Connecting Dynamo Theory with DNS Data: A Computational Analysis of α and β effects
Abstract
We investigate the influence of current helicity on the turbulent magnetic diffusivity β using three complementary derivations of the α and β coefficients, based on the large-scale magnetic field B̅, the turbulent velocity u, and the turbulent magnetic field b. Applying these coefficients to raw DNS data, we reconstruct B̅ and compare the results with the original simulations. In the kinematic regime all models agree well with the DNS data. In the nonlinear regime, however, βvv−vw alone produces unbounded growth of B̅. Including the contribution from turbulent magnetic fields (βbb+jb) suppresses this unphysical growth and restores agreement with the DNS results. We find that kinetic helicity drives β more negative, while current helicity shifts it back toward zero. Weighted combinations of the coefficients further show that the β effect dominates the evolution of B̅ throughout, whereas the α effect becomes important mainly for sustaining the field in the nonlinear regime. The corresponding IDL analysis scripts are provided to facilitate practical implementation of the theoretical models.
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BibTeX
@misc{park2026connecting,
title = {{Connecting Dynamo Theory with DNS Data: A Computational Analysis of $α$ and $β$ effects}},
author = {Kiwan Park},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09767},
eprint = {2609.09767},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09767},
}
RIS
TY - UNPB
TI - Connecting Dynamo Theory with DNS Data: A Computational Analysis of α and β effects
AU - Kiwan Park
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.09767
UR - https://arxiv.org/abs/2609.09767
AB - We investigate the influence of current helicity on the turbulent magnetic diffusivity β using three complementary derivations of the α and β coefficients, based on the large-scale magnetic field B̅, the turbulent velocity u, and the turbulent magnetic field b. Applying these coefficients to raw DNS data, we reconstruct B̅ and compare the results with the original simulations. In the kinematic regime all models agree well with the DNS data. In the nonlinear regime, however, β_vv−vw alone produces unbounded growth of B̅. Including the contribution from turbulent magnetic fields (β_bb+jb) suppresses this unphysical growth and restores agreement with the DNS results. We find that kinetic helicity drives β more negative, while current helicity shifts it back toward zero. Weighted combinations of the coefficients further show that the β effect dominates the evolution of B̅ throughout, whereas the α effect becomes important mainly for sustaining the field in the nonlinear regime. The corresponding IDL analysis scripts are provided to facilitate practical implementation of the theoretical models.
ER -