Fast Magnetic Reconnection Rate
Fast Magnetic Reconnection Rate: τ-value 0.117,vA, observed 0.01–0.1,vA, deviation –.
Prediction
τ-Formula
v_rec = ι_τ² · v_A ≈ 0.117 v_A
Derivation
Observational agreement. The experimental value $C_K = 1.5 ± 0.1$ (Sreenivasan 1995; Yeung and Zhou 1997; Ishihara et al.\ 2009) matches the $τ$-prediction exactly. The central value coincides; the deviation is $0.0%$ (Proposition (prop:ch28-ck-match)).
Why the Kolmogorov constant has been hard to determine.
The experimental determination of $C_K$ has historically been uncertain: values ranging from $1.4$ to $1.7$ have been reported, depending on the experiment, the Reynolds number, and the method of compensating for finite-$Re$ effects. DNS values have converged toward $C_K ≈ 1.5$ as resolution has increased, but the prefactor remains one of the least precisely known ``universal’’ constants in turbulence theory. The $τ$-prediction $C_K = 3/2$ exactly provides a sharp target for future high-resolution experiments.
Source
This prediction is derived in the Physics Ledger (Chapter 65 — collective-dynamics), Books IV–V of Panta Rhei.