Electromagnetic wave scattering from the sea surface in the presence of wind wave patterns
Abstract:The study is concerned with electromagnetic wave (EM) scattering by a random sea surface in the presence of coherent wave patterns. The coherent patterns are understood in a broad sense as the existence of certain dynamical coupling between linear Fourier components of the water wave field. We show that the presence of weakly nonlinear wave patterns can significantly change the EM scattering compared to the case of a completely random wave field. Generalizing the Random Phase Approximation (RPA) we suggest a new paradigm for EM scattering by a random sea surface.
The specific analysis carried out in the paper synthesizes the small perturbation method for EM scattering and a weakly nonlinear approach for wind wave dynamics. By investigating, in detail, two examples of a random sea surface composed of either Stokes waves or horse-shoe ('crescent-shaped') patterns the mechanism of the pattern effect on scattering is revealed. Each Fourier harmonic of the scattered EM field is found to be a sum of contributions due to different combinations of wave field harmonics. Among these 'partial scatterings' there are phase-dependent ones and, therefore, the intensity of the resulting EM harmonic is sensitive to the phase relations between the wind wave harmonics. The effect can be interpreted as interference of partial scatterings due to the co-existence of several phase-related periodic scattering grids. A straightforward generalization of these results enables us to obtain, for a given wind wave field and an incident EM field, an a priori estimate of whether the effects due to the patterns are significant and the commonly used RPA is inapplicable. When the RPA is inapplicable, we suggest its natural generalization by re-defining the statistical ensemble for water surface. First, EM scattering by an 'elementary' constituent pattern should be considered. Each such scattering is affected by the interference because the harmonics comprising the pattern are dynamically linked. Then, ensemble averaging, which takes into account the distribution of the pattern parameters (based on the assumption that the phases between the patterns are random), should be carried out. It is shown that, generally, this interference does not vanish for any statistical ensemble due to dynamical coupling between water wave harmonics. The suggested RPA generalization takes into account weak non-Gaussianity of water wave field in contrast to the traditional RPA which ignores it.
Document Type: Research Article
Affiliations: 1: Department of Mathematics Keele University Keele ST5 5BG UK, Email: email@example.com 2: Nonlinear Wave Processes Laboratory of P. P. Shirshov Institute of Oceanology Russian Academy of Sciences 36 Nakhimovsky prospect Moscow 117218 Russia 3: Environmental Technology Laboratory of the National Oceanic and Atmospheric Administration (NOAA) Boulder 325 Broadway Boulder CO USA
Publication date: December 1, 2003