Energy growth of vortical, acoustic, and entropic components of the second-mode instability in the hypersonic boundary layer

Abstract

The acoustic, vortical, and entropic (thermal) components of the second-mode instability, regarded as an asymptotic behavior of the free-stream counterparts, were found to interact with each other in a well-defined way. However, the mechanisms of the energy growth of each component and the resulting second mode instability remain to be clarified. The present paper provides a quantitative energy analysis of the key sources responsible for the modal growth in the momentum potential theory framework. The acoustic, vortical, and entropic components are governed by energy source effects and interexchange effects, characterized by explicit transport terms and relationships between the growth rate and the energy source. The thermal-acoustic source, induced by the interaction between the fluctuation pressure and the fluctuation entropy, is revealed to be the most pronounced cause of the second-mode instability in the hypersonic boundary layer. The thermal-acoustic source is further decomposed into the dissipative (viscous) part and the non-dissipative (inviscid) part. The dissipative thermal-acoustic source is dominant near the wall surface and destabilizes the second mode. The non-dissipative thermal-acoustic source destabilizes the second mode significantly at the critical layer, while the dissipative thermal-acoustic source stabilizes the second mode in this region.