Why a Spinning Ball Curves — the Magnus Effect and Circulation
·6 min read
Random spin drifts a musket ball sideways. Circulation Γ=2πa²ω sets the side force, and spin 2 misses by 6.90 m, not twice the 3.71 m printed at spin 1.
Waves Hanging in the Sky — The Kelvin-Helmholtz Instability
·7 min read
On air and water the first wave shows up near 6.6 m/s, about 1.69 cm long, growing at 4.89 per second. Below that wind the surface stays calm.
Why Smokestack Plumes Curl Up Instead of Lying Flat — The Jet in Crossflow and Its Counter-Rotating Vortex Pair
·8 min read
With A=1.6 and B=0.33, the centerline at x=10d sits at 5.44d, 8.66d, and 13.78d for r=2, 4, and 8. Doubling r raises height by about 1.59, not by 2.
Two Faces of a Whirl — Free Vortex, Forced Vortex, and Helmholtz
·5 min read
A free vortex revolves with zero vorticity except at the center. The Rankine core spins at 2U/R and meets the 1/r tail smoothly at the core radius r = R.