Numerical Investigations of Nonlinearly Generated Disturbance Waves in High-Speed Boundary Layers

In several experimental investigations of hypersonic boundary-layer transition, higher harmonics of the linearly unstable second mode waves as well as low-frequency waves, which are not related to first mode waves, have been observed. It has been conjectured that the higher harmonics are nonlinearly generated by a self-interaction mechanism of the linearly amplified second mode waves. Several hypotheses regarding the origin of the low-frequency waves and their role in the transition process have been put forth. However, a clear understanding of the origin and role of these low-frequency disturbances in the transition process is difficult to attain from experiments and thus still not completely achieved. The nonlinear generation of higher harmonics and low-frequency disturbances is relevant because in high-speed boundary layers, second modes can reach very large amplitudes, which can lead to a considerable stretching of the transitional regime where these nonlinearly generated waves can then reach significant amplitudes and participate in the transition process. To shed light on this unresolved issue, numerical investigations were carried out for a flared cone at Mach 6. These calculations have shown that nonlinear interactions of sufficiently large-amplitude second mode waves can generate low-frequency disturbances. This was confirmed by a theoretical nonlinear interaction model.