Nonlinear Wave Transformation in Coastal Zone: Free and Bound Waves

Abstract

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.