Effects of nonlinearity and spectral bandwidth on the dispersion relation and component phase speeds of surface gravity waves

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Abstract
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.