CAREER: Unraveling the Multiscale Asymptotic Dynamics of Planetary Dynamos

地球磁场，或称地磁场，有助于保护地球表面免受太阳辐射的影响，并作为导航的重要参考。地磁场是动态的：它表现出几乎稳定的向西运动;它可以表现出所谓的偏移，即磁北极和磁南极向赤道移动;并且，在数十万年到数百万年的时间尺度上，它可以经历磁极完全交换位置的极性反转。尽管这些观察结果众所周知，但控制它们的物理学仍然知之甚少。地磁场的产生是由于地球外核的熔融铁中存在大量的风，但直接观察这些流体运动是不可能的。相反，我们对地核和相关磁场（被称为地球发电机）的大部分理解都来自计算机模型。虽然这些模型继续提供有价值的洞察地球发电机，他们不能准确地代表其特有的极端条件，这个项目将通过使用数学分析和高性能计算机模拟相结合来研究地球的外核流体是如何被不同的力量推和拉，以及这些力量如何影响所产生的动态来解决这个限制。这项工作的成果将是对控制地磁场演变的力量的更好理解，以及在未来建立更好模型的潜力。此外，太阳系内的大多数行星也有全球规模的磁场，这些磁场是通过产生地磁场的相同机制产生的;这项工作也将直接关系到提高对这些行星磁场的理解。与拟议的研究相结合，将为本科生和研究生制作一套公开的教育视频，重点介绍行星磁场的基本物理学。观测表明，行星和恒星发电机在整个宇宙中很常见。理解这些系统的进展是困难的，由于其固有的非线性和不同的时空尺度，其动态特性。目前的模型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，行星内部导电的流动被认为是平衡的，因为两个或更多的力占主导地位。平衡流的概念已被利用，并取得了巨大的成功，有效地模拟地球的大气层，海洋和亚固相线地幔的流体流动;这种简化的模型提供了简化的物理理解和大大降低计算成本相比，非近似的控制方程。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然存在争议。该项目概述了使用数值模拟和微扰理论的详细研究，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。这项工作是基于假设，行星发电机物理本质上是多尺度的，三个占主导地位的长度尺度控制他们的动态，并在这三个尺度上存在不同的平衡。初步结果指出，行星发电机物理学的替代理论，有可能调和目前行星发电机物理学的不同观点。以协同方式将主要研究者的教育和研究活动联系起来，一组由本科生和研究生组成的研究小组将制作一套与拟议工作有关的教育视频，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，并被认为值得通过利用基金会的智力价值和更广泛的影响审查进行评估来支持的搜索.

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.