Vortex Stretching Tornado Lab (2D): Plan View, Rankine Profile and Pressure Deficit

Presets

Playback

Mesocyclone spin Vortex stretching (core radius) RFD convergence strength Tracer density Animation speed

Live readout

Core radiusCore tangential speedCentral pressure deficitRotation period (core)Angular momentum L = omega R^2

What to try

1. Press Stretch the vortex: the core shrinks, the core wind rises as 1/R and the pressure deficit as 1/R^2. 2. Raise RFD convergence to feed tracers inward. 3. Compare the two profile curves: wind peaks at the core radius and pressure is lowest at the centre.

Model checks

The science

The wind field is a Rankine combined vortex: solid-body rotation inside the core, v = omega r for r ≤ R, and an irrotational vortex outside, v = omega R^2 / r for r > R. Outside the core the circulation 2 pi r v is constant. Stretching the column conserves angular momentum, omega R^2 = constant, so as R shrinks omega ~ 1/R^2 and the core wind v = omega R ~ 1/R.

Cyclostrophic balance dp/dr = rho v^2 / r gives the pressure drop. Integrating from the centre to infinity gives p_inf - p_0 = rho omega^2 R^2, rising as 1/R^2 when the vortex is stretched.

Honest simplifications: no real tornado, tracers are passive, the RFD inflow and updraft are simple kinematic rules matching the 3D lab, units are scene units scaled to km/h and hPa by the same factors as the 3D page, and values at extreme stretching exceed any real wind speed.