Caustics of waves in the thermally conducting, viscous atmosphere

Abstract

This paper considers waves in the atmospheric as linear acoustic-gravity waves, in which fluid’s buoyancy and compressibility simultaneously serve as restoring forces. Atmosphere is modeled as an inhomogeneous, moving fluid with nearly horizontal winds and gradual variation of its composition, sound speed and wind velocity having representative spatial scales that are large compared to the wavelength. Uniform short-wave asymptotic expansions of the wave field in the presence of a simple caustic are derived and utilized to quantify and compare the effects of wave diffraction and dissipation. Unlike acoustic waves, the geometric, or Berry, phase plays an important role in the caustic asymptotics of acoustic-gravity waves. The uniform asymptotic expansion of acoustic-gravity wave field in the presence of a caustic agrees with known results in the acoustic limit. Away from the caustic on its insonified side, the uniform asymptotic solution reduces to ray-theoretical results. When the source and receiver are located sufficiently far from the caustic, ray-theoretical calculations of the wave absorption are found to be applicable for rays that approach and leave the caustic.