Metamorphosis of transition between states of limit cycle oscillations in aeroacoustic system

Abstract

Dynamical systems undergoing transition to oscillatory state exhibit change in the nature of the transition from supercritical to subcritical Hopf bifurcation or vice versa upon variation of a secondary parameter. This phenomenon is referred to as change of criticality. Many real-world systems undergo transition to oscillatory state that do not fit in the framework of Hopf bifurcation, and hence the change of criticality. We perform experiments on a ducted turbulent aeroacoustic flow constrained by two orifices separated at a distance apart. We vary the Reynolds number (Re), a bifurcation parameter causing a transition between various limit cycles. We change the distance between the orifices as the secondary parameter. We discover that turbulent aeroacoustic flows exhibit a metamorphosis of the transition from continuous to abrupt through a canard explosion, a bifurcation unique for its continuous yet rapid nature. We observe two distinct abrupt bifurcations, differing in their dynamical states associated with the transition. Understanding this metamorphosis from continuous to abrupt aids in developing low-cost control and preventive strategies for systems undergoing a route to oscillatory instabilities.