Coupling between turbulence scales, acoustic frequency and geometric parameters and its effect on sound propagation in an upward-refracting atmosphere

In an upward-refracting atmosphere, acoustic energy is scattered into the shadow zone due to temperature and wind fluctuations. The strength of this scattering not only depends on turbulence parameters (i.e. turbulence scales and variance of refractive-index fluctuations) but also on the acoustic frequency and geometry (range, source and receiver heights) considered. The smallest turbulent structures involved in acoustic scattering into the shadow zone can be found using Bragg's relation, which links angle of diffraction of acoustic energy with acoustic frequency and turbulent structure/eddy size. To study the largest turbulent structures involved, the Rytov approximation can be used. When writing the correlation function of the logamplitude in the Rytov approximation, a function filtering the turbulence spectrum appears that approaches zero when the eddy size wave number approaches zero. Thus the form of this function can be used to determine the largest turbulent structures involved in acoustic energy scattering into the shadow zone. Source and receiver heights can also limit the size of the turbulent eddies that need to be kept. A parabolic equation approach is used to illustrate the effect of the coupling between turbulence scales, acoustic frequency and geometry on different turbulence spectra.