This is a Rankine vortex: inside the core radius Rc, the air rotates like a solid disk, v(r) = Ωr, so speed rises linearly to a maximum at Rc. Outside Rc the flow is irrotational and speed falls off as v(r) = vmax·(Rc/r) — the same 1/r decay as a free vortex or a bathtub drain, just much faster and bigger.
Radial pressure balance in a vortex is dp/dr = ρv²/r (the pressure gradient supplies the centripetal acceleration). Integrating that profile gives a pressure deficit relative to the far field of ρvmax² at dead center, falling to half that at the core edge, and decaying as 1/r² further out — a genuine Bernoulli/cyclostrophic result, not a cosmetic overlay.
That pressure drop cools the rising air adiabatically; once it drops enough to push the air below its dew point, water condenses and the funnel cloud becomes visible — which is why weak vortices show a thin rope funnel (or none) while violent ones show a wide visible funnel, even though the funnel is only made of condensed water, not the whole wind field.
Debris tracers spiral inward under near-surface convergence (radial inflow proportional to the local tangential speed), then near the core get centrifuged back outward by the same strong rotation, spiral out until the wind weakens, and are drawn back in again — the same inward-then-flung-out path real tornado debris follows.
- Intensity is an EF-scale-like dial: it scales both the core radius and the maximum wind speed together, the way real tornado damage ratings correlate width with violence.
- This models a 2D horizontal cross-section of the vortex core, not the full 3D updraft/downdraft circulation — see the 3D version for the vertical structure.