Abstract:

When the Foldy--Wouthuysen transformation is used to derive the parabolic equation (PE) for a range-dependent environment, a new physical effect associated with small-scale fluctuations of the field is predicted [Wurmser et al., J. Acoust. Soc. Am. 101, 1309--1327 (1997)]. In this presentation, the formalism is applied to the problem of scattering from a rough surface, which is treated as a type of range dependence. The theory predicts the effective impedance boundary conditions proportional to the curvature of the surface, essentially unifying the Biot--Tolstoy theory of scattering from a bossed surface with other modern scattering and propagation theories. The result has been obtained for the two-fluid, Neumann and Dirichlet boundary conditions. The related physical effect is associated with the small-scale cutoff of the field, implying that the wave cannot resolve a surface structure smaller than about 1/12 of a wavelength. The theory also predicts related effects; for example, roughness-induced interface waves for the Neumann and two-fluid boundary conditions. Since the effect on the scattered field is cumulative, its incorporation should improve PE modeling of propagation in waveguides with rough boundaries. [Work supported by ONR.]