Theory for spectral broadening of narrowband signals in the atmosphere and experiment with an acoustic source onboard an unmanned aerial vehicle

Narrowband acoustic signals propagating through inhomogeneous moving media, such as atmospheric turbulence, exhibit spectral broadening. This phenomenon has been previously studied with regard to acoustic remote sensing of the atmosphere with sodars and tonal noise of turbofan aircraft engines. In this paper, spectral broadening is studied for line-of-sight sound propagation in a turbulent atmosphere. The averaged power spectral density of a narrowband signal is calculated from a Fourier transform of the temporal mutual coherence function of the sound field. Spectral broadening is characterized by the width of the spectral density. The spectral width is calculated for the Kolmogorov spectra of temperature and wind velocity fluctuations for both horizontal and slanted propagation in the atmosphere. In the latter case, the height-dependence of the wind speed and turbulence parameters is addressed. The spectral width is studied numerically for different meteorological regimes of the atmospheric boundary layer characterized by the friction velocity and the surface sensible heat flux. Theoretical results are compared to experimental data for propagation from an acoustic multi-tone source onboard an unmanned aerial vehicle to a microphone array located on the ground.