1pPA7: Solver for Complex-Valued Scattering Wavenumber for Sonic Booms in Turbulence

Multiple scattering theory (MST) has recently been applied to sonic boom propagation through atmospheric turbulence to predict the ensemble averaged waveform [J. Acoust. Soc. Am. 154, 3078–3088 (2023)]. In that work, the mean acoustic wavefield was expressed in terms of the acousto-turbulent self energy, whose contribution modifies the effective wavenumber, with the dispersion relation defined by the zeros of the mean field denominator. The present work focuses on obtaining these scattering wavenumbers numerically in the presence of both velocity and sound speed fluctuations, a combination that cannot be treated analytically within the original formulation. A Newton–Raphson iteration scheme is used to solve the complex dispersion relation for exponential turbulence, yielding the turbulence modified wavenumber predicted by MST. This work also extends the formulation to von Kármán turbulence, which was not treated in the original study, enabling evaluation of scattering behavior for an additional turbulence spectrum. The resulting scattering wavenumbers provide a basis for comparing theoretical predictions with previous N wave sonic boom waveforms obtained in a flight test, and for quantifying how turbulence influences the mean field and the associated uncertainty in sonic boom loudness.