Synergistic Explorations of Hydromagnetic Core Turbulence via Simulations and Asymptotics

地球的磁场是由外核深处的铁水运动产生的。由于它的遥远，直接观测核心运动是不可能的。这种限制阻碍了我们理解控制地核和观测到的地磁场的动态和演化的物理学的能力，并强调了更准确的建模技术的发展。拟议的工作将通过开发和模拟新的数学模型来研究核心和相关磁场的物理学，这些模型将允许被认为在核心中重要的成分的系统变化。这是一个跨学科的项目，汇集了来自物理学和应用数学社区的科学家，他们在建模，计算和实验的重要应用领域拥有技能。拟议的工作将为研究生和博士后研究人员提供有价值的培训，在国家重要的科学和数学领域的地球物理学和应用数学。缺乏直接观测的核心阻碍了我们的能力，了解地磁场观测的细节，并作出预测其时间演变。克服这一限制需要进一步发展准确的模型和理论上的理解，各种流动制度，可能在核心。目前，直接数值模拟的地球发电机缺乏共识的核心湍流的主导力量平衡的精确性质，由于缺乏时空尺度分离有限的计算资源。该提案寻求资金，通过数值模拟和渐近模型开发相结合的方法，以正在进行的实验室实验获得的数据为指导，研究被认为与地球液态外核和地磁场相关的动力学机制。一个主要的目标是探索和推进我们的理解的动力学和统计的后果，不同的力平衡在核心湍流设置明确控制的相对强度的外部施加的磁场和系统的旋转速率。

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.