论文标题
水动力不稳定性在开普勒积聚盘中具有噪声：修改的兰道方程
Hydrodynamical instability with noise in the Keplerian accretion discs: Modified Landau equation
论文作者
论文摘要
开普勒积盘中流体动力不稳定性和湍流的起源以及类似的实验室剪切流，例如平面枪口流量是一个长期的难题。这些流是线性稳定的。在这里，我们探讨了在存在额外力的情况下这种流动中扰动的演变。这种力量在自然界中预计会是随机的，因此可能是噪音的，可能是由于天体物理碟片中的热波动（多么小），布朗棘轮，谷物 - 流体的相互作用以及来自天体物理盘流出的反馈等。我们基本上建立了在Coriolis和外部力量和外部力量的情况下，非线性扰动的演变，即Modified Landau equaried Landau equinified Landau。我们表明，即使在适当的强迫和雷诺数下，在线性状态下，原本稳定的扰动也会演变为非常大的饱和振幅，从而导致了非线性和合理的湍流。因此，强迫基本上导致线性稳定模式变得不稳定。我们进一步表明，在力存在下，非线性扰动在较短的时间尺度上有所不同，导致快速过渡到湍流。有趣的是，与原始的基于Landau方程的解决方案不同，非线性的出现仅取决于力，而不取决于扰动的初始幅度。
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.
