Spatio-temporal variability of the amplitude-phase structure of storm waves in the coastal zone of the sea

Abstract

The spatio-temporal variability of individual storm waves in the coastal zone is studied. Wave chronograms were presented as sums of the first and second harmonics with amplitudes slowly varying in time, which are envelopes for the waves of the corresponding frequency bands. The amplitude-frequency structure of individual waves was estimated from the variations in the amplitude of the envelopes. Bi-spectral analysis was applied to estimate the phase composition of the waves. It is shown that, in the initial stage of transformation, the fluctuations of the waves of the first and second harmonics are synchronous. The amplitudes of the second harmonics are proportional to the squared amplitudes of the first harmonics. Thus, a simple model is possible for the description of individual waves based, for example, on the generalization of the Stokes theory. As the waves approach the coast, the ratio of the amplitudes of the first and second harmonics in individual waves varies in time chaotically, thus it is not possible to describe individual waves on the basis of a simple model. The main cause of the chaotic variation of the amplitudes is the backward transfer of energy from the highest harmonics to the first harmonics due to the sub-near resonant triad interaction close to the resonance. The phase composition of individual waves depends on the distance propagated by the waves and on the stage (main or backward) of the energy exchange between the nonlinear harmonics.