Part III of the "Boundary Rigidity in Fluid Dynamics" Series - Constraint-Dependent Phase Randomization and Windowing Sensitivity in Spectral Flux Estimates

Erratum (2026-11-01). The windowing-sensitivity control of this paper (Section 5, Table 1 in §5.2, Figures 2 and 3) was computed on a 512³ subcube assembled from 64³ blocks with transposed axis order inside every block (an extraction-script defect, not a defect of the source data). On the repaired subcube the main sign result is unchanged (window-dependent sign of Π_true; |η_PL| ≤ 2.1 × 10⁻⁴), but 12 of the 24 values of Table 1 change materially and Figures 2 and 3 are corrected. Details: BR-III_Erratum_2026-11-01.pdf; data, code and hashes: BR-III_erratum_seam_2026.zip. The original paper PDF is unchanged.

Part III of the "Boundary Rigidity in Fluid Dynamics" Series

Constraint-Dependent Phase Randomization and Windowing Sensitivity in Spectral Flux Estimates

This work investigates the robustness of spectral energy flux diagnostics under constraint-dependent phase randomization in high-resolution DNS subcubes of isotropic turbulence (Re_λ ≈ 1256).

We compare two randomization operators:

• P0 — component-wise phase randomization
• PL — Leray-projected phase randomization with shell-matched energy rescaling

The study introduces a Δk-matched rescaling procedure and analyzes:

• inertial-range averaged flux
• transfer efficiency η
• divergence diagnostics (Fourier and real-space)
• windowing sensitivity (no-window, Tukey, Hann)

Results show that:

• Naive phase randomization (P0) significantly alters flux structure.
• Leray-projected randomization (PL) suppresses artificial divergence but yields near-zero transfer efficiency under strong windowing.
• Windowing has a first-order impact on flux sign and magnitude in finite subcubes.

The work demonstrates that spectral confinement and constraint enforcement fundamentally alter nonlinear transfer diagnostics. It does not claim resolution of the Navier–Stokes regularity problem. Rather, it provides an empirical falsification protocol for phase-coherence-based mechanisms.

Together with Part I and Part II, this paper forms a structural progression:

• Part I — Global regularity under hard spectral truncation
• Part II — Boundary-induced regularity as structural principle
• Part III — Empirical constraint-sensitivity in full DNS (that document)