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.
Highlights
Waves are the main source of energy in the coastal zone of the sea and wave transformation is a factor determining many dynamic processes
Ofsometimes trigonometric estimates, leads to fluctuations the biphase from −π/2 to theoretical estimation of the phase shift between the first and second frequency π/2. This is clearly seen in Figure 8d. 0028 harmonics can be obtained by reducing both terms of the second harmonic in Formula (3)
It is shown that the space periodic exchange of energy between the first and second frequecy harmonics exist in the field condition where it arises naturally
Summary
Waves are the main source of energy in the coastal zone of the sea and wave transformation is a factor determining many dynamic processes. The main feature of nonlinear wave transformation in the coastal zone over slopping bottom is the generation of high-frequency wave components. The introduction of free and bound waves in the context of nonlinear wave interaction was done in [1] for the case of four wave interactions on deep water. For the dynamic processes on shallow and intermediate water depth, more important is the second harmonic that consists of free and bound modes. This fact is well-known in the coastal engineering community. Detailed description of the influence on coexisting free and bound waves on the evolution of wave parameters in the coastal zone is missing due to absence of analytical solutions and the difficulties to measure the simultaneous time and spatial fluctuations of free surface elevations in physical experiments
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