论文标题
关于Bödewadt-Hartmann层的注释
A note on Bödewadt-Hartmann layers
论文作者
论文摘要
本文解决了由固定水平板界定的轴法旋转流的问题，并受到永久，均匀的垂直磁场（所谓的Bödewadt-Hartmann问题）的问题。目的是找出哪一种科里奥利或洛伦兹力在动力学（因此是边界层厚度）时占主导地位（因此边界层厚度），其比例为Elsasser数字$ a $，各种比率各不相同。在对半无限Ekman-Hartmann问题的现有线性解决方案进行了简要审查之后，给出了弱非线性分析解决方案以及完全非线性的数值解决方案。 然后研究在有限深度流体层中旋转涡流的情况，首先是当在强制旋转下流动稳定，第二次从某种初始状态旋转时。在第一种情况下，第二种情况下的角速度和第二个情况下的衰减时间是根据$ a $的函数来获得$ a $的函数，该函数使用半无限的bödewadt-hartmann问题的弱非线性结果。
This paper addresses the problem of axisymetric rotating flows bounded by a fixed horizontal plate and subject to a permanent, uniform, vertical magnetic field (the so-called Bödewadt-Hartmann problem). The aim is to find out which one of the Coriolis or the Lorentz force dominates the dynamics (and hence the boundary layer thickness) when their ratio, represented by the Elsasser number $A$, varies. After a short review of existing linear solutions of the semi infinite Ekman-Hartmann problem, weakly non-linear analytical solutions as well as fully non-linear numerical solutions are given. The case of a rotating vortex in a finite depth fluid layer is then studied, first when the flow is steady under a forced rotation and second for spin-down from some initial state. The angular velocity in the first case and decay time in the second are obtained analytically as a function of $A$ using the weakly non linear results of the semi-infinite Bödewadt-Hartmann problem.
