Tephra Fallout: Grain-Size Sorting

Eruption Column

Column height 6.0 km

Wind speed (at altitude) 18 m/s

Column intensity

Sub-Plinian

Grain-Size Range

Fine end (min diameter) 0.06 mm

Coarse end (max diameter) 8.0 mm

Live Readouts

Airborne particles

Deposited

Furthest deposit from vent

0.0 km

Deposit Legend

Coarse lapilli (near vent)

Fine ash (far downwind)

How it works

Each tephra clast leaves the eruption column at height H and falls under gravity while a crosswind advects it downwind. Its fall speed is its terminal settling velocity v_t, found by balancing gravity against drag:

Weight = Drag
(π/6) d³ (ρp − ρa) g = Cd · (π/4) d² · ½ ρa v²

→ v_t = sqrt( 4 ρp g d / (3 Cd ρa) )
Cd(Re) = 24/Re · (1 + 0.15 Re^0.687)   [intermediate drag, solved iteratively]
Re = ρa v d / μ

Small clasts (fine ash, tens of microns) sit in the low-Reynolds Stokes regime and fall slowly; large lapilli sit in the high-Reynolds Newtonian regime and fall fast — d appears squared in the fast-falling limit and to the ½ power in the slow-falling limit, so grain size changes fall speed far more than it changes drag shape. Air density ρa is modelled with an exponential atmosphere, ρa(y) = ρ0 e^(−y/8500 m), so the same clast falls faster once it drops into denser low-altitude air.

Downwind landing distance from the vent is approximately

x_land ≈ U · H / v_t

— fast-falling coarse clasts land near the vent, slow-falling fine ash rides the wind for tens of kilometres before settling. Accumulating landing points into distance bins reproduces the two hallmark signatures of a real tephra fall deposit: thinning (less mass per bin with distance) and fining (mean grain size dropping with distance) — exactly the isopach/isopleth pattern volcanologists map in the field to reconstruct plume height and wind conditions after an eruption. The simulation runs at accelerated time (real ash can take hours to settle) — because both fall and drift scale with the same time factor, the physically correct ratio x_land = U·H/v_t is preserved even though the clock is sped up.

Wind →

Airborne tephra Ground deposit (height = thickness)

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