N30 — Fast reconnection rate $v_ rec
N30: Fast reconnection rate $v_ rec. MRX, FLARE, solar observatories, MMS.
Falsification Details
= _^2 v_A$vrec = iota-tau-2 vA. magnetic reconnection!rate prediction pred:n30 $v_ rec = _^2 v_A 0.117 v_A$ (V.T251). Orthodox Sweet–Parker: $v_ rec S^-1/2 v_A 0.1 v_A$. Observed: $0.01$–$0.1 v_A$ (solar flares, laboratory plasmas).
MRX, FLARE, solar observatories, MMS
ongoing–2030.
Context
N30: Prediction
= ι_τ^2\,v_A$vrec = iota-tau-2 vA.
$v_ rec = ι_τ^2\,v_A ≈ 0.117\,v_A$ (V.T251). Orthodox Sweet–Parker: $v_ rec ∼ S^-1/2\,v_A 0.1\,v_A$. Observed: $0.01$–$0.1\,v_A$ (solar flares, laboratory plasmas). Experiment: MRX, FLARE, solar observatories, MMS. Timeline: ongoing–2030.
Derivation Context
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.