Transport Properties of Incompressible Field-Guided MHD Turbulence

当水流移动时，它把液体从一个地方带到另一个地方。通过这种方式，一小块液体逐渐偏离其初始位置。在流体力学实验室中，这可以通过用注射器在流动中的特定点处注射染料来可视化。如果染料被连续释放，那么就可以追踪染料的轨迹。相反，如果在特定的时间点上，一小块液体被染色，那么人们就可以研究这块液体的扩散速度。被动污染物在湍流(无序)流动中的传输是流体力学研究中广泛研究的一个主题，该主题可能与我们的日常生活有很大的相关性，特别是当污染物代表在地球大气中扩散的工业污染物、可能对我们的免疫系统构成威胁的病毒或可能扰乱数周航班的火山灰时。在磁流体动力学(MHD)湍流中，输运研究关注的是与磁场相互作用的导电流动。有必要了解这种流动的基本性质，以便了解地磁暴的行为(这些磁暴可能扰乱通信和导航卫星并导致电网停电)，以及在实验室等离子体实验中研究磁约束聚变用于清洁能源生产的不稳定性是如何发展的。在理解这种复杂的物理系统方面取得进展，首先取决于为更简化的数学模型建立坚实的理论基础。虽然在许多物理情况下，能够理解磁化等离子体中的湍流输运是很重要的，但应用数学家也可以通过研究其输运性质来了解大量关于导电流动的基本动力学和结构。正是湍流传输的这一特殊方面促使我们提出了这项工作。近年来，MHD湍流的基本理论取得了重大进展。这一成功在很大程度上是计算能力大幅提高的结果，这使得一系列高分辨率的数值模拟得以进行。数值结果已经被用来检验相互竞争的理论预测，这些发现催生了许多新的研究途径。特别令人感兴趣的是发现了场制导的MHD湍流所具有的复杂的高度排列的结构。在此，我们建议进一步研究这一有趣的结构及其影响。通过对MHD湍流的一系列高分辨率数值模拟和理论研究，我们将通过监测示踪粒子的轨迹来研究输运效率。我们期望我们的结果将为发展一个全面的强场导磁流体湍流唯象模型，设计未来的等离子体湍流数值模拟，并最终解释观测和实验提供重要的信息。

As a flow moves, it carries fluid from one location to another. In this way, a tiny parcel of fluid gradually wanders away from its initial position. In the fluid dynamics laboratory, this can be visualised by injecting dye with a syringe at a specified point in the flow. If dye is continuously released then one can trace the dye's trajectory. Instead, if at a specific point in time a small patch of fluid is dyed, then one can then study the rate of spreading of the patch. The transport of a passive contaminant in a turbulent (disordered) flow is a topic that is widely studied in fluid dynamics research and the topic can have great relevance to our everyday lives, especially when the contaminant represents an industrial pollutant dispersing in the Earth's atmosphere, viruses that can pose threats to our immune systems, or volcanic ash that can disrupt flight schedules for weeks. In magnetohydrodynamic (MHD) turbulence, transport studies are concerned with electrically conducting flows that interact with magnetic fields. Gaining knowledge of the fundamental properties of such flows is necessary in order to understand how geomagnetic storms behave (these can disrupt communication and navigation satellites and cause black outs in power grids) and how instabilities develop in laboratory plasma experiments studying magnetic confinement fusion for clean energy production purposes. Progress with understanding such complicated physical systems relies, first and foremost, on establishing a solid theoretical foundation for more simplified mathematical models. While there are a number of physical situations in which it is important to be able to understand turbulent transport in magnetised plasmas, it is also the case that applied mathematicians can learn a great deal about the fundamental dynamics and structure of an electrically conducting flow by studying its transport properties. It is this particular aspect of turbulent transport that motivates our proposed work.Over recent years, significant progress has been made with the fundamental theory of MHD turbulence. The success is largely a result of a massive increase in computational power that has enabled a series of high-resolution numerical simulations to be performed. The numerical results have been used to test competing theoretical predictions and the findings have spawned many new avenues of research. Of particular interest is the discovery of the intricate highly-aligned structure that field-guided MHD turbulence takes. Herein we propose to further our investigations into this intriguing structure and its effects. Through a series of high-resolution numerical simulations and theoretical studies of MHD turbulence, we will study the efficiency of transport by monitoring the trajectories of tracer particles. We anticipate that the our results will provide important information for developing a comprehensive phenomenological model of strong field-guided MHD turbulence, for designing future numerical simulations of plasma turbulence, and ultimately for interpreting observations and experiments.