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.

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Calculations of surface wave and radar cross section modulation induced by a spatially varying surface current have been compared with field measurements made with synthetic aperture radar (X and L bands), real aperture radar ( X band), laser slope gauge, and charge‐coupled device video camera during the Joint Canada‐U.S. Ocean Wave Investigation Project (JOWIP), which took place in August 1983. The comparison reveals that (1) many existing wind relaxation models underpredict the hydrodynamic effect of the current, (2) the simple Bragg scattering model underpredicts radar backscatter modulation for higher‐frequency radars (e.g., X band) but appears acceptable at lower radar frequencies (e.g., L band), and (3) the discrepancy between measurements and calculations at high radar frequency is reduced, but not eliminated, when the effects of long surface waves have been accounted for.

The dispersion relation and component phase speeds of surface gravity wavefields and modulated wavetrains are calculated. A parametric study is performed for a range of nonlinearity and spectral bandwidths. It is found that the amount of departure from linear theory increases with the ratio of nonlinearity to spectral bandwidth. The calculated results are compared quantitatively with laboratory and ocean measurements of wavetrains and wavefields with and without wind. The good agreement between theory and experiment suggests that the nonlinearity–dispersion balance is a likely candidate to account for the observed discrepancy between linear theory and data, as well as for the difference in behaviour between laboratory and oceanic wave measurements.

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