Angle dependence of the meridional leaky-ray backscattering enhancement from the end of a tilted finite cylinder. Convolution analysis and a numerical test for shells

Abstract

Reflection of a meridional leaky ray from the far end of a tilted cylinder produces a backscattering enhancement when the tilt angle is close to the leaky wave coupling angle. The ray lies in the meridional plane defined by the incident wave vector and the cylinder’s axis. The peak magnitude of this enhancement was related to the end-reflection coefficient by a convolution surface integral [P. L. Marston, J. Acoust. Soc. Am. 102, 358–369 (1997)]. The more difficult integrals descriptive of the dependence on tilt angle are numerically evaluated in the present study. Though the exact analytical solution of the problem considered is unknown, for comparison an approximate partial-wave series description is available where the boundary conditions at the ends of the cylinder are such that the end-reflection coefficients become unimodular. For antisymmetric leaky Lamb waves on long thick and thin shells, the enhancement width, magnitude, and location each agree with the result from the integral when a unimodular reflection coefficient is also assumed in the convolution formulation. The convolution analysis should also apply to meridional leaky Rayleigh waves reflected by the ends of a solid cylinder. [Work supported by the Office of Naval Research.]