Numerical investigation of transition initiated by a wave packet on a cone at Mach 3.5

Transition initiated by a wave packet in a cone boundary layer at Mach 3:5 has been investigated using LST and DNS. Disturbances have been introduced into the boundary layer by pulsing the wall-normal velocity through a hole on the cone surface. The computational setup is very close to experiments by Corke et al.¹ and Matlis.² The present study can be divided into three parts. In the first part, the linear development of a wave packet is studied in detail. Disturbance spectra in the frequency{azimuthal mode number plane based on wall-pressure amplitudes and time envelopes of the disturbance signal are discussed. The second part of the present study focuses on the identification of possible, asymmetric resonance triads for the most dominant oblique instability waves of the wave packet. New triads have been found that have not yet been reported for a supersonic boundary layer. These triads might explain some major findings in the third and final part of the present work, which focuses on the weakly nonlinear development of a wave packet that was generated by a large amplitude pulse. The initial disturbance development of this wave packet remains still linear, while farther downstream nonlinear wave interactions alter the shape and the disturbance spectrum of the packet. The disturbance spectrum from this study and the results of other investigations performed in parallel (Laible et al.³) suggest that oblique breakdown might be the strongest nonlinear transition mechanism for a supersonic boundary layer.