A deep-water swell is a partitioned circle dance: each parcel loops forward at
the crest, backward in the trough, and barely at all near the seabed — orbit radius decays as e^(−kz), so at
depth λ/2 it's ~4% of the surface value. That's why submarines dive to escape storms. The deep-water speed
formula is beautifully simple: c = 1.25√λ (λ in metres, c in m/s) — long swells outrun short chop, which
is why big clean surf arrives first, hours ahead of the storm that made it.
Run the depth slider down: once depth < λ/2 the orbits flatten into ellipses, speed
depends only on depth (c = √(gd)), the front slows before the back → wavelength shrinks, height grows, crest
outpaces its base and the wave breaks when depth ≈ 1.3 × wave height. Tsunamis are the extreme shallow
case: in 4,000 m ocean they're ordinary-looking waves moving at √(9.81×4000) ≈ 200 m/s — jet speed.