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arXiv 1909.08286astro-ph.GA
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用奇异值分解模拟星系发电机中的湍流输运系数

Turbulent transport coefficients in galactic dynamo simulations using singular value decomposition

Abhijit B. Bendre, Kandaswamy Subramanian, Detlef Elstner, Oliver Gressel

摘要:

盘星系中的相干磁场被认为是由运行在其星际介质中的大尺度(或平均场)发电机产生的。平均磁场增长的一个关键驱动因素是湍流电动势(EMF),它代表了相关的小尺度(或波动)速度和磁场对平均场的影响。电动势通常表示为平均磁场及其导数的线性展开,其中发电机张量作为展开系数。在这里,我们采用奇异值分解(SVD)的方法来直接测量这些湍流输运系数的湍流星际介质,实现了大规模发电机的模拟。具体地说,奇异值分解是用来最小二乘拟合的时间序列数据的EMF与平均场及其衍生物,以确定这些系数。我们证明了从SVD系数重建的EMF的空间分布与直接从模拟中获得的空间分布相匹配。此外,作为一个直接的测试,我们使用的系数来模拟一个1-D平均场发电机模型,并发现发电机模型和直接模拟之间的平均磁场的演变的整体相似性。我们还比较了结果与使用简单回归和以前使用测试场(TF)方法获得的结果,找到合理的定性协议。总的来说,SVD方法提供了一个有效的后处理工具,以确定湍流输运系数的模拟。

英文摘要:

Coherent magnetic fields in disc galaxies are thought to be generated by a large-scale (or mean-field) dynamo operating in their interstellar medium. A key driver of mean magnetic field growth is the turbulent electromotive force (EMF), which represents the influence of correlated small-scale (or fluctuating) velocity and magnetic fields on the mean field. The EMF is usually expressed as a linear expansion in the mean magnetic field and its derivatives, with the dynamo tensors as expansion coefficients. Here, we adopt the singular value decomposition (SVD) method to directly measure these turbulent transport coefficients in a simulation of the turbulent interstellar medium that realizes a large-scale dynamo. Specifically, the SVD is used to least-square fit the time series data of the EMF with that of the mean field and its derivatives, to determine these coefficients. We demonstrate that the spatial profiles of the EMF reconstructed from the SVD coefficients match well with that taken directly from the simulation. Also, as a direct test, we use the coefficients to simulate a 1-D mean-field dynamo model and find an overall similarity in the evolution of the mean magnetic field between the dynamo model and the direct simulation. We also compare the results with those which arise using simple regression and the ones obtained previously using the test-field (TF) method, to find reasonable qualitative agreement. Overall, the SVD method provides an effective post-processing tool to determine turbulent transport coefficients from simulations.

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