NUMERICAL MODELING OF TIDAL EFFECTS IN POLYTROPIC ACCRETION DISKS

A two-dimensional time-dependent hybrid Fourier-Chebyshev method of co llocation is developed and used for the study of tidal effects in accr etion disks, under the assumptions of a polytropic equation of state a nd a standard alpha viscosity prescription. Under the influence of the m = 1 azimuthal component of the tidal potential, viscous oscillation s 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 az imuthal mode), with an elliptic pattern rotating at about a fraction ( approximate to 1/3) of the local Keplerian velocity in the inner disk. The period of the elliptic mode corresponds well to the periods of th e short-period oscillations observed in cataclysmic variables. In cold disks (r Omega/c(s) = M approximate to 40) we also find a critical va lue of the viscosity parameter (alpha approximate to 0.01), below whic h shock dissipation dominates and is balanced by the wave amplificatio n 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 M-s approximate to 1.3.