Low-grazing-angle microwave scattering from a three-dimensional spilling breaker crest: a numerical investigation

The microwave backscattering from a three-dimensional (3-D) target approximating the rough crest of a gently spilling water wave at low grazing angle illumination has been numerically examined. The target surfaces were synthesized from the direct two-dimensional (2-D) measurement of the time evolution of the upwave-downwave cross-section of a wave-tank breaker. The reference scattering was found using the multilevel fast multipole algorithm implemented with impedance boundary conditions and resistive surface loading to suppress nonphysical edge diffraction. The scattering was compared with the predictions of the two-scale model and a synthesis of the 3-D backscattering from individual 2-D calculations. Specular reflection from a bulge feature that appeared on the crest prior to breaking dominated the backscattering at both polarizations, overwhelming even the strong vertical polarization Bragg scattering that appeared in the corresponding scattering from the individual 2-D profiles used to synthesize the 3-D target. The scattering from the surface including the bulge could be accurately modeled using a coherent addition of the scattering from the 2-D profiles. The two-scale model performed poorly whenever there are steep sections on the surface that provide significant quasi-specular back-reflection. Accuracy improved when the specular points were eliminated and the dominant scattering roughness was fully illuminated, but was still sensitive to the surface-roughness scale-separation threshold used in its application.