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Table 1:

Statistical moments and fit parameters of the PDFs of the volumetric density $\rho $ for solenoidal and compressive forcing shown in Fig. 4.

  Solenoidal forcing Compressive forcing
Standardised Moments $\langle \rho \rangle$ $\phantom{-}1.00\pm0.00$ $\phantom{-}1.00\pm0.00$
of $\rho $ $\sigma_\rho$ $\phantom{-}1.89\pm0.09$ $\phantom{-}5.86\pm0.96$
  $\mathcal{S}_\rho$ $\phantom{-}9.03\pm1.06$ $\phantom{-}26.7\pm10.1$
  $\mathcal{K}_\rho$ $\phantom{-}211.\pm69.8$ $\phantom{-}1720\pm2000$
Standardised Moments $\langle s \rangle$ $-0.83\pm0.05$ $-3.40\pm0.43$
of $s=\ln\left(\rho/\langle \rho \rangle \right)$ $\sigma_s$ $\phantom{-}1.32\pm0.06$ $\phantom{-}3.04\pm0.24$
  $\mathcal{S}_s$ $-0.10\pm0.11$ $-0.26\pm0.20$
  $\mathcal{K}_s$ $\phantom{-}3.03\pm0.17$ $\phantom{-}2.91\pm0.43$
Skewed Log-normal Approximation $\xi$ $\phantom{-}0.010\pm0.050$ $-0.048\pm0.133$
using equation (14) $\omega$ $\phantom{-}1.562\pm0.035$ $\phantom{-}4.712\pm0.193$
  $\alpha $ $-0.911\pm0.064$ $-2.163\pm0.173$
4th Order Approximation a0 $-1.3664\pm0.0091$ $-2.5014\pm0.0259$
(including skewness and kurtosis) a1 $-0.4592\pm0.0064$ $-0.3437\pm0.0132$
using equation (17) a2 $-0.3067\pm0.0052$ $-0.0831\pm0.0030$
  a3 $-0.0073\pm0.0011$ $-0.0065\pm0.0011$
  a4 $-0.0002\pm0.0005$ $-0.0004\pm0.0001$

Source LaTeX | All tables | In the text

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