On the energy transfer mechanisms for the supersonic mode

The energy transfer mechanisms for Mack’s second mode and a supersonic mode based on spatial linear stability theory for a Mach 6 flat plate flow with T_w = 0.5T_∞ is investigated. For the current conditions, the supersonic mode is unstable but obtains a relatively low amplification rate in comparison to the second mode. The energy analysis conducted in this paper shows that the total energy of the second mode is available throughout the boundary layer, however, for the supersonic mode, it is concentrated closer to the wall. The combined effect of thermal production and production density dissipates most of the energy away from the critical layer for the supersonic mode. As opposed to the second mode, a significant amount of energy is available in the free-stream in the case of supersonic mode. It is found that the energy is provided from the pressure strain transport term counteracting the shear-work. In the second part of the paper, direct numerical simulations were performed for the same flow conditions, and a decomposition of the disturbance flow field was performed. Some differences in the growth rates especially in the region where the supersonic mode appears was observed. Although the flow decomposition showed that the unstable mode F dominates the disturbance flow field, there appears to be a non-negligible contribution from the stable supersonic mode.