Next-Generation Modeling of the Geodynamo: Development of the First Multi-Scale Dynamo Model

现在我们知道，地球的磁场是地球外核熔融铁内部流体运动的结果。然而，由于缺乏直接观察，这种“发电机”过程仍然是地球科学中最不为人所知的现象之一。计算机模拟已被证明是促进我们对发电机理解的宝贵工具。然而，由于现代技术的限制，目前还不可能捕捉到地核动态相关性的所有时间和空间尺度。pi正在通过开发地球发电机的第一个多尺度数学模型来克服这些限制。在这方面，提议的工作可以被视为一个新的计算和建模框架，它将允许迄今为止地球核心的最高分辨率模拟。此外，这些方法将广泛适用于从分子物理学到细胞动力学的一系列其他科学问题。三维数值模拟极大地提高了我们对对流驱动发电机的理解，但目前的计算限制将它们限制在物理参数上，这些物理参数与地球液态外核的特征相距甚远。这一事实突出了我们对地球发电机的理解存在严重差距，并严重限制了我们将地磁场观测与数值发电机模型的输出直接联系起来的能力。拟议的工作将首次采用行星发电机系统的多尺度渐近方法，以开发能够达到地球核心参数值和物理特性的模型。这样，所提出的模型的渐近状态将提供对地磁场观测的更完整的理解。研究结果将直接适用于恒星、系外行星和太阳系内其他行星上的其他快速旋转、湍流流体系统。此外，用于开发简化方程的数学方法广泛适用于从分子物理学到细胞动力学的一系列其他科学问题。

The Earth's magnetic field is now known to be the result of fluid motion within the Earth's molten iron outer core. This "dynamo" process remains one of the least understood phenomena in the Earth sciences, however, due to the lack of direct observations. Computer simulations have proven to be valuable tools for advancing our understanding of dynamos. Nevertheless, it is not currently possible to capture all the temporal and spatial scales of dynamical relevance in the Earth's core given modern-day technological constraints. The PIs are overcoming these limitations by developing the first multi-scale mathematical model of the geodynamo. In this respect, the proposed work can be viewed as a new computational and modeling framework that will allow for the highest resolution simulations of the Earth's core to date. Additionally, these methods will be broadly applicable to a range of other scientific problems ranging from molecular physics to cellular dynamics.Three-dimensional numerical simulations have vastly improved our understanding of convection driven dynamos, yet computational constraints currently limit them to physical parameters that are distant from those that characterize the Earth's liquid outer core. This fact highlights a serious gap in our understanding of the geodynamo, and severely limits our ability to relate directly geomagnetic field observations and the output of numerical dynamo models. The proposed work will, for the first time, employ the methodology of multiple scale asymptotics to planetary dynamo systems for purpose of developing a model that is capable of reaching parameter values and physical properties of Earth's core. In this way, the asymptotic regime of the proposed model will provide a more complete understanding of geomagnetic field observations. Findings of the research will be directly applicable to other rapidly rotating, turbulent fluid systems on and within stars, extrasolar planets, and the other planets within the Solar System. Moreover, the mathematical methods employed for development of the reduced equations are broadly applicable to a range of other scientific problems ranging from molecular physics to cellular dynamics.