Fig. 4: Velocity circulation scaling exponents.

Exponents of the turbulent (in blue) and the disordered turbulence (in red) cases. For each case, the scaling exponents are defined as \({\langle | {{\Gamma }}{| }^{p}\rangle }_{A} \sim {r}^{{\lambda }_{p}}\) (circles) and \({\langle | {{\Gamma }}{| }^{p}\rangle }_{n} \sim {n}^{{\gamma }_{p}}\) (stars). Error bars indicate 95% confidence intervals. Self-similar predictions for each case are shown as solid lines. Green squares show the relation between the turbulent and disordered systems given by Eq. (5). The blue and red dashed lines show the OK62 prediction combined with the She–Lévêque model (8) with D_∞ = 2.2 (termed “mOK62”) for turbulence and disordered turbulence, respectively. Source data are provided as a Source Data file.