Precise spatial and temporal measurement of gravity-capillary waves and associated radar backscatter

Water waves are generated mechanically in the laboratory to investigate the electromagnetic backscatter from a roughened air-water interface. A ranging X-band radar with a 16 cm footprint remotely senses the interface while precise concurrent non-intrusive surface elevation profiles are recorded using high-speed video imaging. The air-water interface is characterized with a resolution of 0.069 mm/pixel in the vertical and 0.385 mm/pixel in the horizontal. A temporal resolution of 1 ms is achieved. A range of wave maker frequencies of 6-12 Hz with 0.05 Hz increments with fixed stroke and wave maker frequencies over the same range with varying stroke. This frequency regime is replete with internal resonances of the water waves. Precise surface and radar backscatter measurements facilitate a direct comparison between surfaces of known roughness properties and scattered fields. Three methods of predicting backscatter intensity derived from first principles are used: a method based on Bragg scattering, the Kirchoff small perturbation method, and an iterated Kirchoff integral method. Hydrodynamic results include nonlinear wave forms for the gravity capillary waves with wave steepness, ka, as small as 0.005 and multi-crested waves which closely resemble the second-harmonic profile at frequencies as large as 12 Hz, significantly away from the 9.8 Hz wave predicted by theory. Numerical calculations support the existence of these wave forms. It is shown that nonlinear hydrodynamics, over the range of frequencies investigated, which are responsible for lengthening the primary wave, are required to explain the radar backscatter. In addition, it is shown that the neglect of the nonlinearity of the internal resonances in constructing a water surface can invalidate the expected electromagnetic backscatter. Electromagnetic backscatter results demonstrate the potential for multi-valuedness in the so-called Inverse problem. Measured versus predicted radar backscatter results will show the ability of these three approximate techniques to predict radar backscatter precisely