Nonlinear wave interactions in a transitional hypersonic boundary layer

Abstract

The linear and nonlinear evolutions and breakdown of the second modes in hypersonic boundary layers (HBLs) on a flared cone are investigated using Rayleigh-scattering flow visualization and fast-response pressure sensors. Based on two spatially separated pressure signals, cross-bicoherence analysis that permits the distinction of sum- and difference-interactions is utilized to identify the nonlinear interactions. In addition, the visualization temporal and spatial resolution allows fine flow features to be captured to provide additional flow information. Amplitude correlation technique is used to estimate the nonlinear energy transfer between the modes. Our results show that nonlinear interactions between the second mode and the low-frequency wave contribute to the growth of the low-frequency wave, and the difference interactions between the second mode and its first harmonic play a dominant role in modulating the waves in the overall transition process. Amplitude correlation analysis reveals that the spectral energy is nonlinearly transferred from the second mode into its first harmonic and into low-frequency wave, in agreement with the cross-bicoherence analysis. The amplitude modulation of the second mode caused by the difference interaction between the second mode and its first harmonic will reduce the propagation speed of the second mode. However, at the final breakdown stage, this difference interaction vanishes, and the second-mode propagation velocity recovers quickly. Since the frequency of the second mode keeps almost unchanged over the entire transition process, a higher propagation velocity will result in a larger wavelength, indicating an elongation and deformation of the second mode. Eventually, the difference interaction between the second mode and the low-frequency wave accompanying the energy transfer from the second mode to low-frequency waves leads to the final breakdown of the HBLs into a turbulent state.