The thermo-acoustic instability behavior of non-premixed hydrogen combustion is analyzed in the present work with the inlet Reynolds number, Re as the control parameter. It is observed that the dominant frequency (mode) shifts from the fundamental duct-acoustic mode to the first harmonic, as Re is varied. Continuous wavelet transform of the pressure oscillations reveals that at different Re, the dynamical nature of oscillations is topologically different, although they have identical spectral content. An interesting dynamical behavior identified as two-period quasi-periodic oscillations is observed, which has not been reported in prior literature. The state is seen to be unstable to incremental changes in Re and transitioning to limit cycle oscillations subsequently. Further diagnosis employing time-resolved OH* chemiluminescence and particle image velocimetry reveals the amplitude modulation of the quasi-periodic oscillation as a result of staggered vorticity distribution across the bluff body which results in asymmetric heat release rate distribution. A general framework for such oscillations is then applied, leading to identifying specific conditions that need to be satisfied to enable the existence of these oscillations. This study leads to novel observations on the asymmetric nature of shear layers, which can result in hitherto observed dynamical states. Graphic abstract: [Figure not available: see fulltext.] © 2021, The Visualization Society of Japan.