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. Applying the large eddy simulation (LES) method and a high-order numerical code, 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. We show that the 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 found that the large-scale flow motion induced by AFC, operating in a deterministic manner, is fully predictable. Through theoretical derivation and analysis of 3D LES results, we develop a remarkably simple yet precise kinematic model that captures the formation and motion of the 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 analysis of time-averaged data shows that, for a specified set of control parameters, the jets exhibit an unprecedented tendency to increase the entrainment rate (up to 9 times that of the classical jet), accompanied by a simultaneous 5-fold rise in turbulent kinetic energy, resulting in intensified mixing. Analysis of a passive scalar field reveals a substantially more uniform distribution, with up to a sevenfold improvement over the classical jet at five nozzle diameters, and nearly perfect mixing achieved at ten diameters. These findings open new perspectives for both academic researchers and industrial engineers, particularly in combustion science, cooling systems, and jet propulsion, where control of the mixing process is a critical factor for flame stabilization, heat exchange, and noise mitigation.
Wawrzak et al. (Mon,) studied this question.