Small-scale dynamo action in rotating compressible convection
Small-scale dynamo action in rotating compressible convection
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DOI：
10.1017/jfm.2011.429
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发表时间：
2011-10
影响因子：
3.7
通讯作者：
B. Favier;P. Bushby
中科院分区：
文献类型：
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作者：
B. Favier;P. Bushby
摘要我们研究了绕垂直轴旋转的导电可压缩流体对流层中的发电机作用。在上、下界面上，磁场采用理想导电边界条件。考虑了两种不同层次的热力层结。如果磁扩散系数足够小，对流就相当于一台小型发电机。使用基于磁区中层水平积分尺度和水平平均速度的磁雷诺数${R}_{M}$的定义，我们发现旋转倾向于减小观察到发电机作用的临界值${R}_{M}$。增加层内的热力层结水平并不会显著改变旋转计算中的${R}_{M}$的临界值，但在非旋转的情况下，这一临界值确实会减小。在磁雷诺数的最高计算值下，发电机的饱和水平在所有情况下都是相似的，平均磁能密度在平均动能密度的4%到9%之间。为了进一步了解旋转对流和非旋转对流之间的差异，我们通过测量Lyapunov指数来量化每种流动的拉伸特性。在远离边界的情况下，旋转情况下流动引起的拉伸率与深度的依赖程度要比相应的非旋转计算中小得多。研究还表明，旋转效应显著降低了磁层下部的磁能耗散。我们还对发电机饱和机理的某些方面进行了研究。
Abstract We study dynamo action in a convective layer of electrically conducting, compressible fluid, rotating about the vertical axis. At the upper and lower bounding surfaces, perfectly conducting boundary conditions are adopted for the magnetic field. Two different levels of thermal stratification are considered. If the magnetic diffusivity is sufficiently small, the convection acts as a small-scale dynamo. Using a definition for the magnetic Reynolds number ${R}_{M} $ that is based upon the horizontal integral scale and the horizontally averaged velocity at the mid-layer of the domain, we find that rotation tends to reduce the critical value of ${R}_{M} $ above which dynamo action is observed. Increasing the level of thermal stratification within the layer does not significantly alter the critical value of ${R}_{M} $ in the rotating calculations, but it does lead to a reduction in this critical value in the non-rotating cases. At the highest computationally accessible values of the magnetic Reynolds number, the saturation levels of the dynamo are similar in all cases, with the mean magnetic energy density somewhere between 4 and 9 % of the mean kinetic energy density. To gain further insights into the differences between rotating and non-rotating convection, we quantify the stretching properties of each flow by measuring Lyapunov exponents. Away from the boundaries, the rate of stretching due to the flow is much less dependent upon depth in the rotating cases than it is in the corresponding non-rotating calculations. It is also shown that the effects of rotation significantly reduce the magnetic energy dissipation in the lower part of the layer. We also investigate certain aspects of the saturation mechanism of the dynamo.