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Table 4:

Scaling of the structure functions of centroid velocity increments.

Absolute scaling exponents
$\zeta_1$ $\zeta_2$ $\zeta_3$ $\zeta_4$ $\zeta_5$ $\zeta_6$

CVI SFs (10243 sol)
0.62 1.20 1.73 2.21 2.65 3.05
CVI SFs (10243 comp) 0.62 1.13 1.52 1.82 2.05 2.22

Relative Scaling Exponents
$\widetilde{\zeta}_1$ $\widetilde{\zeta}_2$ $\widetilde{\zeta}_3$ $\widetilde{\zeta}_4$ $\widetilde{\zeta}_5$ $\widetilde{\zeta}_6$

CVI SFs using ESSa (10243 sol)
0.36 0.70 1.00 1.27 1.51 1.72
CVI SFs using ESSa (10243 comp) 0.38 0.72 1.00 1.23 1.41 1.56
Polaris Flareb 0.37 0.70 1.00 1.27 1.53 1.77
Polaris Flarec 0.38 0.71 1.00 1.28 1.54 1.80
Intermittency Model SL94d 0.36 0.70 1.00 1.28 1.54 1.78
Intermittency Model B02e 0.42 0.74 1.00 1.21 1.40 1.56

Notes. (a) Using extended self-similarity (ESS) (Benzi et al. 1993).
(b) Measurement of CVI structure functions by Hily-Blant et al. (2008).
(c) Measurement of CVI structure functions by Hily-Blant et al. (2008) using 12CO(2-1) data by Bensch et al. (2001).
(d) Intermittency model $\widetilde{\zeta}_p=p/9+\mathcal{C}\left(1-\left(1-2/(3\mathcal{C})\right)^{p/3}\right)$ defined in Eq. (28) using a fractal co-dimension $\mathcal{C}=2$ (She & Leveque 1994), which corresponds to filamentary structures ( $\mathcal{D}=1$).
(e) Same as d, but for co-dimension $\mathcal{C}=1$ (Boldyrev 2002; Boldyrev et al. 2002) corresponding to sheet-like structures ( $\mathcal{D}=2$).


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