Non-linear fluid dynamics of eccentric discs
Non-linear fluid dynamics of eccentric discs
复制标题
偏心盘的非线性流体动力学
DOI：
10.1046/j.1365-8711.2001.04416.x
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发表时间：
2001
影响因子：
4.8
通讯作者：
Gordon I. Ogilvie
中科院分区：
文献类型：
--
作者：
Gordon I. Ogilvie
提出了一种新的偏心吸积盘理论。从三维基本流体动力学方程出发，导出了描述薄盘的质量、角动量和偏心向量在内应力和外力作用下如何演化的一维基本方程组。该分析在薄盘的极限范围内是渐近精确的，并且允许任意量级的缓慢变化的偏心。对吸积盘中湍流应力的麦克斯韦粘弹性模型进行了详细的理论推导。这推广了传统的α-粘性模型来解释湍流的非零弛豫时间，并且物理上考虑了磁流体湍流的性质。正如Lyubarskj，Postnov和Prokhorov发现的那样，如果采用传统的α粘性模型，圆盘对偏心扰动通常是粘性不稳定的。然而，这种不稳定性通常可以通过引入足够的松弛时间和/或本体粘度来抑制。结果表明，初始均匀偏心的圆盘并不像以前的分析所建议的那样保持其偏心。演化方程在许多应用中应该是有用的，包括理解行星偏心率的起源和测试X射线双星中的准周期振荡理论。
A new theory of eccentric accretion discs is presented. Starting from the basic fluid-dynamical equations in three dimensions, I derive the fundamental set of one-dimensional equations that describe how the mass, angular momentum and eccentricity vector of a thin disc evolve as a result of internal stresses and external forcing. The analysis is asymptotically exact in the limit of a thin disc, and allows for slowly varying eccentricities of arbitrary magnitude. The theory is worked out in detail for a Maxwellian viscoelastic model of the turbulent stress in an accretion disc. This generalizes the conventional alpha viscosity model to account for the non-zero relaxation time of the turbulence, and is physically motivated by a consideration of the nature of magnetohydrodynamic turbulence. It is confirmed that circular discs are typically viscously unstable to eccentric perturbations, as found by Lyubarskij, Postnov & Prokhorov, if the conventional alpha viscosity model is adopted. However, the instability can usually be suppressed by introducing a sufficient relaxation time and/or bulk viscosity. It is then shown that an initially uniformly eccentric disc does not retain its eccentricity as had been suggested by previous analyses. The evolutionary equations should be useful in many applications, including understanding the origin of planetary eccentricities and testing theories of quasi-periodic oscillations in X-ray binaries.
影响因子：
3.2
作者：
V. Mannings;A. Boss;S. Russell
通讯作者：
V. Mannings;A. Boss;S. Russell