Wedge diffractions: Biot-Tolstoy normal coordinate solution and Medwin's lab experiments

Abstract

In the 1960s, the Hudson Labs of Columbia University had coffee hours. The coffee gang included Ivan Tolstoy, Antares Parvulescu, Bob Frosch, Mel Hinich, and Peter Rona. We tested our crazy ideas, scribbled on the blackboard, and listened. Wave propagation in a messy ocean was the problem. We were well beyond ideal layered waveguides with plane interfaces. Tolstoy did normal coordinates and modes [Tolstoy and Clay, Ocean Acoustics (1966, 1986)-AO]. One summer, Hank Medwin joined us and conversations led to research on sound scatter from rough surfaces. Helmholtz-Kirchhoff (H-K) computations were accurate for sound scattered in specular directions, AO Ch. 6. Diffractions are different. The AO (1986) includes Biot-Tolstoy diffraction of impulses by rigid wedges (B-T). Interior wedge angles=[rho]/n have no diffracted waves. Clay and Medwin's Acoustical Oceanography (1977) detailed H-K methods and ignored B-T. Pushing hard, was H-K accurate for all diffraction waves? In 1978--82, Bremhorst, Jebsen, and Hank did wedge experiments and proved B-T is exact and H-K is limited. See Figs. 12.3, 2--3.3 in Medwin and Clay, 'Fundamentals of Acoustical Oceanography' (1998). Chapters 11 and 12 give details. Use normal coordinate B-T for wedges.