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Viscous pulsational instability of the transonic region of isothermal geometrically thin accretion discs. I: Analytic results. (English) Zbl 0641.76033

Viscous instability of the transonic region of the conventional geometrically thin alpha-type accretion discs is examined analytically. For simplicity, isothermal discs and isothermal perturbations are assumed. It is found that when the value of \(\alpha\) is larger than a critical value, the disc is unstable against two types of perturbations. One is local propagating perturbations of inertial acoustic waves. Results suggest the possibility that unstable perturbations develop to overstable global oscillations which are restricted only in the innermost region of the disc. The other is standing growing perturbations localized just at the transonic point. The cause of these instabilities is that the azimuthal component of the Lagrangian velocity variation associated with the perturbations becomes in phase with the variation of the viscous stress force. Because of this phase matching work is done on perturbations, and they are amplified.

MSC:

76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
85A05 Galactic and stellar dynamics
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