Necessary Conditions for Baroclinic Instabilities in Protoplanetary Disks

Details Necessary Conditions for Baroclinic Instabilities in Protoplanetary Disks Necessary Conditions for Baroclinic Instabilities in Protoplanetary Disks

May 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004aas...204.2403s&link_type=abstract

American Astronomical Society Meeting 204, #24.03; Bulletin of the American Astronomical Society, Vol. 36, p.690

Astronomy and Astrophysics

Astronomy

Scientific paper

Numerical simulations of baroclinic 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, we have derived a simplified fluid model based upon the anelastic approximation for a vertically-averaged disk. A linear stability analysis of the model leads to two basic requirements for linear instability: (1) a negative radial temperature gradient maintained by radiative heating from the central star and (2) a rate of radiative damping of temperature perturbations that substantially exceeds the rate of viscous damping of velocity perturbations.
In the absence of radiative damping, the model exhibits neutral oscillations where the temperature perturbations are 90 degrees out of phase with the radial velocity oscillations. Radiative damping causes a phase shift in the temperature perturbations, such that hot gas can be moved down the radial temperature gradient, releasing potential energy. The unstable mode has lower energy than the unperturbed state, so the growing instability is energetically consistent with radiative damping.
This research was supported by NASA's Origins of Solar Systems program.

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