Scenarios of nonlinear wave transformation in the coastal zone

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 energy exchange between the first and second nonlinear wave harmonics depending on the average bottom slope and the Iribarren and Ursell numbers. The results offer a basis for developing vulnerability criteria for the coastal zone taking into account its nonlinear dynamics.     

Abnormally high waves due to spectral instability of surface waves

The outcomes of our laboratory experiments corroborate hypotheses advanced earlier, dedicated to the mechanism of origination of abnormally high waves under the development of spectral instability. We have clarified the characteristics of spectral instability development including the dependences of the value of the downshift of the spectral maximum and distances at which it occurs on the steepness of waves and width of the initial spectrum. In addition, we have revealed the dependence of the number of abnormal waves on the fraction of spectral energy transferred to the low-frequency range and on the stage of spectral instability development. Our results offer the basis for creating a statistical model of the origination of abnormally high waves.     

Frequency-Dependent Energy Dissipation of Irregular Breaking Waves

Results of field experiments and simulation are used to study the hypothesis that energy dissipation from irregular breaking waves can have a nonuniform distribution over the frequency. It was found that the wave energy dissipation in the outer surf zone is practically independent of the frequency and can be approximated by a constant. A quadratic or a selective (at the frequency band of second–third harmonics) dependence of energy dissipation on frequency was found to form in the inner part of the surf zone, where it is controlled by wave asymmetry and bed slope. The dissipation of the energy of breaking waves was shown to proceed in such a way as to compensate for the effect of processes of linear or nonlinear deformation of waves.     

Influence of processes of nonlinear transformations of waves in the coastal zone on the height of breaking waves

Using data from laboratory, field, and numerical experiments, we investigated regularities in changes in the relative limit height of breaking waves (the breaking index) from peculiarities of nonlinear wave transformations and type of wave breaking. It is shown that the value of the breaking index depends on the relative part of the wave energy in the frequency range of the second nonlinear harmonic. If this part is more than 35%, then the breaking index can be taken as a constant equal to 0.6. These waves are spilling breaking waves, asymmetric on the horizontal axis, and are almost symmetric on the vertical axis. If this part of the energy is less than 35%, then the breaking index increases with increasing energy in the frequency range of the second harmonic. These waves are plunging breaking waves, asymmetric on the vertical axis, and are almost symmetric on the horizontal axis. It is revealed that the breaking index depends on the asymmetry of waves on the vertical axis, determined by the phase shift between the first and second nonlinear harmonic (biphase). It is shown that the relation between the amplitudes of the second and first nonlinear harmonics for an Ursell number less than 1 corresponds to Stokes’ second-order wave theory. The empirical dependences of the breaking index on the parameters of nonlinear transformation of waves are proposed.     

On the possibility of biphase parametrization for wave transformation in the coastal zone

Based on experimental data, we study the possibility of parametrizing the spatial variation in the phase shift (biphase) between the first and second nonlinear harmonics of wave motion during wave transformation over an inclined bottom in the coastal zone. It is revealed that the biphase values vary in the range [–π/2, π/2]. Biphase variations rigorously follow fluctuations in amplitudes of the first and second harmonics and the periodicity of energy exchange between them. Wave breaking influences the biphase value, retaining its variations in the negative domain in the range [–π/2, 0]. The formula applied in modern practice to calculate the biphase, which depends on the Ursell number, is incorrect for calculating the biphase for wave evolution in the coastal zone, because it does not take into account periodic energy exchange between the nonlinear harmonics. We propose a linear approximation of the biphase values from the size of the ratio of the current distance to the coast to the possible spacial duration of the exchange period, which is determined by the dispersion relation. We reveal the dependence of biphase variations on the wave transformation scenario and demonstrate the possibility of constructing a separate parameterization of the biphase for each scenario. Our research and the obtained biphase parameterizations can be used to simulate the sea state in the coastal zone, as well as in problems of predicting the development of coasts under the impact of storm waves.