Curl

What to observe

1. Start on Differential rotation, the way a galaxy or a stirred cup turns: everything circles the middle, but the inner rings go round far faster than the outer ones. Drag the wheel from the centre to the rim andwatch it slow to a crawl. Curl is a function of position, and the readout probe ÷ reference tells you how far it has fallen behind the wheel pinned at the middle.
2. Now pick Rigid spin, the one field where dragging changes nothing. The whole plane turns as a solid slab, so every point twists at the same rate and curl really is constant: ω = ½ ∇ × F everywhere. The contrast with the previous field is the whole point, since both of them look like circulation from a distance.
3. Pick Channel: every arrow points horizontally, so nothing goes round anything, yet the layers slide past each other and the wheel still turns. It turns one way above the centreline and the other way below, and sits perfectly still on the line itself where the flow is fastest. A field needn't look swirly to have curl.
4. Pick Radial: flow streams straight outward along rays, clearly not circulating, and the paddle does not spin anywhere. This field has divergence but zero curl, the mirror image of the source in the divergence demo.
5. Vortex pair is the sharpest case. The streaks wind round both centres, but away from the two cores the curl dies off fast, so a wheel carried a long way around the outside orbits without ever spinning. Travelling in a circle and rotating are simply different things.