Aspects of secondary sonic boom propagation

Primary sonic boom leaves a supersonic aircraft downwards, whereas secondary boom leaves upwards but eventually reflects downwards due to inhomogeneities and/or wind in the upper atmosphere. In contrast to primary boom, secondary boom has hardly been investigated. Data from supersonic operations show that the respective signatures are very different, most likely due to the much longer propagation distance of secondary boom. To pinpoint when short-range primary boom models fail to give accurate results, we consider steady supersonic flight of a slender aircraft in a stratified atmosphere. Using linear wave theory, we calculate analytically the geometry of the surface of boom influence for some model atmospheres. Folds in this surface of influence correspond to increased boom intensity. Ray theory yields unphysical, infinite amplitudes at folds. We therefore follow a more detailed, analytical approach yielding a finite wavefield. In more complicated realistic atmospheres the calculation is completed numerically and shows the same qualitative behaviour. Additionally, using the method of matched asymptotic expansions, we derive a weakly nonlinear model with general variations of wind and sound speed. Using nonlinear wave theory, we determine a refined surface of boom influence and a remarkably simple expression for the amplitude variation.