Interaction of second-mode wave packets with an axisymmetric expansion corner

Experiments were performed in a Mach-6 shock tunnel to examine the impact of an abrupt expansion on hypersonic boundary-layer instability waves. The test geometry consisted of a 5 $$^{\circ }$$  half-angle, nominally sharp cone with a cylindrical extension. Ultra-high-speed schlieren ( $$550-747\,\mathrm{kHz}$$ ) was employed as the primary means of flow interrogation, providing a global view of instability development; the high frame rate enabled the use of spectral analysis techniques throughout the entire field of view. Instantaneous schlieren images demonstrated significant decay of both second-mode and turbulent disturbances downstream of the corner. This decay was found to be broadband, though low-frequency content was seen to amplify along the cylinder. Spectral proper orthogonal decomposition (SPOD) was implemented to determine the spatial structure and development of the modal content. Frequency-shifted second-mode waves were identified growing on the cylinder alongside the new low-frequency content. Analysis of the disturbance propagation speeds using the SPOD modes was found to give good agreement with a correlation-based approach. Bispectral analysis was employed to examine nonlinear energy exchange mechanisms within the boundary layer. Significant resonance of the second-mode fundamental was observed along with low-frequency coupling upstream of the corner, though evidence of nonlinearity dissipated downstream.