**DPS 35th Meeting, 1-6 September 2003**

*Session 25. Planet and Satellite Origins I: Disks, Nebulae and Giant Planets*

Oral, Chairs: A. P. Boss and J. J. Lissaurer, Thursday, September 4, 2003, 1:30-3:20pm, DeAnza I-II
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## [25.02] A Simplified Model for Rossby Wave Instabilities in Protoplanetary Disks

*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.