Auralization of atmospheric turbulence-induced amplitude fluctuations in aircraft flyover sound based on a semi-empirical model

Atmospheric turbulence causes well-audible fluctuations in sound amplitude as it propagates through the atmospheric boundary layer. However, the best currently available theoretical model describing amplitude fluctuations is limited to relatively short propagation distances and weak turbulence. This article presents a semi-empirical model for predicting the standard deviation of amplitude fluctuations, combining the existing theoretical model of Ostashev and Wilson with empirical data. Leveraging a dataset of over 5000 aircraft flyovers across diverse meteorological conditions, the model incorporates factors such as frequency- and distance-dependent saturation of amplitude fluctuations, an effective propagation length based on the boundary layer height, turbulence decay time during transitional states of the atmosphere, and turbulence production by nocturnal low-level-jets. The mean absolute error of the semi-empirical model compared to the measurements is 0.4 dB. The application of the semi-empirical model to aircraft auralization is demonstrated for a flyover in two meteorological conditions. The findings will enhance the modeling of outdoor sound propagation for elevated sound sources like aircraft and wind turbines. Enhanced modeling of these fluctuations can considerably improve the realism of the listening experience in aircraft flyover auralization. Further, it helps estimating the measurement uncertainty in measured aircraft noise, particularly for maximum levels.