Doppler Broadening of Acoustic Waves Scattered by Turbulence Flowing With a Horizontal Wind

摘要

This report investigates the scattering of a monochromatic acoustic wave by an assumed unchanging atmospheric turbulence distribution that moves with a uniform constant horizontal wind. The source and detector are at rest at different positions in a ground-fixed frame. Theoretical expressions are derived for the scattered acoustic pressure at the detector. Because distances and scattering angles change with time as any turbulent fluctuation (turbule) flows through the scattering volume, the detector signal has a time-dependent Doppler frequency shift. A simple formula for the consequent frequency broadening is derived. A computer code is developed that calculates the scattered signal and its fast Fourier transform scattered by a single turbule, or by a collection of turbules of many different scale lengths. The code uses a new approximate but quite accurate time-shift algorithm that reduces the calculation time substantially. Several numerical results from this code are presented for a model scenario that is similar to a recent experimental scenario, with good agreement among spectral widths and shapes.