Spectral broadening of sound scattered by advecting atmospheric turbulence

Scattering and spectral broadening of a monochromatic sound wave by atmospheric turbulence that is flowing with a uniform constant horizontal wind is considered. The acoustic source and a detector are at rest and at different positions in a ground-fixed frame. Analytic expressions are derived for the sound pressure scattered to the detector by a single eddy. Since distances and the scattering angle change with time as the eddy flows through the scattering volume, the detector signal has time-dependent amplitude and frequency, for which general formulas are derived. A computer code is developed that calculates the scattered signal and its Fourier transform from a single eddy, or from a steady-state collection of eddies of many different scale lengths that represents isotropic homogeneous turbulence flowing with the wind. The code utilizes a time-shift algorithm that reduces the calculation time substantially. Several numerical results from this code are presented, including simulations of a recent experiment. The predicted spectral shape, including peak width and jaggedness, are in good agreement with experiment.