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，通过这个窗口可以研究地球深部内部的动态过程和结构，这是一种补充地震研究的技术。在过去的二十年中，各种卫星飞行任务大大提高了我们对地球磁场的认识，无论是在空间结构上还是在十年时间尺度上的时间行为上。由于这些观测无法探测到比最低地幔更深的地方，因此必须从模型中获得对产生磁场的流体外核的任何理解，沿着对其时间变化的任何见解。地核的地球发电机模型传统上专注于千年或更长的时间尺度，以了解该领域的长期演变，大部分忽略了较短的时间尺度。我们的目标是调查这些快速的动力学，这是巨大的科学兴趣，是非常的信号，我们有准确的观测。这样一个项目补充了投入最新一代卫星的大量科学努力和费用。我们提出了三个相互联系但又相互独立的项目，分别由利兹大学数学学院和地球与环境学院负责：（i）堆芯激发和快速动力学的数值Cartesian箱模型的建立：（ii）堆芯流动不稳定性的宏观动力学模型的发展;从观测卫星数据中提取地核中的流动加速度并建立模型。对流驱动的球壳地球发电机模拟，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，但它们确实受到一些重要的限制。即使使用最强大的计算机，这些模型也无法解析短尺度和时间尺度，因此必须使用与地球物理学估计的地核参数相差许多数量级的参数来运行。实际上，地球系统是如此复杂，以至于在未来几十年内，几乎没有前景能够以正确的参数值运行能够解决所有时间和空间尺度的模型。然而，我们相信，相当多的洞察力可以从运行模型在正确的参数，但在一个简化的几何形状。我们提出的计算模型（i）和（ii）旨在了解快速时标上地球发电机的特定方面。项目（i）很好地说明了缺乏现实的几何形状的重要性，被集中在快速动态的激励机制。这些被认为是由湍流对流驱动的，湍流对流的发生与任何边界效应无关，并且应该在以地球物理参数值运行的任何3D模型中捕获。特别是，该过程将完全表示在一个Cartesian盒模型，这是更容易研究计算在小粘度比球形模型。通过将项目（i）的激发机制知识与（ii）的核心不稳定性宏观动力学知识相结合，我们将显著提高对快速时标核心过程的理解。验证和使用这些新的见解与观测数据（iii）将有助于解释地磁急动，这是广泛的兴趣。这项研究还将帮助我们研究核心中1-100公里尺度的小长度尺度行为，这在计算上过于昂贵，无法通过球形模拟获得。通过在堆芯的整个相关尺度范围内建立重要的力平衡，将确定开发更现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.