A Physical Model of Wind Waves in the Coastal Zone

The variability of the amplitude-frequency structure of wind waves in space and time during their transformation in the coastal zone are considered. Wave time series, measured synchronously in 15 points along the wave propagation, obtained at field and laboratory experiments, were used for the analysis. Free surface elevation time series were represented as a sum of first and second harmonics with amplitudes slowly varying in time (or envelopes of the waves of corresponding frequency bands). Relative changes of these amplitudes in space and time were studied also. It was revealed, that at the initial stage of the wave transformation, the changes of amplitudes of the first and the second harmonics are similar and amplitudes of the second harmonics are proportional to the squared amplitudes of the first harmonics. At this stage the variability of parameters of individual irregular waves can be explained by Stokes theory. Nearer to the coast the instantaneous values of the amplitudes of the first and the second harmonics varies in time chaotically and is not possible to construct a simple model of the variability of the parameters of individual irregular waves. The main reason for this effect is the backward energy transfer from the second to the first harmonics of the waves during nearly resonant non-linear triad interactions.