Nonaxisymmetric Hydrodynamic Instability and Subcritical Transition to Turbulence in the Inner Region of Thin Keplerian Disks

Abstract

The nonlinear growth of a nonaxisymmetric instability (the Papaloizou-Pringle instability) is followed numerically in thin Keplerian disks with the use of a time-dependent two-dimensional polytropic hybrid Fourier-Chebyshev spectral method of collocation. The nonaxisymmetric instability (a corotation resonance) develops in the inner disk when the inner boundary is rigid (corresponding here to the surface of an accreting compact star). All the modes of the instability have high Q-values and a period of rotation on the order of the Keplerian period at the inner edge of the disk. The high-order modes have growth rates larger than the low-order modes. When the viscosity is large, the higher modes are the first to be damped and saturate at moderate values: the energy is contained in the low-order modes, which dominate the flow. When the viscosity is low, the high-order modes dominate the flow, while the low-order modes do not grow at all: the energy is contained in the higher modes. When the order m and the amplitude a of the unstable mode are high enough (in the present calculations m 15 and a 0.3 for α = 0.001), the flow undergoes a subcritical transition to turbulence. The turbulence is confined in the inner region of the disk, inside the resonant cavity, where it sustains itself because of the overreflection of waves (i.e., like the nonaxisymmetric instability itself). Some of the low-order modes are dominant during transient phases of the turbulent flow. The turbulence obtained in this work cannot account for angular momentum transport in the disk. However, the instability provides a new robust mechanism to explain the appearance of short-period oscillations (dwarf nova oscillations and quasi-periodic oscillations) observed in the inner disk of cataclysmic variables and other related systems.