Prehistory of instability in a hypersonic boundary layer

The initial phase of hypersonic boundary-layer transition comprising excita tion of boundary-layer modes and their downstream evolution from receptivit y regions to the unstable region (instability prehistory problem) is consid ered. The disturbance spectrum reveals the following features: (1) the firs t and second modes are synchronized with acoustic waves near the leading ed ge; (2) further downstream, the first mode is synchronized with entropy and vorticity waves; (3) near the lower neutral branch of the Mack second mode , the first mode is synchronized with the second mode. Disturbance behavior in Regions (2) and (3) is studied using the multiple-mode method accountin g for interaction between modes due to mean-flow nonparallel effects. Analy sis of the disturbance behavior in Region (3) provides the intermodal excha nge rule coupling input and output amplitudes of the first and second modes . It is shown that Region (3) includes branch points at which disturbance g roup velocity and amplitude are singular. These singularities can cause dif ficulties in stability analyses. In Region (2), vorticity/entropy waves are partially swallowed by the boundary layer. They may effectively generate t he Mack second mode near its lower neutral branch.