Lagrangian and Eulerian MHD turbulence and beyond

尽管在理解均匀各向同性拉格朗日和欧拉流体和等离子体湍流方面取得了巨大进展，但在有界几何湍流和动力学尺度上的应用仍处于起步阶段。我们将讨论由VKS和麦迪逊发电机实验激发的有界几何中的湍流。在FOR第一阶段开发的拉格朗日湍流技术将用于更好地理解发电机活动的不同状态（线性，非线性，饱和）。为了实现这一目标，将在光谱模拟框架LaTu中使用惩罚方法实现流体和磁性边界条件。由于在无碰撞等离子体中耗散机制基本上是动力学的，因此将在一组图形卡上进行Vlasov模拟，以了解磁和速度波动在动力学尺度上的对准特性。此外，如果流体（大尺度）和动力学（小尺度）模拟以一致的方式耦合，将开发多尺度-多物理场模拟。

Although enormous progress has been achieved in understanding homogeneous isotropic Lagrangian and Eulerian fluid and plasma turbulence, the application to turbulence in bounded geometries and to the dynamics on kinetic scales is still in its infancy. We will address turbulence in bounded geometries motivated by the VKS and Madison dynamo experiment. The techniques on Lagrangian turbulence developed in the first phase of the FOR will be applied to gain a better understanding of the different regimes of dynamo activity (linear, nonlinear, saturated). To achieve this goal, fluid and magnetic boundary conditions will be implemented using the penalty method in the spectral simulation framework LaTu.Since in collisionless plasmas the dissipation mechanism are essentially kinetic, Vlasov simulations on a cluster of graphics cards will be performed to understand alignment properties of magnetic and velocity fluctuations on kinetic scales. In addition, multiscale-multiphysics simulations will be developed were fluid (large scales) and kinetic (small scales) simulations are coupled in a consistent way.