Build a tornado from three numbers (peak wind, core size, swirl ratio) and one air property (dew-point depression). The wind field is the Burgers–Rott vortex; the pressure drop comes from cyclostrophic balance; the grey funnel is where that pressure drop cools the air below its dew point; debris is lifted and flung by aerodynamic drag.
The science
Wind field. The tangential wind is the Burgers–Rott vortex vθ(r) = Γ/(2πr) · (1 − e−r²/rb²). Its maximum is Vmax = 0.6382 Γ/(2π rb) at r = 1.1209 rb, so the slider Vmax fixes the circulation Γ. Outside the core the flow is irrotational (v ∝ 1/r), inside it is nearly solid-body rotation; the dashed Rankine curve is the simpler textbook idealisation with the same peak.
Pressure. Outside the thin surface layer the flow is close to cyclostrophic balance, ∂p/∂r = ρ vθ²/r. Integrating from infinity gives Δp(0) = ρ (Γ/2πrb)² ln 2 ≈ 1.70 ρ Vmax² (about 130 hPa for 80 m/s). This is an upper bound: real tornadoes have friction, a strong radial inflow and a time-varying core, and measured deficits are typically smaller (tens of hPa). The numbers shown here are a model result, not a forecast.
Inflow, updraught and swirl ratio. The radial inflow is a Burgers-style ur = −a r/2 flattened beyond three core radii, the updraught is w = wmax tanh(a z / wmax) concentrated within 2.5 rb, and the strain rate is chosen as a = Vmax / (2 S rb). That choice is a modelling convenience: a larger swirl ratio S (swirl relative to inflow and updraught, defined after Davies-Jones and Church et al.) means weaker strain, a wider vortex and, in laboratory and numerical experiments, a progression from a one-cell vortex to a two-cell vortex with a downdraught in the core and finally to multiple sub-vortices. The thresholds in the readout are typical qualitative values, not sharp limits, and different definitions of S shift them. The multiple-vortex lobes in the picture are a visual hint, not a solved sub-vortex dynamic.
Why a funnel appears. The pressure drop cools rising air adiabatically, ΔT ≈ κ T Δp / p with κ = 0.2857; the exact Poisson relation differs by under 4 % up to Δp/p = 0.1 (checked above). Air condenses where this cooling exceeds the dew-point depression left after it has been lifted, D(z) = D0 (1 − z / zcb), with cloud base zcb = 125 m/K · D0 + 150 m (lifting-condensation-level rule of thumb plus a lowered wall cloud). The pressure deficit is assumed to decay with height as e−z/2500 m, a modelling assumption. Humid air gives a fat funnel that touches down; dry air keeps the funnel aloft even though the wind near the ground is just as strong: a funnel cloud is not the tornado, the wind is. Latent-heat release, precipitation loading and the real three-dimensional pressure field are ignored.
Debris. Each piece obeys dv/dt = k |u − v| (u − v) − g with k = ρ Cd A / (2m); the table lists each class's fall speed √(g/k). The step uses an exponential relaxation, stable at any frame rate. Lift-off speeds are illustrative values chosen so heavy objects need much more wind than boards or sheets; real lift-off depends on fastening, orientation and turbulence. All debris is inanimate and nothing is damaged or destroyed on screen.
EF scale. The rating uses the standard 3-second-gust wind bands in mph (EF0 65–85, EF1 86–110, EF2 111–135, EF3 136–165, EF4 166–200, EF5 above 200). Real ratings come from damage surveys, not from a wind model.
Checks. The Burgers peak is re-derived by bisection; Δp0 is compared with the closed form and with an independent Simpson integral on a logarithmic grid; the cyclostrophic balance is verified by finite differences of the table; the drag integrator is compared with the exact fall law v = vt tanh(g t / vt).
Landscape, farm buildings and debris models were built in Blender (Cycles-baked textures) and rendered with Three.js. Independent educational model; sizes, colours and the vortex are illustrative.
Educational physics model. Inanimate objects only.