Creeping Waves and Lateral Waves in Acoustic Scattering by Large Elastic Cylinders.

The connection between creeping wave and flat surface wave theory is established by investigating the limit of acoustic scattering from a solid elastic cylinder, imbedded in a fluid, whose radius tends to infinity. First, the asymptotic behavior of the complex circumferential wave numbers is calculated by substituting the appropriate Debye- or Airy-type asymptotic expansions into the 3 x 3 secular determinant and solving it using iterative techniques. It is found that, in the limit of infinite cylinder radius, the wave numbers of the Rayleigh and Stoneley modes tend toward those of the Rayleigh and Stoneley waves on a flat elastic half-space, while the Franz mode wave numbers tend toward the wave number of sound in the fluid. The longitudinal and transverse Whispering Gallery mode wave numbers tend toward the longitudinal and transverse wave numbers in the solid. Graphical results are presented for an aluminum cylinder in water (and in one case, also in vacuum) and show good agreement with existing numerical results. Then, using the Watson-Sommerfeld transformation, the limiting behavior of the solution to the problem of the scattering of a cylindrical wave from a cylinder whose radius tends to infinity is investigated. Using the analytic expressions for the creeping wave numbers, it is shown that the residue sums corresponding to the different classes of circumferential waves tend individually toward the different types of surface waves found on the flat surface.