Lagrangian and Eulerian MHD turbulence and beyond

虽然在理解均匀各向同性拉格朗日、欧拉流体和等离子体湍流方面已经取得了巨大的进展，但在有界几何中的湍流和在动力学尺度上的动力学的应用仍处于起步阶段。我们将在VKS和麦迪逊发电机实验的激励下，在有界几何中解决湍流问题。将应用在FORM第一阶段开发的拉格朗日湍流技术，以更好地了解发电机活动的不同区域(线性、非线性、饱和)。为了实现这一目标，流体和磁边界条件将在光谱模拟框架LaTube中使用惩罚方法来实现。由于在无碰撞等离子体中，耗散机制本质上是动力学的，因此将在一组图形卡上进行Vlasov模拟，以了解磁场和速度涨落在动力学尺度上的排列特性。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.