Presets
Playback
Wind, release and stability
A puff of 3 seconds of emission is released every 3 seconds and drifts with the wind while its size grows as sigma squared = 2 K t. Unstable classes mix faster, so the plume reaches the ground closer to the stack but is diluted sooner.
Model checks
The science
What is modelled
Every three seconds the stack releases a Gaussian puff that is carried by the wind. Its horizontal and vertical variances grow linearly in time with diffusivities that depend on the Pasquill stability class, and the ground reflects the vertical profile. Summing all puffs gives the concentration field; a continuous release at constant wind reduces to the classic Gaussian plume.
Equations
- Puff:
C = m / ((2π)3/2 σh² σz) exp(-r²/2σh²) [exp(-(z-h)²/2σz²) + exp(-(z+h)²/2σz²)],σ² = 2 K t. - Steady plume:
C = Q/(4 π x √(Ky Kz)) exp(-u y²/(4 Ky x)) [...]. - Ground maximum at
x* = u h² / (4 Kz).
Checks run in the page
- Mass conserved by one puff and its image.
- Dense-puff superposition against the steady plume.
- 1/x far-field scaling.
- Numerical search for the ground maximum against x*.
Honest simplifications
A diffusivity (K-theory) puff model with fixed class values rather than distance-dependent Pasquill-Gifford curves, flat terrain, no buoyant plume rise, no deposition or chemistry, one wind speed at all heights and a slow wind-direction wobble. For teaching only; not for emergency or regulatory decisions.
What to try
- Press Unstable, sunny (A) and then Stable night (F): the hot spot moves from near the stack to far away and the concentration changes by orders of magnitude.
- Press Tall stack and watch the ground-level maximum fall.
- Press Turning wind to see the plume swing across the sensors.