The stability of accretion tori. II - Non-linear evolution to discrete planets
The stability of accretion tori. II - Non-linear evolution to discrete planets
复制标题
吸积环面的稳定性。
DOI：
10.1093/mnras/225.3.695
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发表时间：
1987
影响因子：
4.8
通讯作者：
P. Goldreich
中科院分区：
文献类型：
--
作者：
J. Goodman;R. Narayan;P. Goldreich
霍利已经通过二维计算机模拟表明，在一个细长的环面上，一个方位波数为m的线性Papaloizou-Pringle(PP)不稳定性被激发，它会非线性地演化为具有m个几乎不相连的‘行星’的构型。我们提出了一个解析的流体平衡，我们认为它代表了他的数值行星。流体呈椭球状，通过与流体逆行运动有关的科里奥力将其结合在一起。在环面和行星构型之间有一个分叉，正好在PP不稳定性开启的涡度之下。虽然解是三维的，但存在完美的流体静力平衡，运动是
完全是二维的。我们分析了分析行星的线性模式，发现有许多不稳定，尽管它们不像
环面的PP不稳定性。我们还讨论了中性模的能量和涡度，我们认为当环面分裂成行星时，为了守恒总能量和比涡度，可以激发具有负能量和非零涡度的中立模。我们推测，霍利模拟中的流体可能正在接近二维湍流。
Hawley has shown through two-dimensional computer simulations that a slender torus in which a linear Papaloizou-Pringle (PP) instability with azimuthal wavenumber m, is excited evolves non-linearly to a configuration with m nearly disconnected 'planets'. We present an analytical fluid equilibrium that we believe represents his numerical planets. The fluid has an ellipsoidal figure and is held together by the Corio lis force associated with the retrograde fluid motion. There is a bifurcation between the torus and planet configurations at precisely the vorticity below which the PP instability switches on. Although the solution is three-dimensional, there is perfect hydrostatic equilibrium and the motion is
entirely two-dimensional. We analyse the linear modes of the analytical planet and find that there are numerous instabilities, though they are not as violent as the
PP instability in the torus. We also discuss the energy and vorticity of neutral modes, and we argue that when the torus breaks up into planets, neutral modes with negative energy and non-zero vorticity are excited in order to conserve total energy and specific vorticity. We speculate that the fluid in Hawley's simulations may be approaching two-dimensional turbulence.