Acoustic scattering cross section predicted from an accurate model of the spectrum of temperature fluctuations

Abstract

Recent theoretical and experimental advances have produced an accurate model of the power spectrum of temperature fluctuations in turbulent air. This model temperature spectrum and a semiempirical energy spectrum are used to predict the shape of the acoustic scattering cross section as a function of wave number and scattering angle. Experiments have shown that the temperature spectrum in air has a “bump” at high wave numbers, and the model temperature spectrum shows that this feature is expected theoretically. A corresponding bump is predicted to appear in the acoustic scattering cross section. The bump in the cross section is reduced if velocity fluctuations dominate the scattering, because the energy spectrum has no bump. For typical energy dissipation rates in the atmospheric boundary layer, a 2‐kHz acoustic sounder senses scattering attributable to the bump in the cross section. The amount of scattering attributable to the bump depends on the acoustic wave number and the microscale and can be as much as 50% greater than the scattering predicted by the usual theoretical interpretation.