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Pair-exchange dynamics of magnetohydrodynamic turbulence
Abstract
Nonlinear interactions in incompressible magnetohydrodynamic (MHD) and Navier-Stokes turbulence involve three spatial fluctuations conservatively exchanging, e.g., energy. The mathematical structure of a triad interaction does not allow to unambigously determine the specific contribution of each of the participating fluctuations to the resulting exchanges. Presently, only additional assumptions allow for the deconstruction of triad interactions into a sum of pair exchanges. This work proves that in incompressible MHD the simultaneous nonlinear transfer of cross-helicity sufficiently constrains the triad dynamics such that a mathematically unique pair-exchange representation of nonlinear energy and cross-helicity transfer is possible.
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BibTeX
@misc{teissier2026pairexchange,
title = {{Pair-exchange dynamics of magnetohydrodynamic turbulence}},
author = {Jean-Mathieu Teissier and Wolf-Christian Müller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22729},
eprint = {2610.22729},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22729},
}
RIS
TY - UNPB
TI - Pair-exchange dynamics of magnetohydrodynamic turbulence
AU - Jean-Mathieu Teissier
AU - Wolf-Christian Müller
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22729
UR - https://arxiv.org/abs/2610.22729
AB - Nonlinear interactions in incompressible magnetohydrodynamic (MHD) and Navier-Stokes turbulence involve three spatial fluctuations conservatively exchanging, e.g., energy. The mathematical structure of a triad interaction does not allow to unambigously determine the specific contribution of each of the participating fluctuations to the resulting exchanges. Presently, only additional assumptions allow for the deconstruction of triad interactions into a sum of pair exchanges. This work proves that in incompressible MHD the simultaneous nonlinear transfer of cross-helicity sufficiently constrains the triad dynamics such that a mathematically unique pair-exchange representation of nonlinear energy and cross-helicity transfer is possible.
ER -