Formulating a theoretical scaling for dispersion in MHD turbulence

湍流最基本的方面之一是弥散——粒子如何扩散的一种度量。在空气和水等电中性流体中，分散性决定了水分、颗粒或化学物质如何混合到大气或海洋中。其他液体，如液态金属和等离子体，可以携带电荷。它们的运动被磁场的存在从根本上改变，并被磁流体力学所描述。当等离子体在星际介质中扩散时，磁流体中的色散决定了空间天气的特性，恒星核心的化学物质如何混合到外层，以及粒子如何被困在反应堆的液态金属包层中。这个项目的目标是提供一个清晰的理解磁流体动力学色散与在空气或水中观察到的流体力学色散的不同之处。该项目将包括暑期研究学生，使用科学可视化和计算机渲染的计算物理推广计划，以及科学/工业劳动力的技术培训。该项目将利用现代思想和理论技术来修改和扩展由理查森于1926年为流体动力流体开发的色散理论，以设置磁流体动力流体。测试我们的新预测将需要特别密集的模拟；这些模拟将在世界上一些最大的超级计算机上进行。模拟数据将使我们的理论结果能够探索磁流体动力学湍流的基础问题。其中包括湍流如何形成一个优选的运动方向，以及不同部分的流动如何相互作用。我们的理论和计算研究结果将使工程师能够设计出更高效的反应堆，使天文学家能够更好地预测影响地球上生命的太空天气。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

One of the most fundamental aspects of turbulent flows is dispersion – a measure of how particles spread out. In electrically neutral fluids such as air and water, dispersion determines how moisture, particulates, or chemicals mix into the atmosphere or oceans. Other fluids, like liquid metals and plasmas, can carry an electrical charge. Their movement is fundamentally changed by the presence of magnetic fields and is described by magnetohydrodynamics. Dispersion in magnetohydrodynamic fluids determines the properties of space weather as plasma spreads in the interstellar medium, how chemicals from the core of a star are mixed into its outer layers, and how particles are trapped in the liquid metal blankets of reactors. The goal of this project is to provide a clear understanding of how magnetohydrodynamic dispersion differs from dispersion in the hydrodynamic case observed in air or water. This project will include summer research students, a computational physics outreach program using scientific visualizations and computer renderings, and technical training for the scientific/industrial work force.This project will leverage modern ideas and theoretical techniques to modify and extend the theory of dispersion, developed by Richardson in 1926 for hydrodynamic fluids, to the setting of magnetohydrodynamic fluids. Testing our new prediction will require simulations that are particularly intensive; these simulations will be performed on some of the largest supercomputers in the world. The simulation data will allow our theoretical results to probe questions of foundational importance for magnetohydrodynamic turbulence. These include how a turbulent flow develops a preferred direction of movement, and how different parts of the flow interact energetically. The results of our theoretical and computational investigation will allow engineers to design more efficient reactors, and astronomers to better predict the space weather that impacts life on Earth.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.