\begin{table}%t1
\caption{\label{tab:pdfs_vol}Statistical moments and fit parameters of the PDFs of the volumetric density~$\rho$ for solenoidal and compressive forcing shown in Fig.~\ref{fig:solcomppdf}.}
%\centering
\par
\begin{tabular}{lccc}
\hline
\hline\noalign{\smallskip}
~ & ~ & Solenoidal forcing & Compressive forcing\\
\hline
Standardised Moments & $\langle \rho \rangle$      & $\phantom{-}1.00\pm0.00$ & $\phantom{-}1.00\pm0.00$\\
of $\rho$ & $\sigma_\rho$ & $\phantom{-}1.89\pm0.09$ & $\phantom{-}5.86\pm0.96$\\
~ & $\mathcal{S}_\rho$ & $\phantom{-}9.03\pm1.06$ & $\phantom{-}26.7\pm10.1$\\
~ & $\mathcal{K}_\rho$ & $\phantom{-}211.\pm69.8$ & $\phantom{-}1720\pm2000$\\
\hline
Standardised Moments & $\langle s \rangle$      & $-0.83\pm0.05$ & $-3.40\pm0.43$\\
of $s=\ln\left(\rho/\langle \rho \rangle \right)$ & $\sigma_s$ & $\phantom{-}1.32\pm0.06$ & $\phantom{-}3.04\pm0.24$\\
~ & $\mathcal{S}_s$ & $-0.10\pm0.11$ & $-0.26\pm0.20$\\
~ & $\mathcal{K}_s$ & $\phantom{-}3.03\pm0.17$ & $\phantom{-}2.91\pm0.43$\\
\hline
Skewed Log-normal Approximation & $\xi$    & $\phantom{-}0.010\pm0.050$ & $-0.048\pm0.133$\\
using equation~(\ref{eq:skew-log-normal}) & $\omega$ & $\phantom{-}1.562\pm0.035$ & $\phantom{-}4.712\pm0.193$\\
~ & $\alpha$ & $-0.911\pm0.064$ & $-2.163\pm0.173$\\
\hline
4th Order Approximation & $a_0$ & $-1.3664\pm0.0091$ & $-2.5014\pm0.0259$\\
(including skewness and kurtosis) & $a_1$ & $-0.4592\pm0.0064$ & $-0.3437\pm0.0132$\\
using equation~(\ref{eq:skew-kurt-log-normal}) & $a_2$ & $-0.3067\pm0.0052$ & $-0.0831\pm0.0030$\\
~ & $a_3$ & $-0.0073\pm0.0011$ & $-0.0065\pm0.0011$\\
~ & $a_4$ & $-0.0002\pm0.0005$ & $-0.0004\pm0.0001$\\
\hline
\end{tabular}
\end{table}