Objective: Assessing thermoacoustic instability and flame-acoustic coupling is crucial for effectively designing and operating various combustion devices. Owing to the complex coupling among flame, acoustic waves, and the flow field, certain simplified configurations are typically adopted to capture fundamental dynamics. This study employs a propagating flame in semi-confined tubes to investigate these phenomena, focusing specifically on the role of hydrodynamic instability in flame oscillation and the development of thermoacoustic instability. Methods: The flame-acoustic interaction in a narrow, semi-open channel was investigated by numerically solving the compressible Navier-Stokes equations incorporating thermal conduction, mass diffusion, viscosity, and single-step irreversible chemical reaction kinetics. Modal decomposition techniques, specifically, the proper orthogonal decomposition (POD) and the spectral proper orthogonal decomposition (SPOD), were applied to the temperature field near the flame front zone to investigate the impact of hydrodynamic instability on flame oscillation during primary acoustic instability. Results: Numerical simulation results demonstrate that as the flame propagates from the open end toward the closed end of the channel, sustained flame oscillations occur owing to the development of primary acoustic instability. Cells or cusps appear on the flame front, initiating at the leading edge near one channel wall and moving along the flame front surface toward the other wall. This movement resembles the nonlinear process of Darrieus-Landau instability development. Statistical analysis indicates that the most probable wavelength of these cells corresponds closely to the most unstable wavelength predicted by linear theory for Darrieus-Landau instability. The periodic motion of these cells results in a sawtooth-like variation in the burning rate over time. POD analysis revealed that the wavelength of the coherent structure for the first three POD modes matches the most unstable wavelength of Darrieus-Landau instability, capturing flame front wrinkling and resembling the nonlinear process of Darieus-Landau instability development. Higher POD modes also describe similar physical phenomena but focus on smaller structural movements. The time evolution of the decomposition coefficients for different POD modes was also computed and compared. Additionally, a spectrogram of the pressure signal measured at the closed end of the channel was analyzed and compared with the channel eigenfrequency. It shows that during primary acoustic instability, the pressure signal predominantly aligns with the fundamental mode of the channel eigenfrequency, but a small manifestation of the first harmonic is also observed. Subsequently, SPOD was employed to gain a deeper understanding of the frequency-based flame dynamics. SPOD results indicate that the frequency associated with the wrinkle motion on the flame front aligns with the fundamental mode of the channel eigenfrequency. At the first harmonic, SPOD captures cell or cusp movement along the flame front surface, showing a smaller wavelength proportional to the frequency ratio between the harmonic and fundamental modes. Notably, SPOD results at harmonic frequencies exhibit similar structural patterns to those observed in higher POD modes. Finally, SPOD analysis of the vorticity and velocity vector fields identified weak vortices present in higher-frequency modes. These vortices can be captured in higher-frequency modes, which are associated with cusp motion on the flame front. Conclusions: The significance of hydrodynamic instability in flame-acoustic coupling for nonsymmetric flames in semi-open narrow channels is emphasized. Using modal decomposition methods, the study establishes a connection between hydrodynamic instability and flame oscillation frequencies. This connection provides insight into different flame oscillation behaviors at various acoustic modes and resents valuable information for controlling thermoacoustic instability.