Evidence for a Universal β=4 Log-Periodic Mode in DNS Turbulence Spectra Consistent with Unified Substrate Theory

High-resolution direct numerical simulations (DNS) of turbulent channel flow typically display small oscillatory deviations from smooth inertial-range scaling, usually interpreted as numerical noise. A systematic analysis of 39 streamwise one-dimensional energy spectra from the Moser–Kim–Mansour database demonstrates that these residual oscillations are not statistically compatible with random fluctuations. After detrending in log–log coordinates by low-order polynomials, the residuals exhibit a coherent log-periodic component at the fixed angular log-frequency β=4, as predicted by Unified Substrate Theory. For many spectra, residual-preserving permutation tests yield individual significances near 3.3–3.7σ, and Fisher aggregation across all datasets gives a global significance ≥8σ (conservative) or ≈11σ (analytic χ² approximation). The β=4 mode appears across all friction Reynolds numbers and wall-normal positions, indicating a universal discrete spectral structure in turbulence that cannot be attributed to stochastic variability alone and that any fundamental description of the cascade must consequently accommodate.