Critical angle diffraction in high frequency scattering by fluid spheres and cylinders

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Abstract
When plane waves are reflected from a flat surface between ideal fluids, the reflection is total when the angle of incidence θ exceeds θc = sin−1(c1/c2) where c2 > c1; c1 and c2 are the sound speeds, respectively, of the fluid from which the wave is incident and of the second fluid. For an interface of constant curvature, ray acoustics predicts that the scattered intensity has an unphysically divergent angular derivative as the scattering angle φ approaches the critical scattering angle φc = π − 2θc. This divergence is removed by diffraction which is important in an angular region near φc. The width of this region exceeds (a/λ)1/2, where a is the radius of curvature and λ is the wavelength. A simplified approximation for the diffraction, similar to the optical analog described in “Critical angle scattering by a bubble: physical-optics approximation and observations” [P. L. Marston, J. Opt. Soc. Am. 69, 1205–1211 (1979)], is derived. As φ approaches φc, a ringing and decay of the far-field intensity is predicted which may be observable in scattering by fluid spheres and cylinders.

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