Nonlinear behaviour of the Mack mode in a hypersonic boundary layer

Mack-mode waves are measured in a hypersonic boundary layer using high-frequency focusing schlieren deflectometry. Experiments are performed using a 5∘ flared cone at 0∘ angle of attack in the low-disturbance Mach 6 Quiet Tunnel at Texas A&M University across a free-stream unit Reynolds number range of 7.8× 10⁶~m⁻¹ Re 11.0× 10⁶~m⁻¹ . The high-frequency response of the measurement system allows harmonics and other nonlinear behaviour to be measured. Mack-mode waves and several harmonics are clearly observed at a frequency of f₀≈ 250~kHz . Bispectral analysis is used to show that these waves undergo several quadratic phase-coupled sum and difference interactions with themselves to produce harmonics, as well interact with a relatively low-frequency wave that results in amplitude modulation. Bispectral analysis is used to highlight these interactions.