Volcanic Ash Plume and Fallout - 2D Cross-Section: Plume Height, Grain-Size Fall Speed and Wind-Blown Deposit

Presets

Speed

Live readouts

Graphs

Numerical checks

running...

How to use

Pick a preset, then change the wind and the median grain size. Try: (1) raise the mass rate by 100x and watch the plume top rise only about 3x (H scales as the 0.241 power); (2) double the grain size and see the fall speed rise about 4x for fine ash, so the deposit moves toward the vent; (3) set shear to 0 and compare the deposit with the sheared case. The time-acceleration slider speeds up the hours-long fall.

The science

Plume height. Mastin et al. (2009) fitted observed eruptions: H = 2.00 V^0.241 with H in km above the vent and V the dense-rock-equivalent volume rate in m3/s; mass rate = 2500 kg/m3 x V. VEI is estimated from the erupted mass over one hour, log10(M/kg) - 7.

Terminal velocity. A grain stops accelerating when drag equals buoyant weight: (1/2) Cd rho_a v^2 (pi d^2/4) = (rho_p - rho_a) g (pi d^3/6) with the drag coefficient Cd(Re) of a sphere. For small grains (Re < 1) this reduces to Stokes: v = (rho_p - rho_a) g d^2 / (18 mu). The sim solves the full balance by bisection and shows both curves.

Fallout. Each grain is advected by the wind u(z) and falls at v: with uniform wind the landing distance is x = u z0 / v (checked in-page against the stepper). A turbulent diffusivity K spreads grains randomly. The deposit graph is mass landed per kilometre downwind.

Simplifications. Constant air density and viscosity, spherical grains of 2300 kg/m3, one wind direction with linear shear, a schematic bent-over column, number-weighted grain sizes, no aggregation of fine ash, no pyroclastic flows. Treat distances as order-of-magnitude estimates.