Dynamical instability of a Keplerian disk - Dependence on azimuthal wave number, Mach number, and the size of the disk

Details Dynamical instability of a Keplerian disk - Dependence on azimuthal wave number, Mach number, and the size of the disk Dynamical instability of a Keplerian disk - Dependence on azimuthal wave number, Mach number, and the size of the disk

May 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988a%26a...196..152h&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 196, no. 1-2, May 1988, p. 152-158.

Astronomy and Astrophysics

Astrophysics

13

Accretion Disks, Dynamic Stability, Mach Number, Rotating Fluids, Dwarf Novae, Momentum Transfer

Scientific paper

Unstable perturbations in a rotating fluid are investigated for a rotation law of Ω ∝ r-1.5 where Ω and r are the angular velocity and the radial distance, respectively. The growth rate of the unstable perturbation tends to be largest for the mode whose azimuthal wave number is roughly equal to the Mach number. This implies that large scale waves will be excited in a hot disk and small scale waves in a cold disk. The growth rate depends sensitively on the outer radius of the disk when the outer radius is not too large. However, the growth rate becomes insensitive to the outer radius and tends to a finite value as the outer radius tends to infinity. This means that the wave is reflected not at the outer boundary but within the flow when the outer boundary is sufficiently large. The result is applied to evaluate the turbulent viscosity. The viscous parameter α is found to be inversely proportional to the Mach number. This is consistent with the theory of dwarf novae.

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