Origin and control of pseudo-rotating spiral jets

Active flow control (AFC) methods for jet-type flows have been extensively explored since the 1970s. Spectacular examples demonstrating the AFC power and the beauty of fluid mechanics include bifurcating and blooming jets. Recent advances in machine learning-based optimization have enabled efficient exploration of high-dimensional AFC, revealing control solutions beyond human intuition. The present paper focuses on one such discovery: the pseudo-rotating spiral jet. This phenomenon manifests as separate branches disconnected from the main jet stream, formed by vortical structures aligned along curved paths rotating around the initial jet axis. We investigate the origin of these jet-type patterns and formulate new rules for their control, showing that spiral jets belong to a family of multi-armed jets observable only at specific control settings. Furthermore, we demonstrate how human perception of three-dimensional imagery depends on the observable domain and vortex lifetime. Notably, the apparent rotation of spiral arms - despite having a well-defined frequency - is an illusion arising from the tendency to connect neighboring moving objects into continuous patterns. In contrast to the chaotic behavior of small-scale turbulence, we show that large-scale flow motion resulting from AFC operating in a deterministic manner is only seemingly unpredictable. Through theoretical analysis and 3D simulations, we develop a remarkably simple yet precise kinematic model that captures the formation and motion of these vortical paths. This model replicates the outcomes of complex flow simulations, reproduces the apparent jet shape, and facilitates the identification of the actual pattern. The findings offer new perspectives for both academic researchers and industrial engineers.