Spectral reconstruction of uniformized wave fields from nonuniform ray or adiabatic mode forms for acoustic propagation and diffraction

Abstract

Ray acoustic and adiabatic mode representations provide effective means for charting sound transmission in relatively complicated propagation and diffraction environments, under operating conditions that validate the use of such approximate waveforms. A principal limitation of these physically incisive and conveniently implemented algorithms is their failure in transition regions. For ray acoustics, transitions occur near caustics, foci, critical reflection angles, shadow boundaries, etc.; adiabatic modes undergo transitions when cutoff-inducing or other smooth environmental changes transform their initially well trapped into radiated (leaky) energy. Instead of constructing the uniformized spectral representations required in transitional domains by an independent, more general, analysis, it is shown here that the uniformized spectral forms for a large variety of propagation and diffraction phenomena can be synthesized directly from ray acoustic or adiabatic mode data. This feature should be helpful in generalizing existing acoustic ray or adiabatic mode algorithms to accommodate transitional wave processes. The theory is presented for two-dimensional configurations and fluid media, but the same considerations apply also in three dimensions and for multiwave effects due to elasticity or anisotropy.