Atmospheric Tornado

Severe mesocyclone tornadic vortex simulation modeling hyperbolic funnel cone boundary expansion, Rankine tangential velocity shear, and particle suction updraft.

Playground

60 FPS • Canvas 2D

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Live Parameters

Vortex Rotation Rate 1.4

Angular vortex velocity multiplier

Funnel Cone Aperture 1

Hyperbolic cone boundary scaling

Mathematical Formulation

89 chars high

Analytical Equation

v_\theta(r) = \begin{cases} \omega r & r \le R_c \\ \frac{\Gamma}{2\pi r} & r > R_c \end{cases}, \quad R(z) = R_0 + \alpha z^{2.2}, \quad v_z(z) = v_0 \left(1 + \beta z\right)

Compact Formula

v_theta = speed / (0.3 + r*0.7), R_funnel = 20 + z^2.2 * 170, sway = sin(1.5t + 3z)*40z

Renderer Logic

const angularVel = (pSpeed[i] / (0.3 + rNorm * 0.7)) * 4.0;
const funnelR = (20 + Math.pow(pz[i], 2.2) * 170) * funnelWidth;
const posX = centerX + Math.cos(pAngle[i]) * radius;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#tornado #vortex #rankine #fluid #meteorology #atmosphere #weather

Author: Math Art Core Target: 60 FPS

Atmospheric Tornado

Live Parameters

Mathematical Formulation

Mathematical Tags

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