Rapid dynamics in the Earth's core

地球如何产生磁场的问题是当今最突出的科学挑战之一。地磁场的观测和模型提供了一个窗口，通过它可以研究地球深处的动态过程和结构，这是一种补充地震研究的技术。在过去二十年中，各种卫星任务大大提高了我们对地球磁场的认识，包括其空间结构和在年代际时间尺度上的时间行为。由于这些观测不能探测到最下面的地幔，所以对磁场产生的流体外核的任何理解，以及对其时间变化的任何洞察，都必须从模型中获得。地核的地球动力学模型传统上关注千年或更长的时间尺度来理解地核场的长期演变，在很大程度上忽略了较短的时间尺度。我们的目的是研究这些具有重大科学意义的快速动力学，因为我们对这些信号有准确的观测。这样一个项目是对投入最新一代卫星的巨大科学努力和费用的补充。我们提出了三个相互联系但又独立的项目，这些项目将在利兹大学的数学学院和地球与环境学院之间进行分割：(i)核心激励和快速动力学的数值笛卡尔盒模型的构建；（ii）核心区流动不稳定性宏观动力学模型的发展；（三）从观测卫星数据中提取和模拟岩心内的流动加速度。对流驱动的球壳地球动力学模拟，从第一性原理求解基本方程，已经非常成功地解释了观测到的地磁场的许多特征，但它们确实存在一些重要的局限性。即使使用最强大的计算机，这些模型也无法解决短长度尺度和时间尺度的问题，因此必须使用与地球物理对地核的估计相差许多数量级的参数来运行。事实上，地球系统是如此复杂，以至于在未来几十年里，在正确的参数值下运行能够解决所有时间和空间尺度的模型的可能性很小。然而，我们相信，在正确的参数下运行模型，但在简化的几何结构中，可以获得相当大的洞察力。我们提出的计算模型(i)和（ii）旨在了解快速时间尺度上地球动力学的具体方面。项目(i)很好地说明了缺乏现实几何的重要性，重点放在快速动力学的激励机制上。这些被认为是由独立于任何边界效应的湍流对流驱动的，并且应该在地球物理参数值下运行的任何3D模型中捕获。特别是，这些过程将在笛卡尔盒模型中完全表示，在小粘度下比球面模型更容易计算研究。通过将项目(i)的激励机制知识与项目（ii）对核心不稳定性宏观动力学的理解相结合，我们将显著提高我们对快速时间尺度核心过程的理解。用（iii）中的观测数据验证和使用这些新见解将有助于解释引起广泛兴趣的地磁抖动。这项研究还将帮助我们研究在1-100公里尺度上的核心的小长度尺度行为，这对于通过球形模拟来获得计算成本太高。通过建立核心内整个相关尺度范围内的重要力平衡，将确定开发更真实的球壳发电机模型的基本要求。

The problem of how the Earth generates its magnetic field is one of the outstanding scientific challenges of the present time. Observations and models of the geomagnetic field provide a window through which the dynamic processes and structure of the Earth's deep interior can be studied, a technique that complements seismic studies. In the last two decades, a variety of satellite missions have significantly improved our knowledge of the Earth's magnetic field, both in its spatial structure and in its temporal behaviour on decadal time-scales. Because these observations cannot probe deeper than the lower-most mantle, any understanding of the fluid outer core, where the field is generated, along with any insight into its time variability, must be obtained from models. Geodynamo models of the core have traditionally focused on millennial or longer time-scales to understand the long term evolution of the field, for the most part ignoring the shorter time-scales. Our aim is to investigate these rapid dynamics which are of great scientific interest, being the very signal for which we have accurate observations. Such a project complements the vast scientific effort and expense being channelled into the latest generation of satellites. We propose three interlinked yet independent projects which will be split between the Schools of Mathematics and Earth & Environment at the University of Leeds: (i) The construction of numerical Cartesian-box models of the excitation and rapid dynamics in the core; (ii) The development of macrodynamic models of flow instabilities in the core; (iii) The extraction and modelling of flow accelerations in the core from observational satellite data. Convection-driven spherical shell geodynamo simulations, which solve the fundamental equations from first principles, have been remarkably successful in explaining many features of the observed geomagnetic field, but they do suffer from some important limitations. Even with the most powerful computers, the models cannot resolve short length scales and time scales, and so have to be run with parameters many orders of magnitude removed from geophysical estimates of those in the Earth's core. Indeed, the Earth's system is so complicated that there is little prospect of being able to run models which resolve all temporal and spatial scales, at the correct parameter values, for many decades to come. However, we believe that considerable insight can be obtained from running models at the correct parameters but in a simplified geometry. The computational models (i) and (ii) that we propose are targeted at understanding specific aspects of the geodynamo on rapid timescales. Project (i) illustrates well the lack of importance of a realistic geometry, being focussed on excitation mechanisms of the rapid dynamics. These are believed to be driven by turbulent convection which occur independent of any boundary effects, and should be captured in any 3D model run at geophysical parameter values. In particular, the processes will be fully represented in a Cartesian-box model, which is much easier to study computationally at small viscosities than spherical models. By combining knowledge of the excitation mechanisms from project (i) with an understanding of the macrodynamics of core instabilites from (ii), we will significantly improve our understanding of core processes on rapid timescales. Validation and use of these new insights with observational data in (iii) will help explain geomagnetic jerks which are of broad interest. This research will also help us to to investigate the small length-scale behaviour in the core, on scales of 1-100 km, which is too computationally expensive to obtain by spherical simulations. By establishing the important force balance across the whole range of relevant scales in the core, the essential requirements for developing more realistic spherical shell dynamo models will be identified.