Geology & Earth Science
Volcanic Eruption Column
H ≈ 0.3·Q^¼
A buoyant eruption plume rises until it runs out of thermal buoyancy, and because that balance depends on the fourth root of the mass discharge, even a thousandfold surge in eruption rate only lifts the ash column a handful of times higher.
Computed & rendered in pure C# on the frozen OnlyCSharp 1.8 library — animation baked to GIF with the library's own
Gif encoder (no GPU, no ffmpeg, no external packages).