Thermoacoustic Interpretation of Second-Mode Instability

A thermoacoustic interpretation of Mack’s second-mode instability is proposed. It is demonstrated that the fundamental mechanism of second-mode wave growth in hypersonic boundary layers is consistent with standing-wave thermoacoustically driven instability. The resonant nature of such modes is sustained by an acoustic impedance well between the wall (infinite impedance) and near the sonic line (secondary peak in impedance). A Lagrangian approach is adopted to show that such resonant standing waves derive energy from the base flow through thermoacoustic Reynolds stress, which results from the divergence of acoustic power inside the impedance well, and thermodynamic work. This treatment does not represent a complete energy closure (due to the neglect of viscosity), but it does provide insight toward a fundamental energy source and the physical mechanisms governing Mack’s acoustic second mode.