arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1409.6487astro-ph.EPastro-ph.HEastro-ph.SRphysics.flu-dyn
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偏心天体物理盘的局部和全局动力学

Local and global dynamics of eccentric astrophysical discs

Gordon I. Ogilvie, Adrian J. Barker

摘要:

我们制定了一个局部动力学模型的偏心盘,其中的主导运动由椭圆开普勒轨道。该模型是著名的剪切薄板的推广,适用于偏心盘局部动力学的分析和计算研究。它在水平维度上是空间均匀的,但具有以轨道频率振荡的随时间变化的几何形状。我们展示了如何在本地模型中的应力张量的某些平均值确定的大规模的光盘的形状和质量分布的演变。局部模型的最简单解是由圆盘的垂直振荡(一般为非线性)组成的层流。偏心圆盘缺乏垂直的流体静力平衡,因为偏心轨道周围的垂直重力加速度的变化,在某些情况下,因为与偏心率梯度相关的轨道速度场的发散。我们讨论的层流解决方案的属性,表明他们可以表现出极端的压缩行为的偏心率大于约$0.5$,特别是在光盘等温行为。我们还推导出线性演化方程的偏心盘遵循的层流的剪切粘度的情况下。在配套文件中,我们表明,这些解决方案是线性不稳定的,我们确定相关的增长率和不稳定模式。

英文摘要:

We formulate a local dynamical model of an eccentric disc in which the dominant motion consists of elliptical Keplerian orbits. The model is a generalization of the well known shearing sheet, and is suitable for both analytical and computational studies of the local dynamics of eccentric discs. It is spatially homogeneous in the horizontal dimensions but has a time-dependent geometry that oscillates at the orbital frequency. We show how certain averages of the stress tensor in the local model determine the large-scale evolution of the shape and mass distribution of the disc. The simplest solutions of the local model are laminar flows consisting of a (generally nonlinear) vertical oscillation of the disc. Eccentric discs lack vertical hydrostatic equilibrium because of the variation of the vertical gravitational acceleration around the eccentric orbit, and in some cases because of the divergence of the orbital velocity field associated with an eccentricity gradient. We discuss the properties of the laminar solutions, showing that they can exhibit extreme compressional behaviour for eccentricities greater than about $0.5$, especially in discs that behave isothermally. We also derive the linear evolutionary equations for an eccentric disc that follow from the laminar flows in the absence of a shear viscosity. In a companion paper we show that these solutions are linearly unstable and we determine the associated growth rates and unstable modes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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