Low-boom and classical N-wave sonic boom propagation in random inhomogeneous layers using nonlinear wide-angle parabolic equation: statistical data comparison

International audienceA modern concept of supersonic civilian aircraft relies on the idea of fuselage and wings profiling aimed to avoid the coalescence of individual shocks generated by different parts of an aircraft to a single shock. Without profiling, the shock wave propagating from near field to the ground is transformed into a sonic boom with classical N-wave waveform due to acoustic nonlinear effects. The N-wave is perceived as very loud and annoying impulse noise. With profiling, the resulting low-boom waveform usually has a flat-top form or an increased rise time onset and produces much less noise than the N-wave. However, after propagating through the planetary boundary layer sonic boom waveforms are randomly altered due to refraction on sound speed inhomogeneities and wind fluctuations of different scales which are attributed to the turbulence. For example, focusing inhomogeneities result in the formation of caustics where sonic boom peak overpressure is amplified by several times and classical N-wave waveform is transformed to a U-wave. This randomly occurring physical process potentially increases noise level perceived by the public. In this work, a two-dimensional one-way wide-angle nonlinear parabolic equation is used to simulate classical N-wave and model low-boom wave propagation through a layer with random sound speed inhomogeneities constructed from the energy spectrum of homogeneous isotropic turbulence. Using a large number of realizations of random acoustic field we analyzed the statistics of the peak overpressure, the rise time and the shock front steepness at the ground after propagation through the inhomogeneous layer. The advantage of low-boom waveform over classical N-wave in producing less noise is discussed. This work is supported by RSF grant №18-72-00196 and also by the LABEX CeLyA (ANR-10-LABX-0060) of Université de Lyon, within the program «Investissements d’Avenir» (ANR-16-IDEX-0005) operated by the French National Research Agency (ANR)