Table 1 Statistical parameters of the size, shape, and settling velocity distributions (plotted in Figs 1 and 3) of the natural Etna basalt (ETB) and Laacher See phonolite (LSP) ash particles used in the experiments and of the ideal, spherical particles used in the two-way (S2W) and four-way (S4W) coupling numerical simulations.
Experiments | n° tracked particles | Parameter | Mean | Median | Mode | Percentile (25th) | Percentile (75th) | Skewness | Kurtosis |
|---|---|---|---|---|---|---|---|---|---|
ETB | 8551 | ||||||||
de | 252.13 | 223.91 | 154.36 | 183.73 | 297.63 | 1.26 | 4.31 | ||
vp | 2.86 | 2.75 | 1.09 | 2.10 | 3.49 | 0.48 | 2.68 | ||
F | 0.67 | 0.69 | 0.40 | 0.61 | 0.73 | −0.55 | 3.18 | ||
Ψ | 0.74 | 0.75 | 0.76 | 0.71 | 0.76 | −0.69 | 3.95 | ||
LSP | 2453 | ||||||||
de | 745.40 | 745.31 | 654.90 | 648.72 | 833.99 | 0.43 | 5.88 | ||
vp | 2.97 | 2.86 | 2.10 | 2.36 | 3.50 | 1.29 | 7.52 | ||
F | 0.63 | 0.66 | 0.28 | 0.51 | 0.71 | −0.34 | 2.59 | ||
Ψ | 0.71 | 0.72 | 0.64 | 0.64 | 0.78 | −0.36 | 3.78 | ||
Simulations | n° analysed samples | ||||||||
S2W | |||||||||
48 | f1 (10s) | ||||||||
de | 279.63 | 277.11 | 225.80 | 266.48 | 290.73 | 0.54 | 3.48 | ||
vp | 5.96 | 5.96 | 5.52 | 5.85 | 6.03 | 0.98 | 5.35 | ||
182 | f3 (40s) | ||||||||
de | 303.14 | 303.13 | 191.64 | 274.23 | 328.96 | 0.07 | 2.74 | ||
vp | 4.86 | 4.89 | 3.42 | 4.68 | 5.05 | −0.74 | 5.22 | ||
880 | f5 (176s) | ||||||||
de | 277.47 | 277.83 | 252.15 | 260.44 | 295.99 | −0.27 | 3.76 | ||
vp | 2.84 | 2.84 | 2.75 | 2.65 | 3.02 | −0.27 | 3.03 | ||
F | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | ||||
Ψ | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | ||||
S4W | |||||||||
95 | f1 (10s) | ||||||||
de | 282.63 | 282.86 | 202.54 | 267.33 | 296.64 | −0.01 | 3.66 | ||
vp | 4.53 | 4.54 | 3.62 | 4.28 | 4.81 | −0.28 | 2.71 | ||
397 | f3 (40s) | ||||||||
de | 291.37 | 292.51 | 178.01 | 273.42 | 310.76 | −0.36 | 4.03 | ||
vp | 4.07 | 4.12 | 3.69 | 3.80 | 4.38 | −0.48 | 2.91 | ||
705 | f5 (176s) | ||||||||
de | 284.01 | 284.62 | 260.63 | 270.81 | 297.81 | −0.06 | 4.42 | ||
vp | 2.60 | 2.61 | 2.55 | 2.48 | 2.72 | −0.22 | 4.18 | ||
F | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | ||||
Ψ | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | ||||
