Extreme waves play a crucial role in marine inundation hazards and coastal erosion. Prediction of non-linear wave–wave interactions is crucial in assessing the propagation of shallow water extreme waves in coastal regions. In this article, we experimentally study non-linear wave–wave interactions of large-amplitude focused wave groups propagating in a two-dimensional wave flume over a mild slope ($\mathit{\beta }=\mathrm{1}:\mathrm{25}$ ). The influence of the frequency spectrum and the steepness on the non-linear interactions of focused waves are examined. The generated wave trains correspond to Pierson–Moskowitz and JONSWAP (γ=3.3 or γ=7) spectra. Subsequently, we experimentally approach this problem by the use of a bispectral analysis applied on short time series, via the wavelet-based bicoherence parameter, which identifies and quantifies the phase coupling resulting from non-resonant or bound triad interactions with the peak frequency. The bispectral analysis shows that the phase coupling increases gradually and approaches 1 just prior to breaking, accordingly with the spectrum broadening and the energy increase in high-frequency components. Downstream breaking, the values of phase coupling between the peak frequency and its higher harmonics decrease drastically, and the bicoherence spectrum becomes less structured.

The understanding of the occurrence of extreme waves is crucial to simulate the growth of waves in coastal regions. Laboratory experiments were performed to study the spatial evolution of the statistics of group-focused waves that have a relatively broad-banded spectra propagating from intermediate water depth to shallow regions. Breaking waves with different spectral types, i.e., spectral bandwidths and wave nonlinearities, were generated in a wave flume using the dispersive focusing technique. The non-Gaussian behavior of the considered wave trains was demonstrated by the means of the skewness and kurtosis parameters estimated from a time series and was compared with the second-order theory. The skewness and kurtosis parameters were found to have an increasing trend during the focusing process. During both the downstream wave breaking and defocusing process, the wave train dispersed again and became less steep. As a result, both skewness and kurtosis almost returned to their initial values. This behavior is clearer for narrower wave train spectra. Additionally, the learning algorithm multilayer perceptron (MLP) was used to predict the spatial evolution of kurtosis. The predicted results are in satisfactory agreement with experimental findings.

In this paper, we present the influence of irregular random waves on the von Kármán street in the wake of an elastically mounted cylinder. The flow is perpendicular to the long axis of the cylinder which is constrained to oscillate transversally. In our experiments, the generated waves are derived from Pierson-Moskowitz and Joint North Sea Wave Project ($\gamma =3$ or 7) spectra. It was found that the increase of the nonlinearity of the generated waves is accompanied by a decrease of the shedding frequency to half of the pic frequency of the generated waves. Furthermore, the Hilbert transformation was performed to calculate the continuous phases of irregular waves ${\theta }_{\eta }$ and that of the Kármán vortex street ${\theta }_{V_x}$. The temporal evolution of the phase combination $\theta =2{\theta }_{V_x}-{\theta }_{\eta }$ has been investigated as well. It was found that the time evolution of $\theta$ has a steplike shape, i.e., when $\theta =0$, this corresponds to a synchronizationlike effect. This approach enables the temporal variability of the synchronization to be quantified in the presence of random irregular waves.

This research investigates the behavior and frequency evolution of extreme waves in coastal areas through a combination of physical modeling, spectral analysis, and artificial intelligence (AI) techniques. Laboratory experiments were conducted in a wave flume, deploying various wave spectra, including JONSWAP (γ = 7), JONSWAP (γ = 3.3), and Pierson–Moskowitz, using the dispersive focusing technique, covering a broad range of wave amplitudes. Wave characteristics were monitored using fifty-one gauges at distances between 4 m and 14 m from the wave generator, employing power spectral density (PSD) analysis to investigate wave energy subtleties. A spectral approach of discrete wavelets identified frequency components. The energy of the dominant frequency components, d5 and d4, representing the peak frequency (f_p = 0.75 Hz) and its first harmonic (2f_p = 1.5 Hz), respectively, exhibited a significant decrease in energy, while others increased, revealing potential correlations with zones of higher energy dissipation. This study underscores the repeatable and precise nature of results, demonstrating the Multilayer Perceptron (MLP) machine learning algorithm’s accuracy in predicting the energy of frequency components. The finding emphasizes the importance of a multi-approach analysis for effectively monitoring energy in extreme coastal waves.

Vortex shedding behind an elastically mounted circular cylinder in the presence of group focused waves propagating upstream was investigated using a classical approach (time series and FFT) and nonclassical approach (complex 2D Morlet wavelets). Wavelet analysis emerged as a novel solution in this regard. Our results include wave trains with different nonlinearities propagating in different water depths and derived from three types of spectra (Pierson–Moskowitz, JONSWAP (γ = 3.3 or γ = 7)). It was found that the generated wave trains could modify regimes of shedding behind the cylinder, and subharmonic frequency lock-in could arise in particular situations. The occurrence of a lock-in regime in the case of wave trains propagating in intermediate water locations was shown experimentally even for small nonlinearities. Moreover, the application of time-localized wavelet analysis was found to be a powerful approach. In fact, the frequency lock-in regime and its duration could be readily identified from the wavelet-based energy and its corresponding ridges.