The effects of compressibility (Mach number M∞), orientation angle αb, and Reynolds number Re on the two-dimensional flow-induced undamped pitching oscillation of an elliptic cylinder with aspect ratio 0.5 and mass ratio m∗=6.366 are investigated using high-accuracy direct numerical simulations. For a horizontally oriented cylinder (αb=0°) at low Mach numbers, the response exhibits pronounced nonlinear dynamics throughout an extended lock-in region. Near the onset of lock-in, a hybrid of supercritical and subcritical bifurcations gives rise to four distinct states characterized by the mean angular deflection (θ¯), oscillation amplitude, and frequency, accompanied by intermittent switching between two attractors resembling the Lorenz system. Within the lock-in regime, the dynamics exhibit intermittent periodicity, including single- and multiple-orbit cycles, period doubling, quasi-periodicity, and an intermediate shape-reversal bifurcation. Toward the end of lock-in, a wide subcritical hysteretic bifurcation occurs between two periodic states with distinct oscillatory responses and wake dynamics. Increasing Mach number substantially moderates the nonlinear behavior, although the initial supercritical pitchfork bifurcation in θ¯, an intermittent hysteretic regime between periodic dynamics and a modulated quasiperiodic state, and intermittent periodicity with single and multiple orbits as well as quasiperiodic responses persist. Inside the lock-in zone, the cylinder displays significantly higher mean deflection at higher Mach number. While the fluctuation amplitude is significantly larger within the lock-in region at low Mach numbers, it increases monotonically with Mach number in the second desynchronization regime, where the effective spring stiffness decreases. For nonzero orientation angles (αb0°), the flow dynamics differ markedly, indicating non-uniqueness in the cylinder response to flow-induced pitching.
Deepak et al. (Fri,) studied this question.