressed when Ri > -1, i.e. when the shear rate becomesgreater than the growth rate. Disks with a nearly-Keplerian rotation profileand radial gradients on the order of the disk radius have Ri > -0.01 and aretherefore stable to local nonaxisymmetric disturbances. One implication of ourresults is that the ``baroclinic'' instability recently claimed by Klahr &Bodenheimer is either global or nonexistent. We estimate that our simulationswould detect any genuine growth rate > 0.0025\Omega.Comment: 31 pages, 15 figures, accepted for publication in the Astrophysical Journa