天体物理切变流源中湍流发生和自我维持的本质

M. Kavtaradze, G. Mamatsashvili, G. Chagelishvil
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摘要

为了了解亚临界湍流在谱稳定天体物理(恒定)剪切流中的自我维持机制,我们在局部剪切盒近似下对平面流体动力和MHD均匀剪切流中的湍流进行了直接数值模拟,并在谱/傅里叶空间中对动力学过程进行了分析。在MHD的情况下,我们考虑了平行于气流方向的均匀磁场。在这种流动中不存在指数增长模式,而湍流仅由由剪切流动非正态性引起的扰动的傅里叶谐波的线性瞬态增长来能量支持。这种非正态性诱导的生长,也称为非模态生长,在傅里叶空间中是各向异性的,这反过来又导致了该空间中非线性过程的特定各向异性。因此,剪切流中的主要非线性过程是谐波在傅里叶空间中的横向(角)重分布——非线性横向级联——而不是通常的正级联或逆级联。结果表明,对于所有考虑的流动构型,湍流是由线性非模态增长和非线性横向叶栅之间的微妙相互作用维持的。湍流的唯一能量来源是由流动剪切引起的扰动的线性瞬态增长,这是由雷诺兹和麦克斯韦应力介导的,分别从背景流中提取动能和磁能——非线性过程并不直接改变总扰动能量,而只是将其重新分配到扰动的傅里叶谐波中。我们在考虑的情况下提出了湍流维持的基本周期,这清楚地表明了流动自组织中线性和非线性过程的协同作用。对不同背景磁场值进行数值模拟,结果表明,随着磁场的增大,湍流发生的时间增大,湍流强度减小。最后,在一定阈值的背景磁场下,流体完全稳定。值得注意的是,平面和旋转/开普勒天体物理剪切流的能量供应有本质区别:在平面剪切流中,主要的线性过程能量供应湍流是由于运动学(雷诺兹应力),而对于开普勒旋转-是由于磁场(麦克斯韦应力)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The essence of onset and self-sustenance of turbulence in astrophysical shear flows Sources
To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable astrophysical (constant) shear flows, we performed direct numerical simulations of turbulence in plane hydrodynamic and MHD homogeneous shear flows in the local shearing-box approximation with subsequent analysis of the dynamical processes in spectral/Fourier space. In the MHD case, we considered uniform magnetic field directed parallel to the flow. There are no exponentially growing modes in such flows and the turbulence is instead energetically supported only by the linear transient growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in Fourier space, which, in turn, leads to a specific anisotropy of nonlinear processes in this space. As a result, a main nonlinear process in shear flows is transverse (angular) redistribution of harmonics in Fourier space – nonlinear transverse cascade – rather than usual direct or inverse cascades. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade for all considered flow configurations. The only energy supplier for the turbulence is the linear transient growth of perturbations due to the flow shear, which is mediated by Reynolds and Maxwell stresses, extracting, respectively, kinetic and magnetic energy from the background flow – the nonlinear processes do not directly change the total perturbation energy but only redistribute it among Fourier harmonics of perturbations. We propose the basic cycles of the turbulence sustenance in the considered cases, which clearly show the synergy of linear and nonlinear processes in the self-organization of the flow. Performing numerical simulations for different values of the background magnetic field, we show that with the increase of the field, the onset of turbulence occurs at larger times and the power of turbulence reduces. Finally, at definite threshold background magnetic field the flow completely stabilizes. It is significant that, there is an essential difference in the energy supply of plane and rotating/Keplerian astrophysical shear flows: in plane shear flows the leading linear process energetically supplying turbulence is due to the kinematics (Reynolds stress), while for Keplerian rotation – is due to magnetic field (Maxwell stress).
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