Cascade downshifting of peak frequency at wave spectra evolution on mild bottom slope: Experimental investigations

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The evolution of the wave spectrum is important, because often initial wave parameters necessary for modeling and coastal engineering tasks are obtained on the basis of spectral characteristics. The wave spectra evolution over mild sloping bottom was studied. The data of laboratory experiments were used for spectral and bispectral analysis. The spectrum maximum frequency downshifting with discrete step (i.e. the cascade downshifting) was revealed. Its peculiarities depending on initial wave parameters and spectrum width were investigated. The cascade frequency downshifting occurs due to nonlinear processes and difference triad interactions between a) main frequencies of wave spectrum and infragravity frequencies and b) the frequencies of second harmonics and the new forming low-frequency peak in the main frequency range. According to laboratory experimental data the initial spectrum width determines the frequency step of downshifting and the number of cascades. The wider the initial wave spectrum, the less numbers of cascades are observed. It was shown that wave energy dissipation due to wave breaking is not a main reason for peak frequency downshifting and it has no direct influence on this process. The variability of the main wave period due to the cascade peak frequency downshifting can be important for engineering models because many calculations assume a constant wave period in the coastal zone. • During the transformation of waves over a mild slope bottom the peak spectrum frequency is not constant and the frequency downshifting is observed. • The main mechanism of peak frequency downshifting is the difference nonlinear triad interactions between them and infragravity frequencies. • The difference nonlinear interactions between the peak frequency and higher harmonics also contribute in frequency downshifting process. • Discrete multi-step frequency downshifting revealed or by other words - cascade downshifting. • The features of cascade downshifting depending on the wave's parameters are discussed.