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

地球的磁场现在被认为是地球熔融铁外核内流体运动的结果。 然而，由于缺乏直接观测，这种“发电机”过程仍然是地球科学中最不了解的现象之一。 计算机模拟已被证明是推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，目前还不可能捕捉地核中与动态相关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，拟议的工作可以被视为一个新的计算和建模框架，将允许最高分辨率的模拟地球的核心日期。 此外，这些方法将广泛适用于一系列其他科学问题，从分子物理学到细胞dynamics. Three-dimensional数值模拟已经大大提高了我们的对流驱动发电机的理解，但目前的计算限制限制他们的物理参数是远离那些表征地球的液体外核。 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结果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，以开发一个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制度将提供一个更完整的理解地磁场观测。 这项研究的结果将直接适用于恒星、太阳系外行星和太阳系内其他行星上和内部的其他快速旋转、湍流的流体系统。 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.