CAREER: Unraveling the Multiscale Asymptotic Dynamics of Planetary Dynamos

修正地球磁场或地磁场有助于保护地球表面不受太阳辐射的影响，并作为导航的重要参考。地球磁场是动态的：它显示出几乎稳定的向西运动；它可以表现出所谓的北极和南极向赤道移动的漂移；在从数十万年到数百万年的时间尺度上，它可以经历磁极完全互换位置的极性反转。尽管这些观测结果是众所周知的，但控制它们的物理原理仍然知之甚少。存在于地球铁水外核的大量风是产生地磁场的原因，但不可能直接观察到这些流体的运动。相反，我们对地核及其相关磁场，也就是地球发电机的大部分理解，都是从计算机模型中衍生出来的。虽然这些模型继续提供了对地球发电机的宝贵见解，但它们不能准确地代表表征它的极端条件。这个项目将通过结合数学分析和高性能计算机模拟来研究地球外核中的流体如何被不同的力推动和拉动，以及这些力如何影响由此产生的动力学，从而解决这一限制。这项工作的结果将是更好地理解控制地磁场演变的力量，以及在未来建立更好的地磁场模型的潜力。此外，太阳系内的大多数行星也都有全球尺度的磁场，这些磁场是通过产生地球磁场的相同机制产生的；这项工作也将与增进对这些行星磁场的理解直接相关。与这项拟议的研究相结合，将制作一套面向本科生和研究生的公开教育视频，重点介绍行星磁场的基本物理知识。观测表明，行星发电机和恒星发电机在宇宙中很常见。由于固有的非线性和不同的时空尺度表征了这些系统的动力学特性，使得理解这些系统变得困难。目前的模型使用的动力参数与行星发电机的动力参数有许多数量级的不同。然而，行星内部导电的流动被认为是平衡的，因为两种或更多的力是主导的。平衡流动的概念已被成功地用来有效地模拟地球大气、海洋和次固线地幔中的流体流动；与不可近似的控制方程相比，这种简化的模型简化了物理理解，并大大降低了计算费用。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平衡仍存在争议。该项目概述了一项使用数值模拟和微扰理论的详细调查，该调查将通过检查多个长度尺度上的平衡来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，即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态，并且这三个尺度上存在着不同的平衡。初步结果指出了行星发电机物理学的另一种理论，它有可能调和目前关于行星发电机物理学的不同观点。为了以协同的方式将首席研究人员的教育和研究活动联系起来，将与本科生和研究生团队一起开发一套与拟议工作相关的教育视频，并在万维网上提供。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.