Synergistic Explorations of Hydromagnetic Core Turbulence via Simulations and Asymptotics

地球的磁场是由熔融铁外核深处的流体运动产生的。由于地处偏远，对地核运动的直接观测是不可能的。这一限制阻碍了我们理解控制地核动力学和演化的物理学以及观测到的地磁场的能力，并强调了更精确建模技术的发展。拟议的工作将通过开发和模拟新的数学模型来研究地核和相关磁场的物理特性，这些模型将允许对地核中被认为重要的成分进行系统的变化。这是一个跨学科项目，汇集了地球物理学和应用数学领域的科学家，他们在建模、计算和实验等重要应用领域拥有技能。建议的工作将为地球物理和应用数学的国家重要科学和数学领域的研究生和博士后研究员提供宝贵的培训。缺乏对地核的直接观测，阻碍了我们对地磁场观测细节的理解和对其时间演变的预测。克服这一限制需要进一步发展精确的模型，并从理论上理解堆芯内可能存在的各种流动状态。目前，由于计算资源有限，缺乏时空尺度的分离，地球动力学的直接数值模拟对地核湍流中主导力平衡的精确性质缺乏共识。本提案寻求资金，通过数值模拟和渐近模型开发相结合的方法来研究被认为与地球液体外核和地磁场相关的动力学制度，该方法由正在进行的实验室实验获得的数据指导。一个主要目标是通过明确控制外部施加磁场的相对强度和系统旋转速率，探索和推进我们对核心湍流设置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.