Dynamics and transport of magnetorotational instabilities in Taylor--Couette flows

气体的湍流传输是解释天体物理盘中物质吸积和太阳系形成速率的必要物理过程。然而，在这样的圆盘中，角动量呈径向增加，因此根据旋转流体的瑞利准则，气体运动预计是层流的。这个谜题的答案是由磁旋转不稳定性（MRI）提供的，它在气体电离的情况下在磁盘中运行。在过去的二十年里，人们对核磁共振成像的特性进行了大量的数值研究。模拟通常使用剪切片近似进行，这是吸积盘的局部模型。近年来，人们对在实验室实验中获得核磁共振成像产生了相当大的兴趣。核磁共振成像的典型实验是在施加轴向磁场的情况下，液态金属在两个同心且独立旋转的圆柱体之间旋转。对这一问题进行了线性稳定性研究，结果与螺旋磁场的实验结果基本一致。然而，对于核磁共振的非线性饱和、分岔情况、向湍流的转变和输运性质，人们知之甚少，而这些对磁盘吸积至关重要。该项目的主要目标是提供非线性状态下旋转圆柱体之间流动的磁旋转不稳定性的表征。不同类型的核磁共振成像，对应于不同的磁场结构，将相互对比，传输缩放将被计算并用于推断天体物理背景下的性质。结果将与剪切片近似中相同不稳定性的性质进行广泛的比较，在剪切片近似中，施加的径向周期边界条件被认为在湍流的非线性饱和和性质中起关键作用。该项目将为制定基准提供丰富的数据，特别是与已经进行或正在进行或计划进行的实验室实验进行比较。

Turbulent transport of gas is a necessary physical process to explain the rates at which matter accretes and solar systems form in astrophysical disks. However, angular momentum increases radially in such disks and hence gas motion is expected to be laminar according to the Rayleigh criterion for rotating fluids. The solution to this riddle is provided by the magnetorotational instability (MRI), which operates in disks provided that the gas is ionized. In the last two decades there has been a great deal of numerical studies studying the properties of the MRI. Simulations are usually performed using the shearing sheet approximation, which is a local model of an accretion disk. Recently, there has been considerable interest in obtaining the MRI in laboratory experiments. The canonical experiment for the MRI is the swirling flow of a liquid metal between two concentric and independently rotating cylinders with an imposed axial magnetic field. Linear stability studies of this problem have been carried out, and shown to be in reasonable agreement with experiment for helical magnetic fields. However, little is known of the nonlinear saturation, bifurcation scenario, transition to turbulence and transport properties of the MRI, which is crucial for accretion in disks.The main goal of this project is to provide a characterization of magnetorotational instabilities in flows between corotating cylinders in the nonlinear regime. The various flavors of the MRI, corresponding to different magnetic field configurations, will be contrasted with one another, and transport scaling will be computed and used to infer properties in the astrophysical context. The results will be extensively compared with properties of the same instability in the shearing sheet approximation, in which the imposed radially periodic boundary conditions are thought to play a key role in the nonlinear saturation and properties of the turbulent flow. The project will provide a wealth of data for benchmarking and especially for comparison with laboratory experiments that have already been performed or are either under way or planned.