Derivation and precision of mean field electrodynamics with mesoscale fluctuations
Derivation and precision of mean field electrodynamics with mesoscale fluctuations
复制标题
介观涨落平均场电动力学的推导和精度
DOI：
10.1017/s0022377818000375
复制
发表时间：
2017
影响因子：
2.5
通讯作者：
L. Chamandy
中科院分区：
文献类型：
--
作者：
Hongzhe Zhou;E. Blackman;L. Chamandy
平均场电动力学（MFE）有利于长期的，大尺度的天体物理或实验室系统的波动特性的实际建模。从业者通常假设平均值和波动量之间存在大尺度的分离，以证明集合和空间或时间平均值的平等性。然而，真实的系统通常不表现出这种尺度分离。这就提出了两个问题：（一）在中尺度波动的存在下，MFE的适当的广义方程是什么？(II)MFE的理论预测有多精确？我们解决这两个问题，首先推导出不同类型的平均MFE方程，沿着与中尺度校正项，取决于平均尺度的比值的平均值的变化规模。然后，我们表明，即使这些条款是小的，预测的MFE仍然可以有一个显着的精度误差。该误差具有来自发电机输入参数的固有贡献和来自观测和理论通过测量内核投影的方式的差异的滤波贡献。最小化这些贡献的总和可以产生一个最佳的平均尺度，使理论最大限度地精确。在与观测值进行比较时，量化精度误差很重要，因为它量化了预测能力的分辨率。我们重申这些原则的银河发电机，评论更广泛的影响，并确定进一步工作的可能性。
Mean field electrodynamics (MFE) facilitates practical modelling of secular, large scale properties of astrophysical or laboratory systems with fluctuations. Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages. Often however, real systems do not exhibit such scale separation. This raises two questions: (I) What are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (II) How precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a filtering contribution from differences in the way observations and theory are projected through the measurement kernel. Minimizing the sum of these contributions can produce an optimal scale of averaging that makes the theory maximally precise. The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work.
影响因子：
4.8
作者：
F. Gent;A. Shukurov;G. Sarson;A. Fletcher;M. Mantere
通讯作者：
F. Gent;A. Shukurov;G. Sarson;A. Fletcher;M. Mantere
非线性银河发电机：工具箱
影响因子：
4.8
作者：
Chamandy L
通讯作者：
Chamandy L