Modelling statistics of sonic boom parameters in turbulent media using nonlinear parabolic equation

Abstract

Over the past decade, plans to develop a new generation of supersonic passenger aircrafts have spurred interest in sonic boom propagation in the atmosphere. New designs are focused on reducing its loudness on the ground. Sonic boom waves are affected by propagation in turbulence of the planetary boundary layer occurring in few kilometers above the ground. Therefore, sonic boom wave parameters such as peak pressure and rise time, as well as corresponding noise levels, become random, which requires statistical characterization. Theoretical analysis of the effects of the presence of turbulent layer is frequently based on one-way model equations of different complexity, of which the basic equation is the nonlinear parabolic Khokhlov-Zabolotskaya-Kuznetsov-type (KZK) equation. Here, sonic boom propagation through homogeneous isotropic turbulence is simulated using the KZK equation. Classical N-waves with different amplitudes and several examples of low-boom waveforms are considered as input waveforms at the entrance to turbulent layer. Statistical data of the peak pressure, shock front steepness, and perceived loudness metric are analyzed. It is shown than unless sonic boom amplitude exceeds a certain threshold, perceived loudness variability is mainly determined by waveform spectral components at mid-range frequencies around 100 Hz. [Work supported by RSF-18-72-00196 and ANR-10-LABX-0060/ANR-16-IDEX-0005.]