ar X iv : a st ro - p h / 99 06 31 5 v 1 1 8 Ju n 19 99 Stability , Instability , and “ Backwards ” Transport in Stratified Fluids

The stratification of entropy and the stratification of angular momentum are closely analogous. In this paper, we pursue this analogy and some of its consequences. Of particular interest is the behavior of disks in which angular momentum transport is controlled by convection, and heat transport by dynamical turbulence. In both instances we argue that the transport will proceed “backwards” relative to the sense one would expect from a simple diffusion approach. Reversed angular momentum transport has already been seen in computational simulations; reversed heat transport has not been so investigated, but should be numerically accessible as well. The common belief is that accretion disk vertical heat transport is aided by shear turbulence. To the extent that shear turbulence does anything with heat transport, the opposite is likely to be true. These arguments also bear on the observed nonlinearly local stability of Keplerian disks: locally generated turbulence in such a disk would require simultaneous inward and outward angular momentum transport, which is of course impossible. A diffusive instability is described which is analogous to the disk magnetorotational instability. It affects thermal layers when Coulomb conduction and a weak magnetic field are present. The field must be sufficiently weak that it has no dynamical consequences, and the plasma sufficiently dilute that heat is channeled only along field lines, the sole role of magnetism in this problem. The criterion for convective instability goes from one of an outwardly decreasing entropy to outwardly decreasing temperature. The maximum growth rate is of order the sound crossing time over a characteristic scale height, independent of the magnetic field or thermal conductivity. The indifference of the growth rate to the details of the conduction process, its simple dynamical scaling, and the replacement in the stability criterion of a conserved quantity gradient by a free energy gradient are properties similar to those exhibited by the magnetorotational instability in an accretion disk context. Subject headings: accretion, accretion disks—convection— hydrodynamics—instabilities—turbulence