Nonaxisymmetric Hydrodynamic Instability and Subcritical Transition to Turbulence in the Inner Region of Thin Keplerian Disks
Nonaxisymmetric Hydrodynamic Instability and Subcritical Transition to Turbulence in the Inner Region of Thin Keplerian Disks
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薄开普勒盘内部区域的非轴对称流体动力不稳定性和亚临界湍流转变
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发表时间：
1998
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通讯作者：
P. Godon
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作者：
P. Godon
利用含时二维多变混合傅里叶-切比雪夫谱配置方法，数值模拟了非轴对称不稳定性(Papaloizou-Pringle不稳定性)在薄开普勒盘中的非线性增长。当内边界是刚性的(这里对应于吸积致密恒星的表面)时，非轴对称不稳定性(共转共振)在内盘中发展。在盘的内缘，所有的不稳定性模都有一个高Q值和一个开普勒周期量级的旋转周期。高阶模式比低阶模式具有更大的增长率。当粘性较大时，高阶模式首先被抑制，并在中值饱和：能量包含在主导流动的低阶模式中。当粘性较低时，高阶模式主导流动，而低阶模式则完全不增长：能量被包含在高阶模式中。当不稳定模的阶数m和振幅a足够高时(在目前的计算中，m≳15，≳0.3，α=0.001)，流动经历了亚临界到湍流的转变。湍流被限制在圆盘的内部区域，在“谐振腔”内，由于波的过反射(即，就像非轴对称不稳定性本身)，它在那里维持自己。在湍流的过渡阶段，一些低阶模式占主导地位。在这项工作中得到的湍流不能解释圆盘中的角动量输运。然而，这种不稳定性提供了一种新的稳健机制来解释在激变变星和其他相关系统的内盘中观察到的短周期振荡(矮新星振荡和准周期振荡)的出现。
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.