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G.R. Stewart (Univ. of Colorado)
Numerical simulations of Rossby wave instabilities in protoplanetary disks have be published by Li et al. (2001) and by Klahr and Bodenheimer (2003). These simulations exhibit the formation of large-scale vortices that may have an important effect on both planetary formation and angular momentum transport in the disk. In order to explore the physical conditions required for such instabilities to occur, I have derived a simplified fluid model based upon the anelastic approximation for a vertically-averaged disk. In this approximation, the rapid pressure waves are filtered out of the model, so that only the slow Rossby wave modes remain. The model consists of nonlinear evolution equations for the fluid vorticity and entropy. Radial gradients in the surface density and the temperature of the disk can drive vorticity evolution via a baroclinic coupling of the two equations. Radiative damping of entropy perturbations from the basic state has also been included. The linearized equations have a structure similar to classical stratified shear flow problems, so the linear stability can be determined systematically from a numerical eigenvalue problem for any given radial density and entropy profile. Alternatively, transient growth of formally stable disturbances can be evaluated by solving the initial value problem. Surprisingly large transient vorticity and entropy perturbations can form in disks with realistic radial profiles. The Reynolds stress resulting from these perturbations can yield significant radial angular momentum transport in the disk. The only way to suppress these transient disturbances is to introduce a large turbulent viscosity. The conditions required to form nonlinear vorticies is currently under investigation.
This work was supported by NASA's Origins of Solar Systems Program.
The author(s) of this abstract have provided an email address for comments about the abstract: glen@artemis.colorado.edu
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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.