Investigating the role of magnetic fields, instabilities and turbulence in fluid mixing

在流体动力学系统中，许多不稳定性可以从界面层增长。其中包括两个经典的例子，瑞利-泰勒不稳定性，由重力驱动，和开尔文-亥姆霍兹不稳定性，由剪切流驱动。随着这些不稳定性的发展，非线性增长，并在界面处形成湍流层。这些层的一个关键特征是它们随时间的增长，遵循自相似的演化（Zhou et al 2019）。从分析上讲，可以从描述流体运动的耦合偏微分方程组中推导出相似性解，揭示了层膨胀随时间的缩放。这些解决方案可以扩展到包括系统的其他重要物理复杂性，包括密度对比的建模。这是由Hillier（2019）使用多层展开进行的，该展开渐近于平均层特性的模型。有一个模型的平均层属性允许层的重要特性，包括不对称性和包含在湍流速度field.The相同的线性不稳定性的增长和发展的湍流混合层的流体动力学系统中的能量被阐明也出现在磁流体动力学（MHD）系统中的磁场和它们的动力学与流耦合。非线性MHD方程确实允许相似解，但是只有有限的工作试图量化磁场如何改变混合动力学以及相似解。本项目的主要目标是在MHD框架中开发界面湍流混合的相似性解决方案，并将这些解决方案与3D MHD模拟进行基准测试。这项工作可以与工业过程和天体物理流动中的湍流混合联系起来。

In hydrodynamic systems, a number of instabilities can grow from interface layers. These include two classic examples, the Rayleigh-Taylor instability, driven by gravity, and the Kelvin-Helmholtz instability, driven by shear flow. As these instabilities develop, non-linearities grow and a turbulent layer forms at the interface. A key characteristic of these layers is their growth in time which follows a self similar evolution (Zhou et al 2019).Analytically a similarity solution can be derived from the set of coupled PDEs that describe fluid motion, revealing the scaling with time for the expansion of the layer. These solutions can be extended to include further important physical complexities of the system, including modelling of density contrasts. This was performed by Hillier (2019) using a multi layer expansion which asymptotes to a model of the mean layer properties. Having a model of the mean layer properties allows important characteristics of the layer, including asymmetries and energy contained in the turbulent velocity field to be elucidated.The same linear instabilities that grow and develop the turbulent mixing layers in hydrodynamic systems also appear in magnetohydrodynamic (MHD) systems where magnetic fields and their dynamics couple with the flow. The non-linear MHD equations do permit similarity solutions, but there has only been limited work attempting to quantify how magnetic fields alter the mixing dynamics and with it the similarity solution. The key goal in this project is to develop similarity solutions in the MHD framework for interface turbulence mixing, benchmarking these solutions against 3D MHD simulations. This work can connect with turbulent mixing in industrial processes and astrophysical flows.