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arXiv 2006.10075astro-ph.HEphysics.flu-dyn
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Keplerian吸积盘中带噪声的流体动力学不稳定性:修正的Landau方程

Hydrodynamical instability with noise in the Keplerian accretion discs: Modified Landau equation

Subham Ghosh, Banibrata Mukhopadhyay

摘要:

开普勒吸积盘中流体动力学不稳定性和湍流的起源以及类似的实验室剪切流,例如平面Couette流,是一个长期存在的谜。这些流动是线性稳定的。在这里,我们探讨的扰动在这种流动中的存在下,一个额外的力的演变。这样的力,这是预计是随机的性质,因此表现为噪声,可能是热涨落(无论多么小),布朗棘轮,颗粒流体相互作用和反馈的天体物理盘等的外流。我们基本上建立了非线性扰动的发展存在的科里奥利和外力,这是修改的朗道方程。我们发现,即使在线性制度下,适当的强迫和雷诺数,否则最不稳定的扰动演变到一个非常大的饱和振幅,导致非线性和合理的湍流。因此,强迫本质上导致线性稳定模式不稳定。我们进一步表明,非线性扰动发散在一个较短的时间尺度存在的力量,导致快速过渡到湍流。有趣的是,非线性的出现只取决于力,而不是初始扰动振幅,不同于原来的朗道方程为基础的解决方案。

英文摘要:

Origin of hydrodynamical instability and turbulence in the Keplerian accretion disc as well as similar laboratory shear flows, e.g. plane Couette flow, is a long standing puzzle. These flows are linearly stable. Here we explore the evolution of perturbation in such flows in the presence of an additional force. Such a force, which is expected to be stochastic in nature hence behaving as noise, could be result of thermal fluctuations (however small be), Brownian ratchet, grain-fluid interactions and feedback from outflows in astrophysical discs etc. We essentially establish the evolution of nonlinear perturbation in the presence of Coriolis and external forces, which is modified Landau equation. We show that even in the linear regime, under suitable forcing and Reynolds number, the otherwise least stable perturbation evolves to a very large saturated amplitude, leading to nonlinearity and plausible turbulence. Hence, forcing essentially leads a linear stable mode to unstable. We further show that nonlinear perturbation diverges at a shorter timescale in the presence of force, leading to a fast transition to turbulence. Interestingly, emergence of nonlinearity depends only on the force but not on the initial amplitude of perturbation, unlike original Landau equation based solution.

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