OSCILLATORY ALPHA-2-DYNAMO - NUMERICAL INVESTIGATION
OSCILLATORY ALPHA-2-DYNAMO - NUMERICAL INVESTIGATION
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DOI：
10.1002/asna.2113080202
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发表时间：
1987-01-01
影响因子：
0.9
通讯作者：
SHUKUROV, A
中科院分区：
文献类型：
--
作者：
BARYSHNIKOVA, Y;SHUKUROV, A
导出并讨论了描述湍流导电流体薄圆盘中大尺度磁场（α2-发电机）产生的线性和非线性方程。数值计算过程是基于相应的非线性柯西问题的边界条件的有限差分隐式格式。此外，还实现了线性特征值问题的QR-算法，证明了α2-发电机能够产生振荡磁场。振荡周期通常为扩散时间的量级或小于扩散时间。这些振荡被认为是由于边界效应。详细讨论了解对产生效率和盘上平均螺旋度分布的依赖性，振荡周期仅轻微地依赖于盘上平均螺旋度分布的具体形式，主要由螺旋度的大小和螺旋度极值的位置决定：该点越靠近边界，振荡频率越大。当平均螺旋度在不超过圆盘厚度的四分之一处达到最大值时，非线性效应抑制振荡，反之则促进振荡。一维非线性α2-发电机方程组被简化为一个薛定谔型非线性方程。
Linear and nonlinear equations describing the generation of a large‐scale magnetic field (α2‐dynamo) in a thin disc of turbulent conducting fluid are derived and discussed. The numerical procedure is based on a finite‐difference implicit scheme for the corresponding nonlinear Cauchy problem with boundary conditions. In addition, the QR‐algorithm for the linear eigenvalue problem is realized.It is demonstrated that the α2‐dynamo is able to generate oscillatory magnetic fields. The periods of oscillation are typically of the order of or less than the diffusion time. These oscillations are suggested to be due to boundary effects. Dependence of the solutions on the generation efficiency and on the distribution of the mean helicity across the disc are discussed in detail.The period of oscillations only slightly depends on the specific form of distribution of the mean helicity across the disc and is determined mainly by the magnitude of the helicity and by the position of the helicity extremum: the nearer this point to the boundary, the greater the oscillation frequency. Nonlinear effects suppress oscillations when the mean helicity attains its maximum at a depth not more than a quarter of the disc thickness, and promote them otherweise.The one‐dimensional system of nonlinear α2‐dynamo equations is reduced to a single nonlinear equation of the Schrödinger type.