Bounds on the attractor dimension for low-Rm wall-bound magnetohydrodynamic turbulence
Bounds on the attractor dimension for low-Rm wall-bound magnetohydrodynamic turbulence
复制标题
低 Rm 壁束缚磁流体动力湍流吸引子维数的界限
DOI：
10.1063/1.2391841
复制
发表时间：
2006
影响因子：
4.6
通讯作者：
T. Alboussière
中科院分区：
文献类型：
--
作者：
A. Pothérat;T. Alboussière
本文通过对吸引子维数上界的估计，研究了稳态低Rm磁流体动力学（MHD）湍流。本文考虑了两平行壁面间的流动，外加垂直磁场。流动由其最大速度和磁场强度定义。给定相应的雷诺数和哈特曼数，人们可以严格地推导出吸引子的维数的上限，并找出必须选择哪些模式来实现这个界限。这些模式的属性产生的数量，我们比较已知的启发式估计的最小湍流涡流的大小和湍流的各向异性的程度。我们的上限推导是基于已知的非线性惯性项的界限，而低Rm洛伦兹力是线性的，可以相对容易地处理。本文考虑的简单配置使我们能够确定一些边界分离的无量纲参数的空间中不同的模式集，…
Steady low-Rm magnetohydrodynamic (MHD) turbulence is investigated here through estimates of upper bounds for attractor dimension. A flow between two parallel walls with an imposed perpendicular magnetic field is considered. The flow is defined by its maximum velocity and the intensity of the magnetic field. Given the corresponding Reynolds and Hartmann numbers, one can rigorously derive an upper bound for the dimension of the attractor and find out which modes must be chosen to achieve this bound. The properties of these modes yield quantities that we compare to known heuristic estimates for the size of the smallest turbulent vortices and the degree of anisotropy of the turbulence. Our upper bound derivation is based on known bounds of the nonlinear inertial term, while low-Rm Lorentz forces—being linear—can be relatively easily dealt with. The simple configuration considered in this paper allows us to identify some boundaries separating different sets of modes in the space of nondimensional parameters, ...