Mondal Tushar, Bhat Pallavi
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India.
Phys Rev E. 2023 Dec;108(6-2):065201. doi: 10.1103/PhysRevE.108.065201.
Magnetorotational instability-driven (MRI-driven) turbulence and dynamo phenomena are analyzed using direct statistical simulations. Our approach begins by developing a unified mean-field model that combines the traditionally decoupled problems of the large-scale dynamo and angular momentum transport in accretion disks. The model consists of a hierarchical set of equations, capturing up to the second-order correlators, while a statistical closure approximation is employed to model the three-point correlators. We highlight the web of interactions that connect different components of stress tensors-Maxwell, Reynolds, and Faraday-through shear, rotation, correlators associated with mean fields, and nonlinear terms. We determine the dominant interactions crucial for the development and sustenance of MRI turbulence. Our general mean-field model for the MRI-driven system allows for a self-consistent construction of the electromotive force, inclusive of inhomogeneities and anisotropies. Within the realm of large-scale magnetic field dynamo, we identify two key mechanisms-the rotation-shear-current effect and the rotation-shear-vorticity effect-that are responsible for generating the radial and vertical magnetic fields, respectively. We provide the explicit (nonperturbative) form of the transport coefficients associated with each of these dynamo effects. Notably, both of these mechanisms rely on the intrinsic presence of large-scale vorticity dynamo within MRI turbulence.
利用直接统计模拟分析了磁旋转不稳定性驱动（MRI驱动）的湍流和发电机现象。我们的方法首先建立一个统一的平均场模型，该模型将吸积盘中传统上解耦的大规模发电机问题和角动量传输问题结合起来。该模型由一组分层方程组成，可捕捉到二阶相关器，同时采用统计闭合近似来模拟三点相关器。我们强调了通过剪切、旋转、与平均场相关的相关器以及非线性项将应力张量的不同分量——麦克斯韦、雷诺和法拉第——连接起来的相互作用网络。我们确定了对MRI湍流的发展和维持至关重要的主导相互作用。我们的MRI驱动系统的通用平均场模型允许自洽地构建电动势，包括不均匀性和各向异性。在大规模磁场发电机的领域内，我们确定了两个关键机制——旋转 - 剪切 - 电流效应和旋转 - 剪切 - 涡度效应——它们分别负责产生径向和垂直磁场。我们提供了与这些发电机效应中的每一个相关的输运系数的显式（非微扰）形式。值得注意的是，这两种机制都依赖于MRI湍流中大规模涡度发电机的内在存在。
