Distortion and losses of sonic booms through turbulent fields

Abstract

Distortion and losses due to scattering of sonic booms propagating through turbulent fields are investigated using an extended Burgers equation that incorporates an extinction coefficient model previously reported by the author. The extinction coefficient, induced by turbulence, is modeled as a correction to the free field wavenumber using multiple scattering theory. It is a complex-valued function whose real part leads to a frequency dependent attenuation while the imaginary part results in additional dispersion of sonic booms. Numerical calculation of the extinction coefficient is validated using an exact solution derived for a turbulent field with an exponentially decaying correlation function. The model is suitable for direct integration into any Burgers equation that only accounts for geometrical spreading, nonlinear, and atmospheric absorption effects. The extended Burgers equation lends itself to a very efficient algorithm compared to other sonic boom numerical models developed to account for turbulent fields. The algorithm is then used to model sonic boom waveform distortion and loudness variability through randomly generated, realistic turbulent fields. The effects of the intensity and correlation length of the turbulence on the loudness of N-waves and shaped booms are examined and will be presented.