Динаміка торнадо: воронки, обертання та уламки

Vortex Dynamics

A tornado is a rotating column of air stretching from a thunderstorm’s base to the ground, and its defining physics is vortex dynamics: fluid rotating around a central axis with a pressure minimum at the core. Air pressure drops sharply toward the centre because the rotating flow needs a centripetal force to keep curving inward, and that force comes from a radial pressure gradient — lower pressure at the centre, higher at the edge — which is why a tornado’s core has dramatically lower pressure than the surrounding air, and why structures can experience an near-instant pressure difference that adds to wind loading.

From where the rotation comes: tilting horizontal shear

Most tornado-producing supercell thunderstorms get their initial rotation from wind shear: wind speed or direction changing with height creates a horizontal-axis spinning tube of air, like a rolling pin lying on its side. The storm's strong updraft then tilts a piece of that horizontal tube upright, converting horizontal spin into vertical spin, and stretches it — and by conservation of angular momentum, a spinning fluid column that gets stretched thinner spins proportionally faster, the same effect an ice skater uses pulling in their arms. This tilt-and-stretch mechanism is why the broad, slow rotation of a supercell's mesocyclone can concentrate into the much smaller, much faster rotation of a tornado.

conservation of angular momentum (simplified, inviscid):
  L = m * v_tangential * r  =  constant
  column stretches => r decreases => v_tangential increases sharply

The vortex velocity profile: solid core, free vortex outside

A real tornado's tangential wind speed does not simply grow toward the centre forever — it typically follows a Rankine combined vortex profile: inside a core radius r_c the flow rotates roughly like a solid body (speed increasing linearly with radius, like a spinning disk), while outside r_c it behaves like an idealised free vortex where speed falls off as 1/r. The maximum wind speed occurs right at r_c, the boundary between the two regimes — which is why the most destructive winds in a real tornado are concentrated in a fairly narrow annulus, not spread uniformly across the whole funnel.

v(r) = Omega * r,         r <= r_c    // solid-body core, linear growth
v(r) = Omega * r_c^2 / r, r >  r_c    // free vortex outside, falls off as 1/r
                                       // maximum speed at r = r_c

Particles as tracers: why the funnel is visible at all

A tornado’s visible funnel is not the vortex itself — air is transparent — it is condensed water vapour (from the pressure drop cooling the rising air below its dew point) plus whatever dust and debris the near-surface winds pick up and loft along helical paths. On this page, particles are seeded continuously and given a velocity that combines the tangential Rankine-profile rotation with an upward and slightly inward drift, so each particle traces a rising helix rather than a flat circle — visually reproducing the classic funnel-and-debris-cloud look without simulating the underlying fluid pressure field directly. Adjustable intensity and width parameters scale Ω and r_c respectively, and wind drift adds a uniform translation on top so the whole vortex can be dragged across the scene while still rotating internally.

Frequently asked questions

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