Spectral broadening of sound scattered by atmospheric turbulence

Scattering of a monochromatic sound wave by atmospheric turbulent eddies that are moving with the mean wind is described. The source and detector have wide radiation patterns and are at rest in a ground fixed frame. For eddies that make the dominant contribution to the detector signal, scattering angles change substantially with time, so the signal displays a time-dependent frequency which may include the full longitudinal Doppler width. A computer code is developed that calculates the time-dependent detector response and its Fourier spectrum due to one or many eddies, including a steady-state collection of eddies of many different scale lengths that models homogeneous and isotropic atmospheric turbulence. Several numerical results from this code are presented, including one for a simulation of a recent experiment. The predicted spectral characteristics are in very good agreement with the experimental ones. Some possible extensions of the model for describing anisotropic and intermittent atmospheric turbulence are discussed. [Work supported in part by the U.S. Army Research Office under Contract Nos. DAAG55-98-1-0463 and DAAG55-97-1-0178, and an NRC-ETL Research Associateship.]