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Results of an experimental investigation of the evolution of a nonlinear wave train on deep water are reported. The initial stage of evolution is found to be characterized by exponential growth of a modulational instability, as was first discovered by Benjamin ' Feir. At later stages of evolution it is found that the instability does not lead to wave-train disintegration or loss of coherence. Instead, the modulation periodically increases and decreases, and the wave train exhibits the Fermi–Pasta–Ulam recurrence phenomenon. Results of an earlier study of nonlinear wave packets by Yuen ' Lake, in which solutions of the nonlinear Schrödinger equation were shown to provide quantitatively correct descriptions of the properties of nonlinear wave packets, are applied to describe the experimentally observed wave-train phenomena. A comparison between the laboratory data and numerical solutions of the nonlinear Schrödinger equation for the long-time evolution of nonlinear wave trains is given.

Backscattering experiments at microwave frequencies were conducted off the west coast of Scotland in the summer of 1991. Using a dual-polarization, eightfrequency, X band, coherent scatterometer mounted on the bow of a boat, we measured time-resolved backscattering from ocean waves at a range of grazing angles from 10 ø to 70 ø. From the grazing-angle-dependent signals and their Doppler spectra, we are able to differentiate Bragg scattering from non-Bragg scattering and resolve "peak separation" between the vertical and horizontal polarizations. We observe instances of "super" events, i.e., instances when the horizontal polarization return power equals or exceeds the vertical polarization power at particular frequencies. We find that "super" events occur not only at low grazing angles but at any grazing angle for upwind viewing directions and obtain statistics for such occurrences as a function of grazing angle. We study the coherence properties of scatterers and find strong evidence that at low grazing angles, lifetime-dominated, non-Bragg scattering contributes noticeably to returns of both polarizations, but is dominant in providing returns for the horizontal polarization. We examine "spiking" events and find that they can be related to, but need not be limited to, breaking wave events. By comparing the data of upwind runs with cross-wind and circle runs, we obtain wind direction dependence of Doppler spectra, which further assists in the identification of scattering mechanisms. 2591 2592 LEE ET AL.' X BAND MICROWAVE BACKSCATTERING FROM OCEAN WAVESTable 1. Frequency Pairs for Microwave Scatterometer Polarization, GHz Pair Vertical Horizontal 1 9.020 9.021 2 9.170 9.171 3 9.320 9.321 4 9.470 9.471 four quadrature mixers, one for each transmitted frequency. Each mixer generates an in-phase (I) and quadrature (Q) signal with a frequency response of 0 to 1000 Hz. With complex amplitude thus generated for each frequency, there are 16 channels of output. During an experiment the 16 signals are recorded digitally on a multichannel cassette recorder.An absolute calibration of the scatterometer system [Barter et al., 1993] was conducted in a large (10 m x 10 m x 30 m) anechoic chamber using spheres and cylinders of various sizes as well as corner reflector targets. Measurements consisted of establishing the output power and receiver gain of each of the eight frequency channels, the system radiation patterns in two perpendicular planes in the forward half sphere, the range dependence of the signal power, and the cross-polarization isolation of the scatterometer system. The essential results of the calibration are as follows: total power (eight channels), -1 W; nominal receiver gain each channel, -60 dB; system radiation pattern, approximately Gaussian main lobe; azimuthal plane -3 dB beam width, 8.7 ø for VV and 10.3 ø for HH; vertical plane -3 dB beam width, 11 ø for VV and 9.6 ø for HH; average -3 dB beam width, 9.5ø; antenna gain, 26.6 dB; cross-polarization isolation, >35 dB; image rejection ratio, --45 dB. As an ex...

The evolution and interaction of nonlinear wavepackets on deep water is studied both theoretically and experimentally. The nonlinear Schrödinger equation, first derived in this context by Hasimoto and Ono, is shown to be a special case of Whitham’s theory. The exact solution to this equation predicts the existence of stable envelope solitons, which is indeed verified by laboratory experiments. A comparison between laboratory data and a numerical solution of the nonlinear Schrödinger equation is also given.

The stability of a weakly nonlinear wave train on deep water to two- and three-dimensional modulations is investigated using an improved approximation due to Zakharov (1968). The results are expressible in simple analytical forms, and show good quantitative agreement with available experimental data and exact numerical calculations over a broad range of wave steepness in the unidirectional case.