Gerstner WavesDrag to look around, scroll to zoom. Open ocean, built from a stack of travelling swells. The water isn’t just bobbing up and down — each drop circles as the wave passes, which is why real crests come to a peak while troughs stay broad and round.Franz Gerstner wrote this down in 1802, the first exact solution for a wave on deep water: move every particle in a circle and the surface takes a curve called a trochoid. Longer waves travel faster (ω = √(g k)), so a fresh sea sorts itself into the long, clean swell that outruns a storm.