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The Theoretical Study on the Non-1inear Growing Process of Perturbations in the Astrophysical Systems including the Shear Flow.

包括剪切流在内的天体物理系统扰动非线性增长过程的理论研究。

基本信息

批准号：
01540220
负责人：
MIYAMA Shoken
金额：
$ 0.9万
依托单位：
National Astronomical Observatory
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1989
资助国家：
日本
起止时间：
1989 至 1990
项目状态：
已结题

项目摘要

In astrophysical Phenomena, shear flows often exist, i. e., the flow in which there is the velocity gradient along the flow direction. Such flows are found in accretion disks around neutron stars and black holes and in the boundary region between ambient matters and jets from radio galaxies as well as bipolar flows from proto-stars. In hydrodynamics, the shear flows are well-known to be unstable and systems including them become turbulent states. But in astrophysics, the growth process of the unstable perturbations has been not understood yet. Hence the purpose of this proposed study is investigations about the non-linear growth process of the unstable modes which come from the existence of the shear flow.As for the prototype model including the shear flow, we concentrate out study on differentially rotating disks. In order to analyze the non-linear process we use a weak non-linear theory, which is useful approximation method and applicable near the critical point where the growth rate of the linear perturbation is very small. Using this theory, because we can investigate analytically, it is very useful.Since this study is the first attempt to analyze the shear instability in the differentially rotating disks, we take one of the simplest model, i. e., an incompressible cylinder which distribution of specific angular momentum is uniform. As the results we find that the non-linearity suppresses the linear growth and there is a new quasi-stationary state. And we find that the system oscillates with finite amplitudes around that state. These results agree with the numerical results as obtained so far. We consider that non-linear oscillations are very interesting for the mechanism of the angular transfer because they are nonーaxisymmetric waves.

在天体物理现象中，剪切流是经常存在的，即：例如，沿流动方向有沿着速度梯度的流动。在中子星和黑洞周围的吸积盘中，在周围物质和射电星系喷流之间的边界区域以及原恒星的双极流中，都发现了这种流动。在流体力学中，剪切流是众所周知的不稳定和系统，包括他们成为湍流状态。但在天体物理学中，不稳定扰动的增长过程一直没有得到很好的理解。因此，本文的研究目的是研究剪切流存在时不稳定模态的非线性增长过程，对于包含剪切流的原型模型，我们主要研究差动旋转圆盘。为了分析非线性过程，我们使用弱非线性理论，这是有用的近似方法，并且适用于线性扰动的增长率非常小的临界点附近。由于本研究是首次尝试分析差动旋转圆盘中的剪切不稳定性，因此我们选取了一个最简单的模型，即：例如，比角动量均匀分布的不可压缩圆柱体。结果表明，非线性抑制了线性增长，出现了一个新的准定态。我们发现系统在这个状态附近以有限的振幅振荡。这些结果与迄今为止得到的数值结果一致。我们认为，非线性振荡是非常有趣的角转移的机制，因为它们是非线性轴对称波。