Non-Gaussian statistical model of the ocean surface for wave-scattering theories

Abstract

Usually the model of a Gaussian, statistically homogeneous rough surface is used in the theory of rough-surface scattering, not because of physical reasons, but because it is difficult to use a more realistic model. In this paper we apply a version of the theory of non-Gaussian random functions (Tatarskii V I 1995 Waves Random Media 5 243–52) for the ocean surface. We develop the method of obtaining all necessary functional and numerical parameters for the complete statistical description of the random surface of the type described by Tatarskii and having the following properties:

1. The spectrum of the surface describes the range of surface wavelength from fully developed wind waves to the gravity-capillary region (Apel J R 1994 J. Geophys. Res./Oceans 99 16.269-91).

2. The probability distribution function (PDF) of the surface elevations in any single point is non-Gaussian and corresponds to the experimental data obtained by Huang and Long (Huang N E and Long S R 1980 J. Fluid Mech. 101 179–200).

3. The explicit analytical formulae in terms of model parameters can be derived for any mean value, appearing in the wave-scattering theory.

With these given statistical parameters, we present an example of the surface, generated by a Monte Carlo simulation. The method derived easily allows us to incorporate new experimental data if they appear.