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摘要:
地磁场磁流体发电机的数值解按照磁场形态通常分为两类：以轴向偶极磁场形态为主导的偶极子发电机和以多极磁场形态为主导的多极子发电机. 本文旨在分析不同极子主导下的发电机对流模式之间的差异及原因，为此分别计算了不同瑞利数(表征对流驱动力的大小)和磁普朗特数(表征黏性扩散和磁扩散相对强度)的数值模型. 通过对比分析两者的轴向偶极子强度、核幔边界处的磁场强度、极、环型分解动能，发现多极子发电机磁场强度为偶极子发电机场强的5.13倍；同时前者动能大于后者，且极型和环型动能的平均值分别大53.4%和30.1%，总动能的平均值大35.6%. 通过比较两者的平均动能谱、磁能谱，二维动能谱、磁能谱等，发现偶极子发电机的磁能小于多极子发电机，并且其流场和产生的磁场空间尺度相对较大. 发电机模型速度场图、磁场图和力平衡谱的结果进一步阐释上述机制形成原因.
Abstract:Numerical solutions of dynamos are generally divided into two classes according to the magnetic field patterns: dipole dynamos dominated by axial dipole field patterns and multipole dynamos dominated by multipole field patterns. The purpose of this paper is to study the differences of convection modes of dynamos with different pole-dominated and the reasons for them, and for this purpose numerical models are computed for different Rayleigh numbers (characterizing the magnitude of the convective driving force) and magnetic Prandtl numbers (characterizing the relative strengths of viscous and magnetic diffusion), respectively. The axial dipole strength, magnetic field strength at the core-mantle boundary, poloidal and toroidal kinetic energy of the two dynamos are compared, and the magnetic field strength of the multipole dynamo is 5.13 times that of the dipole dynamo. The kinetic energy, magnetic energy and magnetic field intensity at the core and mantle boundary of the multipole dynamo are greater than that of the dipole dynamo, the poloidal and toroidal kinetic energy are larger by 53.4% and 30.1%, while that of the total kinetic energy is 35.6% larger than that of the latter. By comparing the mean kinetic energy spectrum, magnetic energy spectrum, two-dimensional kinetic energy spectrum and magnetic energy spectrum, it is found that the magnetic energy of the dipole dynamo is smaller than that of the multipole dynamo, and the spatial scales of its flow field and the generated magnetic field are relatively larger. Through the analysis of velocity field diagram, magnetic field diagram and force balance spectrum, we can further explain the formation reasons of the above mechanism.
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Key words:
- Geodynamo /
- Dipole /
- Multipole /
- Differences in convection modes
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图 1
模型在0.05 ~ 0.25个时间尺度内的轴向偶极子相对强度(
$ AD/NAD $ )Figure 1.
The relative axial dipole strength of the model over a time scale of 0.05 to 0.25
图 2
模型在0.05 ~ 0.25个时间尺度内的核-幔边界处的磁场强度
Figure 2.
Model magnetic field strength at the core-mantle boundary over a time scale of 0.05 ~ 0.25
图 3
两个模型的平均动能谱，下标
$ {p} $ 和$ {t} $ 分别代表极型(poloidal)分量和环型(toroidal)分量，其中l为球谐阶数Figure 3.
The mean kinetic energy spectrum of the two models, subscripts
$ {p} $ and$ {t} $ represent poloidal and toroidal components, respectively
图 4
极(左)、环(右)型动能时间序列
Figure 4.
Time series of poloidal (Left) and toroidal (Right) kinetic energy
图 10
局部Rossby数沿径向的变化
Figure 10.
Local Rossby number's changes along the radial direction
图 11
模型在赤道平面上的径向速度场和沿地理北方向的磁场
Figure 11.
Model's radial velocity field and magnetic field magnetic field along the geographic north direction in equatorial plane
图 12
模型在
$ \boldsymbol{r}/{\boldsymbol{r}}_{0}=0.981 $ 的径向切面上的径向速度场Figure 12.
Radial velocity field of the model on the radial section of
$\boldsymbol r/\boldsymbol r_0 $ =0.981表 1
模型对应参数
Table 1.
Model corresponding parameter
Model $ E $ $ Ra $ $ Pm $ $ Pr $ 1 1 × 10-4 1.5 × 107 1 1 2 1 × 10-4 2.1 × 107 2 2 
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