3D Dust Devil: Blender Desert, Burgers Vortex and a Size-Sorted Dust Plume

Setting up the desert...

Presets

Live readouts

Graphs

Wind profile of the vortex: tangential speed and inflow against radius (yellow = lift-off wind)

Pressure deficit against radius from the cyclostrophic balance dp/dr = rho v^2 / r

Updraft w = a z against height; horizontal lines = settling speed of the median, 3x and 1/3 grain size

Where the airborne dust is: grains per height bin

Numerical checks

running...

How to use

Pick a preset and watch the grains: brown dots rest on the ground, blue to yellow dots are airborne (colour = height). The grey ring in the top view is the radius of peak wind; grains lift only where the wind exceeds the yellow dashed threshold circle. Try Coarse sand only (the loft height is far above the plume), Weak updraft (low dT) and High threshold. In graph 3 a grain size is lofted when the green line is above its horizontal line at the start height. Raise the time scale to see a full plume build up quickly. Space pauses, R restarts the dust.

Drag to orbit, wheel or pinch to zoom, camera buttons jump to presets. The desert terrain, mesa, rocks, shrubs and the weather mast were modelled in Blender with baked textures; all flow physics runs in JavaScript.

The science

The vortex. A dust devil is a vortex fed by a shallow superheated layer of air above sun-baked ground. The axisymmetric Burgers vortex is an exact solution of the Navier-Stokes equations that balances inward advection of angular momentum against viscous (here eddy) diffusion, in a uniform strain a: u_r = -a r / 2, w = a z, v_theta(r) = Gamma / (2 pi r) [1 - exp(-r^2 / r_c^2)], r_c^2 = 4 nu / a The tangential speed peaks at r = 1.1209 r_c with v_max = 0.6382 Gamma / (2 pi r_c); inside the core the air spins almost like a solid body, outside it follows the potential vortex v = Gamma / (2 pi r). Continuity (1/r) d(r u_r)/dr + dw/dz = 0 holds exactly.

Pressure. Away from the ground the radial momentum balance is cyclostrophic, dp/dr = rho v_theta^2 / r, so the pressure falls toward the axis by Delta p = integral of rho v^2 / r dr (graph 2): a couple of hectopascals for a 10 m/s dust devil. This low pressure is part of why loose dust is sucked up the core.

Convective strain. The updraft is driven by buoyancy. Heated air of excess temperature dT in a layer of depth H reaches the Deardorff convective velocity w* = sqrt(g dT H / T_0); the page uses the strain rate a = w* / H so that w = a z reaches w* at the top of the layer.

Dust. Grains rest on the ground until the wind exceeds the lift-off speed (random gusts of +/-20%). Once airborne a grain of diameter d falls at its terminal speed v_s (Stokes (rho_p - rho) g d^2 / (18 mu) with the Schiller-Naumann correction 1 + 0.15 Re^0.687) and moves vertically at dz/dt = a z - v_s. Above the loft height z* = v_s / a the updraft wins and the grain rises to the top; below it the grain falls back. Fine dust (tens of micrometres) is lofted from the ground, sand (hundreds) is not: that is why the plume is size-sorted.

Honest simplifications. The flow is the steady Burgers vortex in the vortex frame (no turbulence modelling beyond a small random walk, no translation of the vortex, no boundary-layer Ekman inflow, no thermal plume structure, no electrification); grains follow the air except for settling (no inertial spin-out); the plume lean is a simple shear shift; the lift-off rule is a threshold rather than a saltation law. Real dust devils last minutes and are far less regular than this idealisation.

Checks run in the page. Peak wind and its radius against the closed forms; continuity at four points; the circulation at the peak radius; the pressure deficit at two resolutions; the terminal fall speed of a 20 micrometre grain from a drag ODE against the settling function and Stokes; and the loft-height threshold using ODE runs just above and below it.