Watch a rotating supercell updraft tilt a horizontal wind-shear roll upright, then squeeze it into a narrow, fast vortex. Change the storm ingredients and read the wind speed, pressure drop and Enhanced Fujita (EF) rating that a simple physical model predicts.
CAPE = convective available potential energy (J/kg) sets the updraft strength. Shear = change of horizontal wind over the lowest 6 km. The last two sliders describe how strongly the rotating column is squeezed and how much of its spin survives friction.
Scene scale: 1 km = 10 scene units; the landscape is 18 km wide. Time is sped up by the chosen factor. Trees and poles lean with the local model wind; the windmill spins with it.
1. Ingredients. A supercell needs unstable air (CAPE) and wind that changes with height (shear). Parcel theory gives the maximum updraft w = sqrt(2 CAPE); real updrafts reach about half of it, which the model uses.
2. Horizontal vorticity. Wind increasing with height rolls the air about a horizontal axis: omega_h = dU/dz = shear / 6000 m.
3. Tilting. An updraft that varies sideways lifts part of the roll upright. The vertical vorticity grows as d(zeta)/dt = omega_h dw/dy. Over about 400 s in a 2.5 km wide updraft this gives zeta of a few hundredths per second: the mesocyclone. For solid-body rotation v = zeta r / 2.
4. Spin-up. When a rotating column is stretched and narrowed, angular momentum per unit mass v r stays constant, so the wind rises as the radius falls. Friction and mixing destroy part of it, modelled by the "circulation kept" fraction eta.
5. Rankine vortex. A simple model of the finished tornado: solid-body rotation inside the core radius and v = vmax Rc / r outside, so the wind peaks at the core radius. Cyclostrophic balance dp/dr = rho v^2 / r then gives a central pressure deficit Delta p = rho vmax^2 (rho about 1.15 kg/m3); half of it is outside the core and half inside.
6. Visible funnel. The low pressure cools the air adiabatically, Delta T = T (R/cp) Delta p / p. Condensation shows only where this cooling exceeds the dew-point depression (about cloud-base height / 125 m per kelvin), so a high cloud base gives a funnel that does not reach the ground, while the dust whirl does.
7. EF scale. The Enhanced Fujita scale rates damage and assigns an estimated 3-second gust: EF0 65-85 mph, EF1 86-110, EF2 111-135, EF3 136-165, EF4 166-200, EF5 over 200. The model's maximum wind is mapped to that band; actual ratings are made from surveyed damage.
Honest simplifications. This is a teaching chain, not a forecast model. Real tornadogenesis is not fully understood: the role of the rear-flank downdraft, baroclinic vorticity and surface friction is still debated, and many mesocyclones never produce a tornado. The numbers (tau, R0, eta, the 0.5 updraft factor) are representative values chosen for illustration; the wind is capped at 135 m/s, the highest value ever measured by mobile radar. The Rankine profile has no inflow layer, no multiple vortices and no ground friction. The landscape is generic and the objects are inanimate scenery. This tool is not a warning or forecasting tool.