Erasing and Regenerating the Turbulent Cascade Arrow
Abstract
Which information tells a turbulent flow which way to cascade? We apply Haar-distributed Hermitian phases that retain prescribed same-mode quadratic information, including modal amplitudes, the energy spectrum, and same-mode two-time correlations. For the phase-Haar ensemble, the expectation of any integrable odd flux functional is zero. Finite ensembles strongly suppress mean transfer and forward-event bias in the primary block. An independent block retains sign separation but fails the scale-8 mean criterion. In matched evolution protocols, nonlinear Navier-Stokes dynamics restores the selected signed-flux scalar close to its natural reference, whereas linear evolution and an amplitude-matched frozen control do not. Flux and a local cubic geometry scalar recover together, yet high local correlation can survive erasure of the arrow. Signed transfer thus requires information beyond the retained quadratic record; the tested nonlinear dynamics rebuilds it.
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BibTeX
@misc{zhao2026erasing,
title = {{Erasing and Regenerating the Turbulent Cascade Arrow}},
author = {Yang Zhao and Daocheng Zhou and Hongfu Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07449},
eprint = {2610.07449},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07449},
}
RIS
TY - UNPB
TI - Erasing and Regenerating the Turbulent Cascade Arrow
AU - Yang Zhao
AU - Daocheng Zhou
AU - Hongfu Zhang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07449
UR - https://arxiv.org/abs/2610.07449
AB - Which information tells a turbulent flow which way to cascade? We apply Haar-distributed Hermitian phases that retain prescribed same-mode quadratic information, including modal amplitudes, the energy spectrum, and same-mode two-time correlations. For the phase-Haar ensemble, the expectation of any integrable odd flux functional is zero. Finite ensembles strongly suppress mean transfer and forward-event bias in the primary block. An independent block retains sign separation but fails the scale-8 mean criterion. In matched evolution protocols, nonlinear Navier-Stokes dynamics restores the selected signed-flux scalar close to its natural reference, whereas linear evolution and an amplitude-matched frozen control do not. Flux and a local cubic geometry scalar recover together, yet high local correlation can survive erasure of the arrow. Signed transfer thus requires information beyond the retained quadratic record; the tested nonlinear dynamics rebuilds it.
ER -