| The primary aim of this thesis is to investigate the physical processes related to the stability of steep gravity waves, and their effect on the scattering of electromagnetic waves. It has been known for some time that periodic water waves are subject to a variety of shape-altering instabilities. It is generally believed that a certain class of these instabilities, which is relevant to steep waves, is responsible for spilling breakers. Empirical and theoretical research on these instabilities has suggested that the dominant mechanisms in nonlinear interactions in the wave field result in three-dimensional periodic structures. This fortuitous result allows us to treat the resulting surface as an optical grating, thus capturing the multi-path reflection effects (to which sea clutter is often attributed) in an exact solution. Additionally, effects such as shadowing, and other complexities, are included.; An extended boundary condition method, commonly used in optical studies, is formulated to compute the scattering of an electromagnetic plane wave incident upon an arbitrary doubly periodic surface. This particular generalization of the method, which we provide for the first time, allows for the exact calculation of the fields corresponding to a linear, isotropic, conducting, dielectric scattering medium. Results from commonly-used test cases compare very favorably with those from other methods presented in the literature.; The full water wave equations are solved numerically, and highly accurate solutions corresponding to three-dimensional steep wave instabilities are obtained. The scattered electromagnetic fields resulting from these profiles are then computed using the extended boundary condition method. The computational requirements, however, are large, and we have implemented the method in parallel on a Sharcnet Canada high-performance 144-processor cluster.; We believe that we are the first to propose that steep wave instabilities may trigger anomalous returns in radar signals. Results are examined for various surface wave configurations, and incidence data. Scattering returns with HH to VV polarization ratios greater than unity, which are characteristic of sea-spike events, have been observed. |
