Transport Properties of Incompressible Field-Guided MHD Turbulence

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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.