A kinematic theory of large magnetic Reynolds number dynamos
A kinematic theory of large magnetic Reynolds number dynamos
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大型磁雷诺数发电机的运动学理论
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发表时间：
1972
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通讯作者：
A. Soward
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作者：
A. Soward
对某些以大磁雷诺数 R 为特征的流动的磁感应方程进行了渐近分析。一个新颖的特征是针对该问题的混合方法。利用欧拉坐标和拉格朗日坐标的组合。在某些条件下，问题可以简化为求解一对仅依赖于两个空间坐标的耦合偏微分方程（参见 Braginskii 1964 a）。考虑两种主要情况。首先检查这种情况，其中通过轴向流中的剪切从子午磁场产生的方位磁场可以忽略不计。结果表明，项 J（类似于电流）与决定磁场的矢量 B 线性相关。 （请注意，B 不是磁场矢量：参见（1.33）和（2.35 b）。）电流 J 可能会维持发电机作用。其次，考虑这样的情况，其中子午磁场的剪切是产生方位磁场的主要机制，并且上述效应是从方位磁场产生子午磁场的一种机制。结果表明，J 项不仅与 B 线性相关，而且还有一个额外的贡献 Px (V x B)，其中 P 用流量来表征（见（4.15））。先前在湍流运动产生的发电机作用理论中已经预测了这两种效应。在某些限制条件下，第二种情况下的方程可简化为 Braginskil (1964 a, b) 的近对称发电机公式。这里使用的术语不是通常意义上的方位角和子午线。术语的差异是坐标变换的结果。
An asymptotic analysis is made of the magnetic induction equation for certain flows characterized by a large magnetic Reynolds number R. A novel feature is the hybrid approach given to the problem. Advantage is taken of a combination of Eulerian and Lagrange coordinates. Under certain conditions the problem can be reduced to solving a pair of coupled partial differential equations dependent on only two space coordinates (cf. Braginskii 1964 a). Two main cases are considered. First the case is examined, in which the production of azimuthal magnetic field from the meridional magnetic field by a shear in the aximuthal flow is negligible. It is shown that a term J (analogous to electric current) is related linearly to the vector B which determines the magnetic field. (Note that B is not the magnetic field vector: see (1.33) and (2.35 b).) The current J is likely to sustain dynamo action. Secondly, the case is considered, in which shearing of meridional magnetic field is the principal mechanism for creating the azimuthal magnetic field and the effect described above is one mechanism for creating meridional magnetic field from the azimuthal magnetic field. It is shown that the term J is not only linearly related to B, but has an additional contribution Px (V x B), where P is characterized by the flow (see (4.15)). Both these effects have been predicted previously in theories of dynamo action produced by turbulent motions. Under certain restrictive conditions the resulting equations in the second case reduce to Braginskil’s (1964 a, b) formulation for nearly symmetric dynamos. The words azimuthal and meridional are not used here in the usual sense. The difference in terminology is a consequence of a coordinate transformation.