Mach cutoff phenomenon of sonic boom in temperature inversion layers

Abstract

The Mach cutoff of sonic boom occurs when shock waves propagate from supersonic to subsonic regions in a stratified atmosphere. In this study, numerical simulations are performed to clarify Mach cutoff behaviors in atmospheric temperature inversion layers, which have not yet been investigated. The two-dimensional Euler equations with a gravitational source term are solved in a horizontally stratified atmosphere. Surface and non-surface temperature inversion layers include three and four supersonic–subsonic mixing layers, respectively. Computations are made to analyze the propagation characteristics of a conventional N-shaped waveform. The results show that multiple upward and downward cutoffs occur owing to atmospheric temperature inversions, with multiple outgoing and evanescent waves, and multiple shock wave focusing. The upward and downward cutoffs act similarly. The positive- and negative-pressure regions are inversed when a cutoff occurs twice; thus, each cutoff shifts a phase by π/2, as expressed in the linear theory of caustics. A waveform transition occurs owing to wave splitting in a cutoff region, in addition to the phase shift. For surface temperature inversion, upward cutoffs make the waves between the cutoff and ground surfaces persist, resulting in rumbling. For non-surface temperature inversion, upward and downward cutoffs occur alternately, and the waves between them persist as well. Therefore, multiple cutoffs in temperature inversion layers play an important role in sonic boom evaluation during low supersonic flight.