Wave scattering on a fractal surface
A generalized Von Koch surface was constructed. On the basis of Freedman' s formulation for wave scattering and by applications of the Lipchitz transform under Holder conditions in fractals, a demonstration was given that the Hausdorff dimension of the solid-angle discontinuity on the scattering surface is the same as the one of the surface itself, and an expression of the scattering strength of the fractal surface has been given. A comparison with the Schulkin-Shaffer empirical formula for the sound scattering from sea surface proposes that, in this situation, the generalized (continuous) Koch surface seems to degenerate into the (discrete) four-two Cantor sets, only the latter make a contribution to the backscattering.
Qian
ZW
National Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing, People's Republic of China. qzwnoe@ihw.com.cn