CAREER: Unraveling the Multiscale Asymptotic Dynamics of Planetary Dynamos

地球的磁场或地磁场有助于保护地球表面免受太阳辐射，是导航的重要参考。地磁场是动态的：它几乎稳定地向西运动；它可以表现出所谓的偏移，即磁北极和磁南极向赤道移动；而且，在数十万年到数百万年的时间尺度上，它可能会经历磁极完全交换位置的极性逆转。虽然这些观测结果是众所周知的，但控制它们的物理学仍然知之甚少。地球外核熔融铁中的巨大风是产生地磁场的原因，但对这些流体运动的直接观察是不可能的。相反，我们对地核和相关磁场（即地球发电机）的大部分理解都来自计算机模型。虽然这些模型继续为地球动力学提供有价值的见解，但它们不能准确地代表其特征的极端条件。该项目将利用数学分析和高性能计算机模拟相结合的方法来解决这一限制，以研究地球外核中的流体如何受到不同力的推动和拉动，以及这些力如何影响所产生的动力学。这项工作的结果将是提高对控制地磁场演化的力的理解，并有可能在未来建立更好的地磁场模型。此外，太阳系内的大多数行星也有全球范围的磁场，它们是通过产生地磁场的相同机制产生的；这项工作也将与提高对这些行星磁场的理解直接相关。与提议的研究相结合，将为本科生和研究生创建一套公开可用的教育视频，突出行星磁场的潜在物理学。观测表明，行星和恒星发电机在整个宇宙中很常见。由于其固有的非线性和不同的时空尺度特征，对这些系统的理解很难取得进展。目前的模型所使用的动力学参数与行星发电机的动力学参数有许多数量级的不同。然而，在两种或两种以上的力占主导地位的情况下，行星内部的电流被认为是平衡的。平衡流动的概念已被成功地用于有效地模拟地球大气、海洋和亚固体地幔中的流体流动；与未近似的控制方程相比，这种简化的模型提供了简化的物理理解并大大降低了计算成本。目前还没有类似的模型来理解行星的球形发电机区域。此外，控制行星发电机的力量平衡仍然存在争议。该项目概述了使用数值模拟和摄动理论的详细调查，将通过检查多个长度尺度上的平衡系统地揭示行星发电机的动力学行为。这项工作是基于这样的假设：行星发电机物理本质上是多尺度的，三个主要的长度尺度控制着它们的动力学，并且在这三个尺度上存在不同的平衡。初步结果指出了行星发电机物理的另一种理论，它有可能调和目前关于行星发电机物理的不同观点。为了将首席研究员的教育和研究活动以一种协同的方式联系起来，将与一组本科生和研究生一起制作一套与拟议工作有关的教育录像，并通过万维网提供。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

make revisionsThe magnetic field of the Earth, or the geomagnetic field, helps to shield Earth’s surface from solar radiation, and serves as an important reference for navigation. The geomagnetic field is dynamic: it shows a nearly steady westward movement; it can exhibit so-called excursions in which the magnetic north and south poles move toward the equator; and, on timescales ranging from hundreds of thousands of years to millions of years, it can undergo polarity reversals in which the magnetic poles swap positions entirely. Although these observations are well-known, the physics that controls them remains poorly understood. Massive winds present in the molten iron outer core of the Earth are responsible for the generation of the geomagnetic field, yet direct observation of these fluid motions is not possible. Instead, much of our understanding of the core and associated magnetic field, known as the geodynamo, is derived from computer models. While these models continue to provide valuable insight into the geodynamo, they cannot accurately represent the extreme conditions that characterize it. This project will address this limitation by using a combination of mathematical analysis and high-performance computer simulations to examine how fluid in the Earth’s outer core is pushed and pulled by different forces, and how these forces influence the resulting dynamics. The outcome of this work will be an improved understanding of the forces that control the evolution of the geomagnetic field, and the potential for building better models of it in the future. Additionally, most of the planets within the Solar System also have global-scale magnetic fields that are created through the same mechanism that creates the geomagnetic field; this work will also be of direct relevance for improving understanding of these planetary magnetic fields. In conjunction with the proposed research, a set of publicly available educational videos will be created with both undergraduate students and graduate students that highlights the underlying physics of planetary magnetics fields.Observations suggest that planetary and stellar dynamos are common throughout the universe. Progress on understanding these systems is made difficult due to the intrinsic nonlinearity and disparate spatiotemporal scales that characterize their dynamics. Current models utilize dynamical parameters that are many orders of magnitude different than those of planetary dynamos. However, the flows within the electrically conducting interiors of planets are thought to be balanced in the sense that two or more forces are dominant. The concept of balanced flows has been exploited with great success to efficiently model fluid flow in the Earth's atmosphere, oceans and sub-solidus mantle; such reduced models provide simplified physical understanding and substantially reduced computational cost in comparison to the un-approximated governing equations. No analogous model currently exists for understanding the spherical dynamo regions of planets. Moreover, the force balance that controls planetary dynamos is still debated. This project outlines a detailed investigation using both numerical modeling and perturbation theory that will systematically unravel the dynamical behavior of planetary dynamos by examining balances on multiple length scales. The work is based on the hypotheses that planetary dynamo physics is intrinsically multiscale, that three dominant length scales control their dynamics, and that distinct balances on these three scales exist. Preliminary results point to an alternative theory of planetary dynamo physics that has the potential to reconcile the current divergent viewpoints on planetary dynamo physics. To link the education and research activities of the principal investigator in a synergistic manner, a set of educational videos related to the proposed work will be developed with a team of undergraduate research students and graduate students and made available through the world wide web.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.