Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields
Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields
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DOI：
10.1111/j.1365-246x.2006.03009.x
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发表时间：
2006-07-01
影响因子：
2.8
通讯作者：
Aubert, J.
中科院分区：
文献类型：
--
作者：
Christensen, U. R.;Aubert, J.
我们研究了一组广泛的发电机模型在旋转球壳，改变所有相关的控制参数至少两个数量级。对流由刚性边界之间的固定温度差驱动。有两个不同的类的解决方案与强和弱偶极子贡献的磁场，分别。非偶极发电机是当惯性在力平衡中起重要作用时发现的。在偶极区，自持发电机的临界磁雷诺数为50阶，与磁普朗特数Pm无关。然而，只有在足够低的埃克曼数E时，才存在低Pm的发电机。对于偶极区的发电机，我们试图建立适合我们的数值结果的标度律。假设扩散效应不起主要作用，我们引入无量纲参数，是独立的任何扩散。这些是基于热（或浮力）通量Ra*（Q）的修改的瑞利数，测量流速的罗斯比数Ro，测量磁场强度的洛伦兹数Lo，以及平流热流的修改的努塞尔数Nu*。第一近似，我们所有的发电机结果可以折叠成简单的幂律依赖于修改后的瑞利数，与近似指数的2/5，1/2和1/3的Rossby数，修改后的Nusselt数和洛伦兹数，分别。与扩散有关的参数（E，Pm，普朗特数Pr）的残差依赖性很弱。我们的标度律与磁场强度由可用功率而不一定由力平衡控制的假设一致。的Elsasser数λ，这是传统的措施的比例的洛伦兹力，科里奥利力，发现变化很大。我们试图通过研究涡度拟能（平方涡度）的源和汇来评估各种力的相对重要性。一般来说，科里奥利力和浮力是相同量级的，惯性力和粘性力的贡献较小且可变，而洛伦兹力是高度可变的。忽略一个可能的弱依赖于普朗特数或埃克曼数，一个令人惊讶的预测是，磁场强度是独立的电导率和旋转速率，基本上是由浮力通量控制。估计浮力通量在地球的核心使用我们的Rossby数标度和一个典型的速度从地磁长期变化推断，我们预测一个小的增长率和年老的内核，并获得一个合理的磁场强度为1 mT的核心内。从观测到的木星热流，我们预测一个8 mT的内部场，与木星的外部场比地球强10倍。
We study numerically an extensive set of dynamo models in rotating spherical shells, varying all relevant control parameters by at least two orders of magnitude. Convection is driven by a fixed temperature contrast between rigid boundaries. There are two distinct classes of solutions with strong and weak dipole contributions to the magnetic field, respectively. Non-dipolar dynamos are found when inertia plays a significant role in the force balance. In the dipolar regime the critical magnetic Reynolds number for self-sustained dynamos is of order 50, independent of the magnetic Prandtl number Pm. However, dynamos at low Pm exist only at sufficiently low Ekman number E. For dynamos in the dipolar regime we attempt to establish scaling laws that fit our numerical results. Assuming that diffusive effects do not play a primary role, we introduce non-dimensional parameters that are independent of any diffusivity. These are a modified Rayleigh number based on heat (or buoyancy) flux Ra*(Q), the Rossby number Ro measuring the flow velocity, the Lorentz number Lo measuring magnetic field strength, and a modified Nusselt number Nu* for the advected heat flow. To first approximation, all our dynamo results can be collapsed into simple power-law dependencies on the modified Rayleigh number, with approximate exponents of 2/5, 1/2 and 1/3 for the Rossby number, modified Nusselt number and Lorentz number, respectively. Residual dependencies on the parameters related to diffusion (E, Pm, Prandtl number Pr) are weak. Our scaling laws are in agreement with the assumption that the magnetic field strength is controlled by the available power and not necessarily by a force balance. The Elsasser number Lambda, which is the conventional measure for the ratio of Lorentz force to Coriolis force, is found to vary widely. We try to assess the relative importance of the various forces by studying sources and sinks of enstrophy (squared vorticity). In general Coriolis and buoyancy forces are of the same order, inertia and viscous forces make smaller and variable contributions, and the Lorentz force is highly variable. Ignoring a possible weak dependence on the Prandtl numbers or the Ekman number, a surprising prediction is that the magnetic field strength is independent both of conductivity and of rotation rate and is basically controlled by the buoyancy flux. Estimating the buoyancy flux in the Earth's core using our Rossby number scaling and a typical velocity inferred from geomagnetic secular variations, we predict a small growth rate and old age of the inner core and obtain a reasonable magnetic field strength of order 1 mT inside the core. From the observed heat flow in Jupiter, we predict an internal field of 8 mT, in agreement with Jupiter's external field being 10 times stronger than that of the Earth.