Biot rough surface boundary conditions and boundary waves Free

Given radiation of wavenumber k incident upon a plane z = c with roughness elements of mean separation h and dimensions d ≅ h or d ⩽ h, assuming kh ⩽ 1, the calculation of the coherent scatter is equivalent to solving the wave equation with a linear boundary condition applied at z = c. This condition was first derived by Biot [J. Acoust. Soc. Am. 44, 1616–1622 (1968)] for the case of a perfectly rigid wall. The result has since been elaborated and extended to the case of a rough boundary between liquids of different densities [I. Tolstoy, J. Acoust. Soc. Am. 66, 1135–1144 (1979); 68, 258–268 (1980)]. A result of the theory which has been verified experimentally [H. Medwin et al., J. Acoust. Soc. Am. 66, 1131–1134 (1979)], is a new type of boundary wave. A result which awaits experimental confirmation is that this wave offers an efficient mechanism for the transmission of energy into regions of shadow. Since analogous boundary conditions can be derived for the electro‐magnetic case [M. A. Biot, J. Appl. Phys. 29, 998 (1958)] this mechanism is also relevant to the transmission of electromagnetic waves beyond the horizon. [Work supported by ONR.]