Fuks I.

Scattering of the underwater acoustical signal by the disturbed sea surface is investigated analytically as well as by computer simulation. The sea surface is modeled as a sequence of nonlinear Gestner’s waves, which are the exact solutions of the hydrodynamic equations for non-potential flow. As distinct from the traditional representation of the sea surface roughness as a statistically uniform Gaussian field, the chosen profile of a non-linear surface wave allows us to consider one of the most important features of the real sea surface roughness, namely, sharp crests and flat troughs. In the geometrical optics (GO) limit at normal incidence, backscattering is caused by the set of specular points located at the wave crests and troughs. Because of the surface curvature difference at these specular points, the intensities of signals backscattered by the wave crests and troughs are different, which results in the bias (lowering in average) of the travel time of reverberating signals. The diffraction corrections to the GO results are obtained from the high-frequency asymptotic series of diffracted fields. The diffraction corrections to phase have the opposite signs for signals scattered by crests and by troughs. The explicit equations for these corrections depend not only on curvature radius but on the third and the fourth order derivatives of surface profile at the specular points. The diffraction corrections to the backscattering cross-sections by crests exceed that ones backscattered by troughs.They depend on the surface profile derivatives up to the sixth order. The diffraction corrections to the propagation time of backscattered signals are caused by phase corrections as well as by corrections to backscattering cross-sections. In conclusions, we discuss how the effective Gerstner’s wave parameters can be estimated from the real sea surface power spectra.