Dynamic Alignment or Angular Persistence?

Abstract

Dynamic alignment in magnetohydrodynamic turbulence is commonly inferred from the decrease of an amplitude-weighted average of the mutual angle between Elsässer increments toward smaller separations. That decrease, however, need not imply that the increments themselves rotate toward alignment: large-angle fluctuations can simply lose more amplitude than small-angle ones. We therefore study the joint evolution of increment amplitude and mutual angle using finite-step conditional transition probabilities. In forced incompressible full MHD and in balanced strong-guide-field reduced MHD, we find that, at fixed initial angle, large-amplitude Elsässer-increment pairs undergo smaller angular changes than small-amplitude pairs, including when they begin at large angles. We call this amplitude-dependent angular persistence. Independently, normalized amplitude moments increase toward smaller separation, while stronger amplitude weighting produces progressively smaller angular averages and stronger scale dependence, linking apparent alignment to the intermittent large-amplitude tail. In RMHD, a source-state decomposition of the Politano-Pouquet third-order moment shows that initially large-angle, high-amplitude populations contribute with the sign associated with transfer toward smaller perpendicular scales despite their comparatively small angular changes. Time-resolved full-MHD data reproduce the same amplitude ordering, and the local Elsässer advective term closely tracks the conditional dependence of both angular and amplitude changes on the initial state. These results show that the conventional dynamic-alignment diagnostic reflects the joint statistical evolution of amplitude and angle and, by itself, is not evidence for a population-wide dynamical rotation toward alignment.