Quantitative ray methods for scattering by tilted cylindrical shells

Abstract

Starting with a review of ray methods and phenomena associated with high frequency scattering by spheres and cylindrical shells in water viewed broadside, generalizations to tilted shells will be summarized. These extensions were found to be useful for meridional as well as helical ray backscattering enhancements associated with leaky (or supersonic) waves on shells [Morse and Marston, J. Acoust. Soc. Am. 112, 1318–1326 (2002); Blonigen and Marston, J. Acoust. Soc. Am. 112, 528–536 (2002)]. For such enhancements Fermat’s principle is useful for identifying ray paths of interest. In the case of helical waves (and in the broadside special case), the scattering amplitude can be expressed in terms of a Fresnel patch area where the guided wave is excited on the shell. Fresnel patches also give insight into the relatively large magnitude of meridional ray contributions. The coupling coefficient is proportional to the radiation damping of the leaky wave on the shell and in some cases it is necessary to take into account the anisotropy of the phase velocity. Computational benchmarks include scattering into the meridional plane by tilted infinite cylinders. Related phenomena include enhancements from subsonic guided waves and applications to sonar imaging and time-frequency analysis. [Work supported by ONR.]