Rapidly rotating Rayleigh-Bénard convection in liquid metals

液态金属中的旋转Rayleigh-Bénard对流被认为是许多地球物理和天体物理环境中发生的磁流体动力学过程的理想模型系统，例如行星核心和恒星对流区。从流体动力学的角度来看，这些流量区分自己的低普朗特数，导致固有的不同的不稳定机制和更早的过渡到湍流，相比，中等和高普朗特数流量。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，实验中的视觉访问有限，因此研究很少。因此，基本的物理，特别是振荡对流，没有得到很好的理解。因此，建议的研究的目的是丰富我们的知识，在液态金属的对流。为此，应在快速旋转和磁场影响下，在具有各种纵横比的圆柱形容器中进行小普朗特数对流的高分辨率DNS。特别是，该制度的地转湍流，这是很少探讨，但在地球物理环境中最相关的。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）使用液体镓作为工作流体的独特旋转磁对流装置完全匹配。这允许一对一的比较，并为复杂的分析技术提供了基础。为了解释和分析所获得的数据，应将湍流对流理论、系统识别和实验室地球物理流体动力学的方法结合在一起。这意味着，除了使用传统的研究光谱的方法，平均值，均方根和高阶统计矩，动力学模式分解（DMD）应加以利用。DMD将直接将实验中发现的频率和DNS与实际流动结构联系起来，并进一步允许研究它们的时间演变。同时，借鉴系统辨识理论的方法，对这一问题提出了新的见解。它的目的是设计一个动态观测器，它基于单个热敏电阻测量，并与DNS相结合，将能够重建整个流动，否则视觉上无法访问的实验。

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.