The Illusory Spiral

Machine learning optimization of active flow control discovered something unexpected: spiral jets. When certain control inputs are applied to a round jet, the flow organizes into helical arms that appear to rotate around the jet axis. The pattern is visually striking — separate branches of fluid disconnect from the main stream and spiral outward, as if the jet were a rotating sprinkler.

The spiral doesn’t spin (arXiv:2509.00763). The apparent rotation is an optical illusion, created by the human tendency to connect spatially adjacent moving objects into continuous trajectories — a fluid-mechanical instance of the gestalt principle of common fate. Individual vortical structures are born, travel outward along curved paths, and die. New structures are born at slightly different angular positions. The succession creates the appearance of continuous rotation even though no fluid element is rotating.

The rotation has a well-defined frequency. It’s measurable, consistent, reproducible. And it’s entirely an artifact of perception.

The authors show that spiral jets belong to a family of multi-armed jet patterns observable only at specific control settings. The number of arms, their pitch, and their apparent rotation rate all depend on the forcing parameters. Human perception of the three-dimensional structure depends on the observation domain and the vortex lifetime — change either, and the same physical flow looks qualitatively different.

The structural insight: machine learning found this pattern because it was optimizing without the perceptual biases that would have prevented a human from recognizing its significance. The spiral jet is real physics discovered by an algorithm, but its most striking feature — the rotation — exists only in the observer. Even fluid mechanics can produce gestalt illusions, and it took a perceptually naive optimizer to reveal them.

“Origin and control of pseudo-rotating spiral jets,” arXiv:2509.00763 (2025).