whatA drop of ink falls into still water. It plunges as a smooth laminar plume, its edges begin to scallop and roll into a train of curls, the curls swallow one another, and slowly the whole figure thins and fades away. Drawn only as the contour lines of ink, never as smoke. Click anywhere to drop your own blob; left alone, the water drops one now and then.

whyThe scalloped rolling at the plume's edge is the Kelvin-Helmholtz instability, the same one that curls cirrus clouds, ocean waves and the bands of Jupiter. Wherever two sheets of fluid slide past each other, any ripple between them gets stretched into a spiral. Nobody draws the spiral; the shear does.

howThe water is a coarse grid solved by Stam's stable-fluids method: each instant, the velocity field carries itself and the ink along its own flow, and a pressure solve keeps the water incompressible. A vorticity term re-sharpens the small whirls the coarse grid would otherwise blur away, which is what lets the frills grow. A dropped blob is a puff of ink and a push; the shear between the moving plume and the still water does everything else. The ink slowly dissipates. The readout tracks blobs, ink mass and total swirl; the sparkline is the swirl rising with every drop and decaying after. One integer seeds where the water drops ink by itself.