tide · the ratchet — lakes on a spinning floor (looking down the axis)

In the rotating frame the potential is −½ω²r², so a liquid surface is an arc concentric with the axis — never a secant line: a chord mid-span sits r(1−cos φ) closer to the axis than its ends, spurious head the water runs off. On a smooth cylinder there are no lakes at all, just a film. Lakes need carved topology: ratchet teeth — a steep scarp prograde of each lake, a long glide descending into the next basin — so the Coriolis-drifted jet sheet either drains home or ratchets forward, lake to lake. Terrain here is radially exaggerated (250 m on an 8 km radius is sub-pixel at true scale); the water arcs of the jets stay true-scale. ← fountain & sun · tide ↑

The terrain (the ratchet)

Slide the crest to 50 m and the lake spreads; in the smooth-cylinder limit it becomes a film over the whole rim — the terrain is what makes a lake possible. The scarp is the ratchet's tooth face: it pens the lake on the prograde side and decides how far the jet must throw to feed the next basin.

The jet (from the lake)

The fan irrigates its own slope and the runoff collects back home — the closed local loop. A tight jet past ~180 m/s lands beyond the crest: every lake then feeds the next lake prograde, and the water circulates the rim as a ratchet river.

Cross-section — terrain exaggerated, water arcs true-scale

The lake (per basin)

Why not a secant? A chord is an equipotential only in uniform linear gravity. Here level means constant radius, so the surface is an arc — the secant sag gauge is how far a chord would dip below level at mid-span. Bed pressure is the exact rotating-frame hydrostatic ½ρω²(R²−rw²).

The river (runoff routing)

Landing markers on the slope: green drains back to its own lake, gold has crossed the crest and drains to the next. The animated dots are the runoff finding its basin.