Axisymmetric perturbations of thin gaseous disks. I - Unstable convective modes and their consequences for the solar nebula

Details Axisymmetric perturbations of thin gaseous disks. I - Unstable convective modes and their consequences for the solar nebula Axisymmetric perturbations of thin gaseous disks. I - Unstable convective modes and their consequences for the solar nebula

Jun 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988apj...329..739r&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 329, June 15, 1988, p. 739-763. NASA-supported research.

Astronomy and Astrophysics

Astrophysics

57

Accretion Disks, Hydrodynamic Equations, Perturbation Theory, Rotating Disks, Solar System, Star Formation, Adiabatic Conditions, Angular Momentum, Brunt-Vaisala Frequency, Turbulent Mixing

Scientific paper

The axisymmetric perturbations of a thin, differentially rotating gas disk in which the vertical temperature stratification is superadiabatic are analyzed. The growth rate of adiabatic convective normal modes is calculated, departures from simple polytropic disk models are briefly discussed, and the detailed vertical structure of the eigenfunctions is analyzed. The stabilizing effect of radiative diffusion on convective modes is considered. It is found that rotation and compressibility tend to reduce the rate of growth of the disturbances, and that the growth rate increases without limit and is proportional to the square root of the radial wavenumber in polytropic equilibria. The maximum radial size of convective eddies scales like the square root of the degree of superadiabaticity times the size of the convective zone. There is significant convective penetration into radiatively stable layers only for the fundamental and low-order harmonic modes, whose vertical wavelength is comparable to the size of the convective layer.

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