On the basis of field experiments and numerical modeling, we show that coastal zones are classifiable according to manifestations of wind wave nonlinearity, which herein is recognized as periodic...

An analysis of the variability of wave climate and energy within the Black Sea for the period 1960–2011 was made using field data from the Voluntary Observing Ship Program. Methods using wavelet analysis were applied. It was determined that the power flux of wave energy in the Black Sea fluctuates: the highest value is 4.2 kW/m, the lowest is 1.4 kW/m. Results indicate significant correlations among the fluctuations of the average annual wave heights, periods, the power flux of wave energy, and teleconnection patterns of the North Atlantic Oscillation (NAO), the Atlantic Multi-decadal Oscillation (AMO), the Pacific Decadal Oscillation (PDO) and the East Atlantic/West Russia (EA/WR). It was revealed that, in positive phases of long-term periods of AMO (50–60 years) as well as PDO, NAO, and AO (40 years), a decrease of wave energy was observed; however, an increase in wave energy was observed in the positive phase of a 15-year period of NAO and AO. The positive phase of changes of EA/WR for periods 50–60, 20–25, and 13 years led to an increase of wave energy. The approximation functions of the oscillations of the average annual wave heights, periods, and the power flux of wave energy for the Black Sea are proposed.

The nonlinear transformation of waves in the coastal zone over the sloping bottom is considered on the base of field, laboratory, and numerical experiments by methods of spectral and wavelet analyses. The nonlinearity leads to substantial changes of wave shape during its propagation to the shore. Since these changes occur rapidly, the wave movement is non-periodical in space, and the application of linear theory concepts of wavenumber or wavelength results in some paradoxical phenomena. When analyzing the spatial evolution of waves in the frequency domain, the effect of periodic energy exchange and changes in the phase shift between the first and second wave harmonics are observed. When considering the wavenumber domain, the free and bound waves of both the first and second harmonics with constant in space amplitudes appear, and all spatial fluctuations of the wave parameters are caused by interference of these four harmonics. Practically important consequences such as the wave energy spatial fluctuations and of anomalous dispersion of the second harmonic are shown and discussed.

We present a study of the physical characteristics of traveling waves at shallow and intermediate water depths. The main subject of study is to the influence of nonlinearity on the dispersion properties of waves, their limiting heights and steepness, the shape of solitary waves, etc. A fully nonlinear Serre–Green–Naghdi-type model, a classical weakly nonlinear Boussinesq model and fifth-order Stokes wave solutions were chosen as models for comparison. The analysis showed significant, if not critical, differences in the effect of nonlinearity on the properties of traveling waves for these models. A comparison with experiments was carried out on the basis of the results of a joint Russian–Taiwanese experiment, which was carried out in 2015 at the Tainan Hydraulic Laboratory, and on available experimental data. A comparison with the experimental results confirms the applicability of a completely nonlinear model for calculating traveling waves over the entire range of applicability of the model in contrast to the Boussinesq model, which shows contradictory and unrealistic wave properties for moderate wavelengths.

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.