Numerical modeling of tidal effects in polytropic accretion disks.
A two-dimensional time-dependent hybrid Fourier-Chebyshev method of collocation is developed and used for the study of tidal ejects in accretion disks, under the assumptions of a polytropic equation of state and a standard alpha viscosity prescription. Under the inNuence of the m\1 azimuthal component of the tidal potential, viscous oscillations in the outer disk excite an m\1 eccentric instability in the disk. While the m\2 azimuthal component of the tidal potential excites a Papaloizou-Pringle instability in the inner disk (a saturated m\2 azimuthal mode), with an elliptic pattern rotating at about a fraction of the local Keplerian velocity in the inner disk. The period of the elliptic mode corresponds (B13) well to the periods of the short-period oscillations observed in cataclysmic variables. In cold disks (r)/cs\MB40) we also found a critical value of the viscosity parameter (aB0.01), below which shock dissipation dominates and is balanced by the wave amplifcation due to the wave action conservation. In this case the double spiral shock propagates all the way to the inner boundary with a Mach number MsB1.3.
|Main Author:||Godon, Patrick.|