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arXiv · 2610.07449

Erasing and Regenerating the Turbulent Cascade Arrow

Yang Zhao·Daocheng Zhou·Hongfu Zhang
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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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Yang Zhao, Daocheng Zhou, Hongfu Zhang. 2026-10-05. Erasing and Regenerating the Turbulent Cascade Arrow. https://arxiv.org/abs/2610.07449

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