Triple Decomposition of Field Gradient Tensors in Space Plasmas

Abstract

Characterizing local topology in magnetohydrodynamic (MHD) turbulence is fundamental to understanding energy dissipation, intermittency, and coherent structures in space plasmas. Classical double decomposition of velocity ($A_{ij}$) and magnetic ($Z_{ij}$) field gradient tensors into symmetric strain and anti-symmetric rotation components conflates rigid-body rotation with planar sliding shear. Here, we extend the real-Schur-based Triple Decomposition framework to MHD flows, rigorously isolating irrotational normal strain ($N, M$), residual pure shear ($H, K$), and true rigid-body rotation ($R, B$). Applying this method to high-resolution NASA-MMS multi-spacecraft observations in the solar wind and Earth's magnetosheath reveals distinct topological signatures. Solar wind dynamics are predominantly strain-dominated due to spherical radial expansion, whereas magnetosheath turbulence is overwhelmingly shear-dominated, driven by boundary interactions. Crucially, cross-term contributions ($2RH$ and $2KB$) are suppressed to $\le 7\%$ across both plasma regimes, contrasting sharply with neutral fluid turbulence ($\sim 13\%$). This suppression is driven by background magnetic-field-induced anisotropy ($k_\perp \gg k_\parallel$), which confines shearing motions perpendicular to the primary rotation axes. By cleanly separating genuine vortex cores from current sheets and shear layers, the Triple Decomposition provides an objective framework for characterizing plasma turbulence and analyzing data from future multi-spacecraft missions.