论文标题
磁水动力流的浅水模型与湍流Hartmann层
A shallow water model for magnetohydrodynamic flows with turbulent Hartmann layers
论文作者
论文摘要
我们建立了一个浅水模型，用于在均匀的两个平行平面之间构成均匀的静态磁场中电流体的流动，其中湍流的Hartmann层。这是通过使用PrandTL的混合长度模型在这些层中对壁剪应力进行建模的方法，而Albousssière\＆lingwood的作者也是如此（Phys。Fluids，2000）。这种新模型的想法源于以前的浅水模型的失败，该模型假设层层hartmann层恢复了在成熟实验的某些方案中发现的正确量的耗散量。该实验是由Messadek \＆Moreau的作者（J。FluidMech。2002）进行的，由在横向磁场中的差速器旋转中进行电动驱动的一层薄层。在该实验配置中，我们的新模型的数值模拟使我们能够在Hartmann层处于充分发达的湍流状态时，将全局角动量和局部速度的实验值恢复到最高百分之几。因此，我们提供了一个证据，表明在这些特定方案中观察到成熟的耗散水平是由哈特曼层中的湍流引起的。通过模型的简单性使流动的参数分析也表明，哈特曼层中的湍流摩擦阻止了准2D湍流变得更加强烈，并且限制了大尺度的大小。
We establish a shallow water model for flows of electrically conducting fluids in homogeneous static magnetic fields that are confined between two parallel planes where turbulent Hartmann layers are present. This is achieved by modelling the wall shear stress in these layers using the Prandtl's mixing length model, as did the authors of Albousssière \& Lingwood (Phys. Fluids, 2000). The idea for this new model arose from the failure of previous shallow water models that assumed a laminar Hartmann layer to recover the correct amount of dissipation found in some regimes of the MATUR experiment. This experiment, conducted by the authors of Messadek \& Moreau (J. Fluid Mech. 2002), consisted of a thin layer of mercury electrically driven in differential rotation in a transverse magnetic field. Numerical Simulations of our new model in the configuration of this experiment allowed us to recover experimental values of both the global angular momentum and the local velocity up to a few percent when the Hartmann layer was in a sufficiently well developed turbulent state. We thus provide an evidence that the unexplained level of dissipation observed in MATUR in these specific regimes was caused by turbulence in the Hartmann layers. A parametric analysis of the flow, made possible by the simplicity of our model, also revealed that turbulent friction in the Hartmann layer prevented quasi-2D turbulence from becoming more intense and limited the size of the large scales.
