Sonic Boom Propagation Through AN Inhomogeneous, Windy Atmosphere.

One of the primary obstacles to NASA's proposed High Speed Civil Transport is the sonic boom produced by the aircraft. Features of the sonic boom that are of primary importance are the amplitude and rise time of the wave received on the ground. In this paper, the propagation of the sonic boom from the aircraft to the ground is investigated by the ray theory approach. Courant and Hilbert's theory of characteristics is used to derive the ray path equation for a moving, inhomogeneous medium. The atmosphere is assumed to be horizontally stratified and quasi-stable, but no symmetry requirements are placed on the wavefronts. The lossless, nonlinear energy transport equation along these ray paths is derived. Losses are included directly in the numerical solution. A variable transformation is introduced which converts the transport equation into the lossless Burgers' equation, which has well-known solutions. A computer model, called ZEPHYRUS, is constructed which solves these equations numerically. The effects of numerical propagation through reflections and caustics are considered. A number of results of ZEPHYRUS are presented. Comparisons are made with known analytical results, and with the Hayes program. Several physically interesting results are discussed, including the dependence of rise time on humidity, the wind field, and the initial waveform shape. It is demonstrated that stable shocks may have a longer characteristic formation distance than previously believed, and in general have not formed when the sonic boom reaches the ground. Also discussed are unusual effects of dispersion observed at 50% relative ground humidity, and an investigation of the possible occurrence of the "waveform freezing" phenomenon.