This thesis investigates the response of a canonical hydrodynamically self-excited jet to external acoustic forcing, with the aim of identifying the synchronization features, routes to chaos, and optimal closed-loop control laws for suppressing harmful self-excited oscillations. When forced at frequencies around its natural global frequency, the jet is found to exhibit a variety of nonlinear dynamical states, including limit-cycle attractors, quasiperiodicity on a 2-torus, strange non-chaos, and low-dimensional chaos. The chaos emerges via the Ruelle-Takens-Newhouse route and the intermittency route, with the latter involving crisis-induced intermittency and type-II intermittency from the Pomeau-Manneville scenario. Phase synchronization of chaos and chaos-destroying synchronization are...[ Read more ]

This thesis investigates the response of a canonical hydrodynamically self-excited jet to external acoustic forcing, with the aim of identifying the synchronization features, routes to chaos, and optimal closed-loop control laws for suppressing harmful self-excited oscillations. When forced at frequencies around its natural global frequency, the jet is found to exhibit a variety of nonlinear dynamical states, including limit-cycle attractors, quasiperiodicity on a 2-torus, strange non-chaos, and low-dimensional chaos. The chaos emerges via the Ruelle-Takens-Newhouse route and the intermittency route, with the latter involving crisis-induced intermittency and type-II intermittency from the Pomeau-Manneville scenario. Phase synchronization of chaos and chaos-destroying synchronization are also observed. The self-excited oscillations of the jet are then subjected to machine learning control, a data-driven model-free control framework based on genetic programming (GP). The results demonstrate that GP closed-loop control is more effective than both GP open-loop control and conventional open-loop control in suppressing the dominant global mode of the jet, providing a deeper understanding of the receptivity of self-excited shear flows. Overall, this thesis provides novel insights into the wide range of dynamics that can manifest in self-excited shear flows, laying the groundwork for the development of advanced theoretical models and improved control strategies for these flow systems.