N28 — She–Lévêque from $^3$
N28: She–Lévêque from $^3$. high-Re DNS, wind-tunnel data.
Status boundary
Falsification status is a program-side tracking label. It separates current internal stance from formal verification, empirical support, and external acceptance; it is not a claim that the wider scientific community has accepted the result.
Falsification Details
tau-3 fibration. She–Leveque formula@She–Lévêque formula!prediction pred:n28 $ = (T^2)/(^3) = 2/3$ (V.T248). Not a fit: derived from fibration dimensions. $_p = (p/9)(1 - (2/3)^p/3)$ matches DNS data to $< 1%$ for all measured $p$.
high-Re DNS, wind-tunnel data
ongoing.
Context
N28: Prediction
tau-3 fibration.
$β = (T^2)/(τ^3) = 2/3$ (V.T248). Not a fit: derived from fibration dimensions. $ζ_p = (p/9)(1 - (2/3)^p/3)$ matches DNS data to $< 1%$ for all measured $p$. Experiment: high-Re DNS, wind-tunnel data. Timeline: ongoing.
Derivation Context
The structure function exponents of fully developed turbulence are
ζ_p \;=\; p(τ^3)^2 \;+\; (T^2) [ 1 - ( (T^2)(τ^3) )^!p/(τ^3) ] \;=\; p9 \;+\; 2![ 1 - (23)^!p/3 ],
The agreement with experiment (Theorem (thm:ch28-sl-agreement)) is better than $1%$ for all $p ≤ 12$:
| $p$ | $ζ_p^\,τ$ | |||||||||||||||||||||||||||||||
| $ζ_p^\,exp$ | ||||||||||||||||||||||||||||||||
| K41 | ||||||||||||||||||||||||||||||||
| Deviation | ||||||||||||||||||||||||||||||||
| 1 | 0.364 | $0.37 ± 0.01$ | 0.333 | $-1.6%$ 2 | 0.696 | $0.70 ± 0.01$ | 0.667 | $-0.6%$ 3 | 1.000 | $1.00$ (exact) | 1.000 | $0.0%$ 4 | 1.280 | $1.28 ± 0.02$ | 1.333 | $0.0%$ 6 | 1.778 | $1.77 ± 0.04$ | 2.000 | $+0.5%$ 8 | 2.211 | $2.21 ± 0.07$ | 2.667 | $0.0%$ 10 | 2.598 | $2.59 ± 0.10$ | 3.333 | $+0.3%$ 12 | 2.948 | $2.93 ± 0.15$ | 4.000 | $+0.6%$ |
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