Relaxation and turbulence effects on sonic boom signatures

The rudimentary theory of sonic booms predicts that the pressure signatures received at the ground begin with an abrupt shock, such that the overpressure is nearly abrupt. This discontinuity actually has some structure, and a finite time is required for the waveform to reach its peak value. This portion of the waveform is here termed the rise phase, and it is with this portion that this presentation is primarily concerned. Any time characterizing the duration of the rise phase is loosely called the 'rise time.' Various definitions are used in the literature for this rise time. In the present discussion the rise time can be taken as the time for the waveform to rise from 10 percent of its peak value to 90 percent of its peak value. The available data on sonic booms that appears in the open literature suggests that typical values of shock over-pressure lie in the range of 30 Pa to 200 Pa, typical values of shock duration lie in the range of 150 ms to 250 ms, and typical values of the rise time lie in the range of 1 ms to 5 ms. The understanding of the rise phase of sonic booms is important because the perceived loudness of a shock depends primarily on the structure of the rise phase. A longer rise time typically implies a less loud shock. A primary question is just what physical mechanisms are most important for the determination of the detailed structure of the rise phase.