Variable phase coupling coefficient for leaky waves from resonance scattering theory and physical aspects of background contributions

Abstract

Approximations are examined for the coupling coefficient Gl for the launching and detachment of leaky waves having application to situations where thin shell theory is not applicable. The approach is based on a comparison of ray and resonance scattering theory (RST) formulations which includes effects on the phase of Gl of higher‐order Debye approximations of Hankel functions and derivatives [P. L. Marston, Wave Motion (accepted for publication)]. The comparison includes a frequency dependent transition (between soft and rigid limits) for the RST background factor in the product expansion of the S function. The transition is formulated such as to not affect ‖Gl‖. The high frequency phase of Gl for limiting background cases previously examined [P. L. Marston and K. L. Williams, J. Acoust. Soc. Am. Suppl. 1 83, S94 (1988)] S94 (1988)] is recovered. A variable phase term depending on the background transition function corresponds to a term given by the convolution formulation of variable curvature scattering [P. L. Marston, 34–41 (1995)] when applied to thin circular cylindrical shells. Other correlations with shell theory are evident. Diffractive and inertial aspects of the background contribution are also examined. [Work supported by the Office of Naval Research.]