Universal Scaling of Coherence Statistics in High-Reynolds-Number Turbulence: A Parameter-Free Prediction from Dynamic Closure Theory and Consistency Test against DNS

We derive a parameter-free prediction for the one-point statistics of a coherence eld C (x, t) ∈ (0, 1) in high-Reynolds-number turbulence, based on the Dynamic Closure Theory (DCT), a rst-principles framework for coherence dynamics in dissipative systems introduced in this paper. The central result is that dimensionalconsistency of the DCT energy variable, combined with the logistic structure of the Dynamic Closure Equation (DCE), uniquely xes the inertial-range scaling exponents =−1 in C∝εs, where ε (x, t) is the local energy dissipation rate. No free parameters enter this prediction. The scaling s = −1 has a direct, testable statistical consequence: under the well established lognormal model for ε in the inertial range, the coherence eld inherits the same logarithmic standard deviation as the dissipation eld, σₗn C = σₗn ε, and the same coe cient of variation, CVC = CV_ε. Crucially, the Reynolds-number independence of CV_ε reported in the DNS literature is then a predicted consequence of the DCT framework, not an independent empirical observation. We perform a systematic consistency test against the high- delity direct numerical simulation (DNS) dataset of Yeung, Donzis & Sreenivasan 5, which spans Re_λ ≈ 140~1000 and is widely regarded as a benchmark for dissipation statistics in forced isotropic turbulence. The DNS data report CVε ≈ 1. 0 ± 0. 05, Reynolds number independent across this range. Our prediction gives σlnC = √ln2 ≈ 0. 833 and CVC ≈ 1. 0, consistent with the DNS statistics within reported uncertainty, with no adjustable parameters. The universality of s = −1 across Reynolds numbers distinguishes this prediction from empirical closure models and provides a concrete, falsi able signature of the DCTcoherence mechanism. Direct measurement of CVC via a DNS-based coherenceproxy (e. g. Q-criterion) would provide a de nitive test and is identi ed as a natural next step