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arXiv 1302.7140astro-ph.EP
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行星发电机的标度律

Scaling Laws for Planetary Dynamos

P. A. Davidson

摘要:

我们提出了行星发电机的性质的新的标度律。特别是,Rossby数,磁雷诺数,磁动能的比率,欧姆耗散时间尺度和柱状对流单体的特征纵横比都被预测为两个可观测量的幂律函数:磁偶极矩和行星自转速率。由此产生的标度律构成了Christensen & Aubert(2006)和Christensen(2010)提出的标度的稍微修改版本。主要的区别在于,鉴于行星核心的Rossby数很小,我们坚持认为非线性惯性项(u.grad)u可以忽略不计。这改变了幂律中的指数,幂律将流体发电机的各种性质与行星的偶极矩和旋转速率联系起来。我们的标度律与现有的数值证据是一致的。

英文摘要:

We propose new scaling laws for the properties of planetary dynamos. In particular, the Rossby number, the magnetic Reynolds number, the ratio of magnetic to kinetic energy, the Ohmic dissipation timescale and the characteristic aspect ratio of the columnar convection cells are all predicted to be power-law functions of two observable quantities: the magnetic dipole moment and the planetary rotation rate. The resulting scaling laws constitute a somewhat modified version of the scalings proposed in Christensen & Aubert (2006) and Christensen (2010). The main difference is that, in view of the small value of the Rossby number in planetary cores, we insist that the nonlinear inertial term, (u.grad)u, is negligible. This changes the exponents in the power-laws which relate the various properties of the fluid dynamo to the planetary dipole moment and rotation rate. Our scaling laws are consistent with the available numerical evidence.

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