Evaluation of numerical predictions of sonic boom level variability due to atmospheric turbulence

A numerical model of full-scale N-wave sonic boom propagation through turbulence is described based on the nonlinear Khokhlov-Zabolotskaya-Kuznetzov (KZK) propagation equation and the most advanced turbulence model used in atmospheric acoustics. This paper presents the first quantitative evaluation of a KZK-based model using data from the recent Sonic Booms in Atmospheric Turbulence measurement campaigns, which produced one of the most extensive databases of full-scale distorted N-waves and concurrent atmospheric parameters. Simulated and measured distributions of the perceived level (PL) metric, which has been used to predict public annoyance due to sonic booms, are compared. For most of the conditions considered, the present model's predictions of the PL variances agree with the measurement to within normal uncertainty, while about half of the mean value predictions agree. The approximate PL distribution measured for high turbulence conditions falls within about 2 dB of the simulated distribution for nearly all probabilities. These favorable results suggest that the KZK-based model is sufficiently accurate for approximating the N-wave PL distribution, and the model may therefore be useful for predicting public reaction to sonic booms in turbulent conditions.