罗斯贝波和$α$效应
Rossby waves and $α$-effect
摘要：
在快速旋转的球壳中，在热对流不稳定性开始时，在方位方向上漂移的罗斯贝波是一个共同的特征。它们也可能是由Stewartson剪切层的不稳定性引起的，该剪切层是由法国格勒诺布尔的液体钠实验（英语：Liquid Na experiment）中的差分旋转产生的。解释为什么罗斯贝波可以参与发电机过程的一种常用方法可以追溯到Busse（1975）。在他的图片中，流动几何形状是与旋转轴对齐的平行辊的圆柱形阵列。轴向流分量（平行于旋转轴线的分量）在每个辊的中间最大，并且从一个辊到下一个辊改变其符号。它是由含流体壳体边界处的埃克曼抽吸产生的。相应的发电机机制可以解释在一个$α$ -张量与非零系数的对角线。在快速旋转的物体，如地球的核心（或在一个快速旋转的实验），罗斯贝波发生在小埃克曼数（$\approx 10^{-15}$）的限制。在这种情况下，轴向流分量的主要来源不是埃克曼抽吸，而是由于流体容纳壳体的球形形状而产生的"几何斜率效应“。这意味着轴向流分量（ii）在辊的边界处而不是在中心处最大。如果假设是静止的，这样的滚动将导致$α$ -张量的对角线上的系数为零，使得发电机的效率可能更低（如果可能的话）。实际上，轧辊漂移作为一个波，我们表明，这种漂移意味着非零系数的对角线上的$α$张量。这些新系数本质上与情形（i）中得到的系数有很大不同，不能用Busse（1975）的启发式描述来解释。
英文摘要：
Rossby waves drifting in the azimuthal direction are a common feature at the onset of thermal convective instability in a rapidly rotating spherical shell. They can also result from the destabilization of a Stewartson shear layer produced by differential rotation as expected in the liquid sodium experiment (DTS) working in Grenoble, France. A usual way to explain why Rossby waves can participate to the dynamo process goes back to Busse (1975). In his picture, the flow geometry is a cylindrical array of parallel rolls aligned with the rotation axis. The axial flow component (the component parallel to the rotation axis) is (i) maximum in the middle of each roll and changes its sign from one roll to the next. It is produced by the Ekman pumping at the fluid containing shell boundary. The corresponding dynamo mechanism can be explained in terms of an $α$-tensor with non-zero coefficients on the diagonal. In rapidly rotating objects like the Earth's core (or in a fast rotating experiment), Rossby waves occur in the limit of small Ekman number ($\approx 10^{-15}$). In that case, the main source of the axial flow component is not the Ekman pumping but rather the ``geometrical slope effect'' due to the spherical shape of the fluid containing shell. This implies that the axial flow component is (ii) maximum at the borders of the rolls and not at the centers. If assumed to be stationary, such rolls would lead to zero coefficients on the diagonal of the $α$-tensor, making the dynamo probably less efficient if possible at all. Actually, the rolls are drifting as a wave, and we show that this drift implies non--zero coefficients on the diagonal of the $α$-tensor. These new coefficients are in essence very different from the ones obtained in case (i) and cannot be interpreted in terms of the heuristic picture of Busse (1975).
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