ASA 127th Meeting M.I.T. 1994 June 6-10

1aSA5. Merging of launching or detachment points of weakly damped leaky waves on S-shaped surfaces and complex launching or detachment points.

Philip L. Marston

Dept. of Phys., Washington State Univ., Pullman, WA 99164-2814

In previous work, Fermat's principle and properties of leaky waves on flat surfaces were combined to obtain a high-frequency approximation to scattering by cylinders of slowly varying curvature [P. L. Marston, J. Acoust. Soc. Am. 94, 1861 (A) (1993)]. The usual assumption was made that only the first derivative of optical-path length (with respect to path variation) vanishes. The present work considers situations where the second (or higher) derivatives vanish at launching or detachment points. The simplest example is for coupling to (or detachment from) a tilted S-shaped surface. Such surfaces may have pairs of launching or detachment points; the pairs can merge at an appropriate surface tilt that results in a k[sup 1/6] amplitude enhancement coefficient. The launching or detachment factor becomes proportional to an Airy function of complex argument and launching or detachment in a shadow region of the Airy factor is described approximately by a complex ray. Higher-order launching or detachment points may also result from a sufficiently rapid dependence of the leaky-wave phase velocity on position. [Work supported by ONR.]