Scattering of Acoustical Waves by a Spinning Atmospheric Turbule
Abstract
Theory is developed for acoustical scattering by localized quasistatic turbulent structures (turbules) that contain both flow and density variations. The quasistatic density variation is shown to be proportional to v2, where v is the (presumably small) ratio of flow speed to asymptotic acoustical wavespeed. The flow contributes terms o(v2) to the scattering cross sections, while the density variations contribute terms o(v4). Differential and total cross sections are calculated for a Gaussian spinning turbule modal of effective radius a, for size parameters ka from 0.25 to 2.0, where k - 2 pi/lambda, lambda = wavelength, using the first Born approximation which is estimated to be valid for-ka 2 for vmax < 0.1. The contributions of the density variation are about three orders of magnitude smaller than those of the flow. The latter are proportional to (ka)6 and sin2 theta cos2 theta sin2 theta alpha sin(phi-phi alpha), where. (theta, phi) are the P (polar, azimuthal) scattering angles, and (theta alpha, phi alpha) are the spin axis angles. The contributions of the density Variations go like (ka)4 and have a somewhat Rayleigh-like dependence on theta. A digitized Green function approach and computer algorithm are also developed, for the o(v2) flow contributions only. In principle, this method would allow treatment of turbules of arbitrary structure, shape. and size.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1992
- Accession Number
- ADA258783
Entities
People
- George H. Goedecke