Validation of a sonic boom model through atmospheric turbulence with flight test data

Abstract

This paper presents a validation of an extended Burgers equation that accounts for mean scattering effects of turbulence in the atmospheric boundary layer (ABL). The scattering effects are calculated from a scattering wavenumber formulated using the multiple scattering theory and are incorporated as an additional linear term in a Burgers equation commonly used to model sonic boom propagation. The scattering wavenumber represents the interaction of an acoustic wavefield, including backscattering, with a turbulent field and gives rise to signal attenuation and distortion. Numerical models obtained using the extended Burgers equation are compared to measured sonic booms from conventional supersonic aircraft. The acoustic measurements are supplemented by measurements of the turbulence conditions as well as the thickness of the ABL. Results show that the mean effects of scattering on sonic booms smooth out shocks in the waveforms, reduce the peak amplitudes, and thus reduce the loudness. The results also indicate that the loudness reduction is dependent on the variance, correlation length, and thickness of the turbulent field. The performance of the extended Burgers equation is compared to that of existing signal processing-based approaches developed to represent turbulence effects on sonic booms through the ABL.