Linear and non-linear evolution of the vertical shear instability in accretion discs
Linear and non-linear evolution of the vertical shear instability in accretion discs
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吸积盘垂直剪切不稳定性的线性和非线性演化
DOI：
10.1093/mnras/stt1475
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发表时间：
2013
影响因子：
4.8
通讯作者：
Nelson R
中科院分区：
文献类型：
--
作者：
Nelson R
我们分析了幂律吸积盘模型的稳定性和非线性动力学。它们具有遵循径向幂律的中面密度，并且具有严格的圆柱半径R的幂律函数的温度或熵分布。我们采用了两种不同的流体动力学代码进行高分辨率的2D轴对称和3D模拟，检查长期演变的光盘模型的幂律指数的温度或熵，光盘scaleheight，流体的热弛豫时间和光盘粘度的函数。我们提出了一个伴随的稳定性分析的问题，渐近方法的基础上，我们用它来指导我们的模拟结果的解释。我们发现，轴对称圆盘模型的温度或熵分布使平衡角速度随高度变化，对扰动的增长是不稳定的，最明显的特征是水平和垂直波数满足|kR/kZ| 2001年。只有当流体的热力学响应是等温的，或者热演化时间与局部动力学时间尺度相当或更短时，才发生不稳定性。这些圆盘似乎表现出Goldreich-Schubert-Schoolke或“垂直剪切”线性不稳定性。对模拟结果的仔细检查揭示了两种不同模式的增长。第一个的特点是非常短的径向波长的扰动，迅速增长，在高纬度地区的磁盘，并下降到较长的时间尺度上的中平面。我们称之为“手指模式”，因为它们显示kR/kZ = 1。第二个出现在光盘主体的稍晚的时间，包括接近中平面。这些“体模”具有稍长的径向波长。在早期，它们表现为基本的呼吸模式，但随着关于中平面的对称性被打破，它们很快就变成了呼吸模式。非线性饱和态的显著特征是双模态，导致圆盘中面强烈的垂直振荡。在纵横比H/r= 0.05的粘性圆盘中，当粘性参数α < 4 × 10−4时，不稳定性发生。在三维空间中，不稳定性产生准湍流，相关的雷诺应力产生波动的有效粘性系数，其平均值在模拟结束时达到α <$10 − 3。在天体物理盘模型中，垂直剪切不稳定性的演化和饱和，其中包括热物理的现实处理，还有待审查。然而，如果它发生在全球或局部尺度上，我们的结果表明，它将对它们的内部动力学、传输特性和观察外观产生重大影响。
We analyse the stability and non-linear dynamics of power-law accretion disc models. These have mid-plane densities that follow radial power laws and have either temperature or entropy distributions that are strict power-law functions of cylindrical radius,R. We employ two different hydrodynamic codes to perform high-resolution 2D axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the disc scaleheight, the thermal relaxation time of the fluid and the disc viscosity. We present an accompanying stability analysis of the problem, based on asymptotic methods, that we use to guide our interpretation of the simulation results. We find that axisymmetric disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of perturbations whose most obvious character is modes with horizontal and vertical wavenumbers that satisfy |kR/kZ| ≫ 1. Instability occurs only when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time-scale. These discs appear to exhibit the Goldreich–Schubert–Fricke or ‘vertical shear’ linear instability. Closer inspection of the simulation results uncovers the growth of two distinct modes. The first are characterized by very short radial wavelength perturbations that grow rapidly at high latitudes in the disc, and descend down towards the mid-plane on longer time-scales. We refer to these as ‘finger modes’ because they displaykR/kZ≫ 1. The second appear at slightly later times in the main body of the disc, including near the mid-plane. These ‘body modes’ have somewhat longer radial wavelengths. Early on they manifest themselves as fundamental breathing modes, but quickly become corrugation modes as symmetry about the mid-plane is broken. The corrugation modes are a prominent feature of the non-linear saturated state, leading to strong vertical oscillation of the disc mid-plane. In a viscous disc with aspect ratioH/r= 0.05, instability is found to operate when the viscosity parameter α < 4 × 10−4. In three dimensions the instability generates a quasi-turbulent flow, and the associated Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches α ∼ 10−3by the end of the simulation. The evolution and saturation of the vertical shear instability in astrophysical disc models which include realistic treatments of the thermal physics has yet to be examined. Should it occur on either global or local scales, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties and observational appearance.
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DOI：
--
发表时间：
2011
期刊：
影响因子：
--
作者：
S. Fromang;W. Lyra;F. Masset
通讯作者：
F. Masset
影响因子：
6.5
作者：
M. Fragner;R. Nelson
通讯作者：
M. Fragner;R. Nelson
DOI：
10.1086/344743
发表时间：
2002-11
期刊：
The Astrophysical Journal
影响因子：
--
作者：
H. Klahr;Peter Bodenheimer UCOLick Observatory;C. Physics;I. F. A. U. Astrophysik;U. Tuebingen;H Germany
通讯作者：
H. Klahr;Peter Bodenheimer UCOLick Observatory;C. Physics;I. F. A. U. Astrophysik;U. Tuebingen;H Germany
DOI：
--
发表时间：
1987
期刊：
影响因子：
--
作者：
D. Lin;J. Pringle
通讯作者：
J. Pringle
剪切和密度分层联合影响下吸积盘的水动力稳定性
DOI：
--
发表时间：
2002
期刊：
影响因子：
--
作者：
Günther Rüdiger;Rainer Arlt;D. Shalybkov
通讯作者：
D. Shalybkov