Synergistic Explorations of Hydromagnetic Core Turbulence via Simulations and Asymptotics

地球磁场是由铁水外核深处的流体运动产生的。由于地处偏远，不可能直接观测到地心运动。这一限制阻碍了我们理解控制核心和观测到的地磁场的动力学和演化的物理学的能力，并将重点放在开发更准确的建模技术上。这项拟议的工作将通过开发和模拟新的数学模型来研究地核及其相关磁场的物理学，这些模型将允许系统地改变被认为是地核中重要成分的成分。这是一个跨学科项目，汇集了来自地球物理学和应用数学界的科学家，他们拥有建模、计算和实验等重要应用领域的技能。这项拟议的工作将在地球物理和应用数学等国家重要科学和数学领域为研究生和博士后研究员提供宝贵的培训。缺乏对地磁场观测的直接观测阻碍了我们了解地磁场观测的细节和预测其时间演变的能力。克服这一限制需要进一步开发准确的模型，并从理论上了解核心内可能存在的各种流动状态。目前，由于有限的计算资源导致缺乏时空尺度分离，对地球发电机的直接数值模拟在岩心湍流中主导力量平衡的精确性质上缺乏共识。这项提议寻求资金，以研究被认为与地球液态外核和地磁场有关的动力机制，方法是采用数值模拟和渐近模型开发相结合的方法，该方法以正在进行的实验室实验获得的数据为指导。一个主要目标是通过明确控制外部施加的磁场和系统旋转速度的相对强度，来探索和推进我们对核心湍流环境中不同力平衡的动力学和统计结果的理解。

The Earth's magnetic field is generated by fluid motions deep within the molten iron outer core. Owing to its remoteness, direct observations of core motions are not possible. This limitation hinders our ability to understand the physics that control the dynamics and evolution of the core and the observed geomagnetic field, and places an emphasis on the development of more accurate modeling techniques. The proposed work will investigate the physics of the core and associated magnetic field via the development and simulation of new mathematical models that will allow systematic variation of the ingredients thought to be important in the core. This is an interdisciplinary project that brings together scientists from both the geophysics and applied mathematics communities who possess skill-sets in the important application areas of modeling, computation and experimentation. The proposed work will provide valuable training for a graduate student and postdoctoral researcher in the nationally important scientific and mathematical fields of geophysics and applied mathematics.The lack of direct observations of the core hinders our ability to understand the details of geomagnetic field observations and make predictions on its temporal evolution. Overcoming this limitation requires the further development of accurate models and the theoretical understanding of various flow regimes that might be possible within the core. Presently, direct numerical simulations of the geodynamo lack consensus on the precise nature of the dominant force balances in core turbulence due to lack of spatiotemporal scale separation resulting from finite computational resources. This proposal seeks funding to investigate dynamical regimes that are thought to be relevant for the Earth's liquid outer core and the geomagnetic field via a combined approach of numerical simulations and asymptotic model development that is guided by data obtained from ongoing laboratory experiments. A major goal is to explore and advance our understanding of the dynamical and statistical consequences of differing force balances in core turbulence settings by explicitly controlling the relative strengths of an externally imposed magnetic field and the system rotation rate.