Vortex Stretching: Tornado Formation Simulator

Vortex Stretching

Vertical stretching rate 2.2×

Initial radius 1.8

Stretch factor S

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Core radius r

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Tangential speed at core (v = ω·r)

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How it works

Every parcel of rotating air carries angular momentum L = I·ω, where the moment of inertia I = m·r² depends on how far the mass sits from the spin axis. With no outside torque, L stays constant. When the storm's updraft squeezes the rotating column — stretching it vertically and shrinking its radius r — I falls, so ω must rise to keep L fixed. That is exactly how a figure skater spins faster by pulling their arms in.

L = I·ω = m·r²·ω = const
ω(t) = ω₀ · (r₀ / r(t))² = ω₀ · S(t)

Vertical stretching rate — how far the column is squeezed at the peak of each cycle (the stretch factor S); higher values shrink the core more and spin it up faster, just like a tighter rear-flank-downdraft convergence in a real supercell.
Initial radius — the starting width of the slow, broad mesocyclone before any stretching begins.
Velocity vectors — toggle a ring of arrows showing local tangential velocity, so you can see speed grow as the core narrows.
Reset column — reseeds the particle column with a fresh random distribution.

The cycle here compresses minutes of real storm dynamics into seconds: watch the wide, gently turning mesocyclone column pull inward and upward, then relax back out, over and over — angular momentum conservation is what forces the spin-up every time the radius shrinks.

Slow / wide (mesocyclone) Fast / narrow (tornado core) Velocity vector

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