Comparing the statistics of interstellar turbulence in simulations and observations - Solenoidal versus compressive turbulence forcing

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Volume 512 (March-April 2010)

A&A, 512 (2010) A81

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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 ESS^a (1024³ sol)	0.36	0.70	1.00	1.27	1.51	1.72
CVI SFs using ESS^a (1024³ comp)	0.38	0.72	1.00	1.23	1.41	1.56
Polaris Flare^b	0.37	0.70	1.00	1.27	1.53	1.77
Polaris Flare^c	0.38	0.71	1.00	1.28	1.54	1.80
Intermittency Model SL94^d	0.36	0.70	1.00	1.28	1.54	1.78
Intermittency Model B02^e	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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