Tornado Simulation

This simulation provides a simplified 3D visualization of a tornado. Tornadoes form under conditions of high atmospheric instability and significant wind shear, which together create a rotating vortex.

Theoretical Background:
A common model used to approximate the wind profile in a tornado is the Rankine vortex model. In this model, the tangential wind speed \(V_t(r)\) is given by:

$$ V_t(r) = \begin{cases} V_{\text{max}} \left(\frac{r}{R}\right) & \text{if } r \le R, \\\\ V_{\text{max}} \left(\frac{R}{r}\right) & \text{if } r > R, \end{cases} $$

where:
- \( r \) is the radial distance from the tornado center,
- \( R \) is the radius of the vortex core,
- \( V_{\text{max}} \) is the maximum tangential wind speed.

In our simulation, we do not solve the full fluid dynamics equations but instead adjust the tornado’s rotational speed and internal particle motion based on two key parameters:

• Atmospheric Instability: A higher instability leads to a faster rotating vortex (higher \( V_{\text{max}} \)).
• Wind Shear (m/s): Greater wind shear can stretch and tilt the tornado, affecting its structure.

The simulation uses these parameters to control the rotation of a funnel-shaped tornado model and the swirling motion of particles within it.

Atmospheric Instability: Wind Shear (m/s): Update Tornado