Dynamic mode decomposition analysis for three-dimensional density structure of shock-associated noise source in underexpanded supersonic jets

Dynamic mode decomposition (DMD) is employed to investigate coherent structures relevant to shock-associated noise in underexpanded supersonic jets at a nozzle pressure ratio of 2.18. A double-pulsed three-dimensional background-oriented schlieren measurement is utilized, enabling DMD analysis despite the non-time-resolved nature of the measurement system. Among the numerous extracted DMD modes, the present study focuses on those corresponding to screech and broadband shock-associated noise (BBSAN) frequencies. DMD modes at the screech frequency are identified for the first four azimuthal wavenumbers and exhibit standing-wave patterns. The screech feedback loop for the azimuthal wavenumber m=2 is closed by upstream-propagating disturbances arising from the interaction between the Kelvin–Helmholtz wavepacket and the first shock-cell mode, consistent with the resonance mechanism for the azimuthal wavenumber m=0. In contrast, for azimuthal wavenumbers (m=1,3), no upstream-propagating disturbances are found to close the screech feedback loop. These results suggest that coherent structures associated with screech are present for azimuthal wavenumbers (m=0,2), whereas such structures are absent or not clearly discernible for azimuthal wavenumbers (m=1,3). For BBSAN, all downstream-propagating waves extracted from the DMD modes within the BBSAN frequency range generate disturbances associated with this noise through interactions with the shock-cell structures, indicating that these modes are directly linked to BBSAN generation. Further analysis reveals that the contribution of shock-cell modes to BBSAN generation varies with radiation angle. At low radiation angles, BBSAN generation is dominated by the first shock-cell mode, while at high radiation angles it is governed primarily by higher-order shock-cell modes.