This study employs spectral proper orthogonal decomposition (SPOD) on direct numerical simulation data from a low-pressure turbine (LPT) operating under high freestream turbulence levels. The impacts of upstream wakes on the transition process are assessed by considering both cases with and without wakes, modeled by a moving cylinder placed upstream of the LPT blade. In the absence of upstream wakes, the SPOD eigenvalues decreases almost monotonically as frequency increases. At high frequencies, the spectra reveal a broadband interval with minimal elevation, corresponding to the Kármán vortex streets formed downstream of the blade's trailing edge. The SPOD modes in this inflow condition show fully attached boundary layers across the entire blade, suggesting that the boundary layers may be transitional. When subjected to upstream wakes, however, the SPOD spectra display several intense peaks linked to the wake passage frequencies. The associated SPOD modes reveal turbulent spots and lambda vortices on the rear suction side of the blade, typical indicators of turbulent boundary layers. Between the fundamental passage frequency and its harmonics, a series of tones emerge, representing the Doppler-shifted wakes. Triadic interactions between modes involving upstream wakes and their translation induce a cascade of these intermediate components, as verified by the bispectrum map. The SPOD modes capture interactions of structures carried by upstream wakes and the freestream flow with the blade boundary layers, manifested as low- and high-velocity streaks whose breakdown promotes the transition. High-frequency modes describe coherent structures break down into the vortex streets at the trailing edge.

High-fidelity large-eddy simulations are conducted for a 4:1 rectangular supersonic nozzle at under-expanded screeching conditions. By creating a small groove on the nozzle surface, we numerically modify the boundary layer inside the nozzle and the resulting jet initial shear layer. A total of 5 cases with different groove sizes are studied and compared with the no-groove baseline case. Near-field flow statistics and far-field acoustics are analyzed. The geometric tripping method is shown to increase the turbulent kinetic energy and boundary layer thickness at the nozzle exit. The slight modification in the initial shear layer state leads to different shear layer thicknesses and shock cell decay rates near the end of the jet potential core. Screech tone amplitude variation is observed, with largest difference measured to be 2.9 dB compared to the baseline value. The dominant coherent structures associated with screech generation are studied with spectral proper orthogonal decomposition. The amplitudes of the internal upstream-traveling wave and the downstream-traveling Kelvin-Helmholtz wave are calculated. The differences in the screech tone amplitude are found to be related to the strength of the Kelvin-Helmholtz wave, which is a result of the modified receptivity of the initial shear layer.