Acoustic scattering by atmospheric turbules

Abstract

Atmospheric turbulence is modeled as a collection of self-similar localized eddies, called turbules. Turbulent temperature variation and solenoidal velocity structure function spectra and the corresponding average acoustic scattering cross sections are calculated for several isotropic homogeneous turbule ensembles. Different scaling laws for turbule strengths, number densities, and sizes produce different power-law spectra independent of turbule morphology in an “inertial range” of the spectral variable K. For fractal size scaling and Kolmogorov power law ∝K−11/3 in the inertial range, not only do turbule strengths scale like the one-third power of the size, but also the turbule packing fractions are scale invariant, as are the expressions derived for the structure parameters (CT2,Cv2). The inertial range boundaries of the spectral variable and scattering angles are easily estimated from the inner and outer scales of the turbulence. They depend weakly on turbule morphology, while the spectra and cross sections outside the inertial ranges depend strongly on it. Scattering at angles outside the inertial range, which occurs in practical cases, is much weaker than predicted by the Kolmogorov spectrum. For Gaussian turbule ensembles, quasianalytic forms are obtained for the spectra and scattering cross sections and for the structure functions themselves.