Nonlinear resonance of low- and high-frequency waves in a cooled hypersonic boundary-layer

Abstract

We investigated non-linear resonance of low- and high-frequency waves (LHFWs) in a cooled hypersonic boundary layer. First, an experimental campaign was conducted in the high-enthalpy shock tunnel at the Japan Aerospace Exploration Agency using a circular-cone model. The results allowed us to identify early-developing low-frequency waves and strong cross-bicoherence among LHFWs, indicating that non-linear phase couplings existed. Second, to explain the mechanisms involved, stability analyses were performed under the test conditions. In a region upstream of the experimental transition point, a linear analysis of the frequencies of dominant fluctuations in the experiment clarified the existence of several wave triads that satisfy a resonance condition, requiring phase synchronization among three waves. Assuming that the initial amplitude of the low-frequency mode was higher than the initial amplitudes of the high-frequency modes, a weakly non-linear analysis was conducted. The results suggest that as the initial amplitude of the low-frequency mode was increased, the remaining two high-frequency modes deviated from the linear behaviour: the mode at lower frequency was slightly destabilized, whereas the higher-frequency mode was stabilized. It followed that the spectral broadening to lower-frequency bands was relatively enhanced.