Asymptotic analysis of the field on the exterior surface of an open semi-infinite thin circular pipe

• Published in: Wave motion Vol. 23; no. 3; pp. 215 - 235
• Main Author: Michaeli, A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1996
• Subjects: Marine
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/0165-2125(95)00047-X

We analyze the asymptotic high-frequency behavior of the field (or its normal derivative) on the exterior surface of an open-ended semi-infinite thin circular pipe illuminated by a scalar ring source coaxial with the pipe, of uniform strength and linear phase progression. Both the hard and the soft acoustic boundary conditions are considered. The azimuth angle is assumed to vary in an infinite Riemann space from − ∞ to ∞ instead of the true physical range of 2 π. The scattering problem is solved rigorously by reducing it to a Hilbert problem, and the solution is investigated in the asymptotic limit for different domains of incident ray directions, including grazing incidence. The importance of the resulting solution is that it furnishes, together with the two-dimensional solution developed elsewhere for a curved wedge with a straight edge, a canonical basis for asymptotic approximation of the surface field on a general curved wedge with a curved edge illuminated by a ray field.