Low Frequency Atmospheric Acoustic Propagation.

In this thesis we shall study several interesting problems in atmospheric acoustic propagation. Two approaches will be used, both normal mode and ray analyses. We first look at normal mode solutions to the equations of atmospheric acoustics. We obtain the Green's function for a two layered isothermal atmosphere and apply our results to some scattering problems. Transmission and reflection coefficients are obtained and analyzed for several model inhomogeneities of the earth and atmosphere. We next look at a situation where the lower layer of the atmosphere decreases in height. We find that, as the waveguide narrows, propagating modes successively disappear from the waveguide, their energy dissipating into the upper half space. Finally, we employ the geometrical acoustics approximation for a three dimensional atmosphere with a shear flow, and a source on the ground. The discussion includes both the theoretical derivation of the ray equations and the amplitude equation, as well as the numerical solution of the ray equations for a given atmospheric profile. The sound speed profile and the shear flow focus the rays, and caustic surfaces are formed. These can be determined numerically and plotted. A boundary layer analysis is used to find the solution near the caustic. The amplitude near a caustic is found to be greater than the source by a factor of k^{1/6} , where k is the wavenumber. Thus there are regions of intense acoustic pressures which could be easily measured by proper receiver location in an actual experiment.