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

在流体动力系统中，许多不稳定性可以从界面层中生长出来。其中包括两个经典的例子，由重力驱动的Rayleigh-Taylor不稳定性和由剪切流驱动的Kelvin-Helmholtz不稳定性。随着这些不稳定性的发展，非线性增长，并在界面形成湍流层。这些层的一个关键特征是它们在时间上的增长遵循自相似的演化(周等人，2019)。从分析上，可以从描述流体运动的一组耦合的偏微分方程组推导出相似解，揭示了层的扩展随时间的缩放。这些解决方案可以扩展到包括系统更重要的物理复杂性，包括密度对比度的建模。这是由Hillier(2019)使用多层展开进行的，该展开渐近于平均层属性的模型。建立平均层性质的模型，可以解释流体力学系统中湍流混合层的重要特性，包括湍流速度场中的非对称性和能量。在磁场及其动力学与流体耦合的磁流体(MHD)系统中，也会出现同样的线性不稳定性，这些线性不稳定性也会发展湍流混合层。非线性MHD方程确实允许相似解，但试图量化磁场如何改变混合动力学以及随之而来的相似解的工作有限。这个项目的关键目标是在MHD框架中开发界面湍流混合的相似解决方案，并将这些解决方案与3D MHD模拟进行基准比较。这项工作可以与工业过程中的湍流混合和天体物理流动联系起来。

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.