Development and Application of Turbulence Models in Numerical Geodynamo Simulations

地球物理和天体物理流动的数值模拟是研究各种情况下过程的有力工具。所有这些应用都面临着在大范围的空间尺度上解决流动问题的挑战。在大多数情况下，应用程序的计算需求超过了可用资源的限制，因此研究人员将注意力集中在最大规模的流动上，并将小尺度湍流的影响参数化。由于行星旋转、流体分层和磁场的存在，所有这些因素都改变了小尺度流的结构，并影响了该流的参数化方式，因此可能会产生复杂性。我们的项目解决了迫切需要一种灵活和自适应的方法，将实际的复杂性纳入小尺度湍流模型。该项目开发的工具将直接有助于我们了解地球磁场的起源，为更好地预测磁场的变化提供前景。同样的方法也可以扩展到其他应用，包括大气和海洋中的地球物理流动，以及恒星和其他物体周围吸积盘中的天体物理流动。这项提议的工作代表了近十年来建立一个预测模型的努力的高潮，该模型可以在没有特别或可调参数的情况下定量地解释湍流的影响。该方法基于比例相似模型的自适应实现，该模型已在平面层和球壳发电机模型中成功地进行了测试。研究人员计划在一个开源的发电机代码Calypso中实现比例相似模型，以解决产生地球磁场的过程。他们保守地估计，新的发电机模型将使研究人员能够将模拟中使用的流体特性改进两个数量级，从而大大提高数值模拟的可靠性和从中得出的科学推论。在美国能源部INCITE计划的支持下，他们将使用来自地球动力学计算基础设施（CIG）的独立高分辨率模拟的输出来测试他们的实现。在模拟中利用类似的资源，结合湍流模型，将使研究小组极大地突破目前可行的极限。他们期望对产生地球磁场的过程获得新的见解，并为解释现代卫星观测和预测磁场变化提供一个计算框架。

Numerical simulations of geophysical and astrophysical flows are a powerful tool for studying processes in various contexts. All of these applications share the challenge of resolving flow over a vast range of spatial scales. In most cases the computational requirements of the application exceed the limits of available resources, so researchers confine their attention to the largest-scale flows and parameterize the influence of small-scale turbulence. Complications can arise from contributions due to planetary rotation, fluid stratification, and the presence of a magnetic field, all of which alter the structure of the small-scale flow and affect the way this flow should be parameterized. Our project addresses the pressing need for a flexible and adaptive method for incorporating practical complications into models for small-scale turbulence. The tools developed in this project will directly benefit our understanding of the origin of the Earth's magnetic field, offering the prospect of better forecasts for changes in the magnetic field. The same approach can also be extended to other applications, including geophysical flows in the atmosphere and oceans, as well as astrophysical flows in accretion disks around stars and other objects.The proposed work represents the culmination of nearly ten years of effort to build a predictive model that quantitatively accounts for the influence of turbulence with no ad hoc or tunable parameters. The approach is based on an adaptive implementation of the scale-similarity model, which has been successfully tested in both plane-layer and spherical-shell dynamo models. The investigators plan to implement the scale-similarity model in an open-source dynamo code, Calypso, to address the processes responsible for generating the Earth's magnetic field. They conservatively estimate that the new dynamo model will allow the investigators to refine the fluid properties used in simulations by two orders of magnitude, substantially improving the reliability of numerical simulations and the scientific inferences drawn from them. They will test their implementation using output from an independent high-resolution simulation from the Computational Infrastructure for Geodynamics (CIG) with support from the DOE INCITE Program. Harnessing similar resources in simulations that incorporate turbulence models will allow the team to dramatically push the limits on what is currently feasible. They expect to gain new insights into the processes that generate the Earth's magnetic field and provide a computational framework for interpreting modern satellite observations and for forecasting changes in the magnetic field.