Rapidly rotating Rayleigh-Bénard convection in liquid metals

在许多地球物理和天体物理环境中，如行星核心和恒星对流区，液态金属中的旋转瑞利-巴姆纳德对流被认为是磁流体动力学过程的理想模型系统。从流体动力学的角度来看，这些流动以其低普朗特数来区分自己，与中等和高普朗特数的流动相比，导致内在不同的不稳定机制和更早地过渡到湍流。然而，由于直接数值模拟（DNS）的分辨率要求更高，并且由于金属的不透明性，实验中的视觉访问受限，研究很少。因此，潜在的物理，特别是振荡对流，并没有得到很好的理解。因此，所提出的研究的目的是丰富我们对液态金属对流流动的认识。为此，小普朗特数对流的高分辨率DNS需要在不同宽高比的圆柱形容器中，在快速旋转和磁场的影响下进行。特别地，地转湍流的制度将被覆盖，这是很少探索，但最相关的地球物理设置。控制参数的选择将与加州大学洛杉矶分校模拟行星内部实验室（SPINlab）独特的旋转磁对流装置完全匹配，该装置使用液态镓作为工作流体。这允许一对一的比较，并为复杂的分析技术提供基础。为了解释和分析获得的数据，湍流对流理论、系统识别和实验室地球物理流体动力学的方法必须结合在一起。这意味着，除了使用传统的谱、均值、均方根和高阶统计矩的研究方法外，还需要利用动态模态分解（DMD）。DMD将直接将实验中发现的频率与实际流结构的DNS联系起来，并将进一步研究它们的时间演变。此外，借鉴系统识别理论的技术可以获得一个新的视角。它的目的是设计一个动态观测器，它基于单个热敏电阻的测量，并与DNS相结合，将能够在视觉上无法实现的实验中重建整个流。

Rotating Rayleigh-Bénard convection in liquid metals is considered to be an ideal model system of the magnetohydrodynamic processes occurring in many geophysical and astrophysical settings, such as planetary cores and stellar convection zones. From a fluid dynamical point of view these flows distinguish themselves by their low Prandtl number, leading to inherently different instability mechanisms and a much earlier transition to turbulence, when compared to moderate and high Prandtl number flows. However, due to the much more demanding resolution requirements for direct numerical simulations (DNS) and the limited visual access in experiments because of the metal's opaqueness, studies are sparse. Consequently, the underlying physics, notably oscillatory convection, is not well understood. The objective of the proposed research is thus to enrich our knowledge about convective flows in liquid metals. For this purpose, high-resolution DNS of small Prandtl number convection shall be conducted in cylindrical containers with various aspect ratios, both under the influence of rapid rotation and of magnetic fields. In particular, the regime of geostrophic turbulence will be covered, which is little explored and yet the most relevant in geophysical settings. The control parameters will be chosen to match exactly the unique rotating magnetoconvection device at the Simulated Planetary Interiors Laboratory (SPINlab) at UCLA which uses liquid gallium as working fluid. This allows for a one-to-one comparison and provides the foundation for sophisticated analysis techniques. To interpret and analyse the obtained data, approaches from turbulent convection theory, system identification, and laboratory geophysical fluid dynamics shall be brought together. This means, besides using the traditional methods of studying spectra, the mean, root mean square, and higher-order statistical moments, the dynamical mode decomposition (DMD) shall be exploited. The DMD will directly link the frequencies found in the experiments and the DNS with actual flow structures and will further allow the study of their temporal evolution. Moreover, a novel view on this problem shall be gained by borrowing techniques from system identification theory. It is aimed to design a dynamic observer, which based on single thermistor measurements and in conjunction with the DNS, will be able to reconstruct the entire flow in the otherwise visually inaccessible experiment.