Abstract
Abstract. 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 (β=1:25). 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.
Highlights
Extreme wave propagation is a highly non-linear process observed in both open seas and coastal regions
The linear NewWave theory (Tromans et al, 1991), which is able to generate targeted waves at a prescribed location and time by combining sinusoidal components of different frequencies, is used as input for the generated focused wave trains. This theory was validated at deep water locations, at intermediate water depth locations (Taylor and Williams, 2004) and at coastal regions (Whittaker et al, 2016); for kh < 0.5)
We do not distinguish which wave components participate in the wave–wave interactions, nor do we distinguish the wave modes that undergo the strongest non-linear interactions
Summary
Extreme wave propagation is a highly non-linear process observed in both open seas and coastal regions. Dong et al (2008) studied the spatial evolution of non-linear interactions between different wave components in the shoaling and de-shoaling region by carrying out two random wave experiments based on JONSWAP spectra with varying peak wave periods and root-mean-square wave heights They showed that the degree of quadratic phase coupling increases in the shoaling region and achieves its highest level prior to wave breaking. Non-linear transformation of unidirectional irregular waves propagating over a complex bathymetry (1.06 < kph < 2.2; where kp is the peak wavenumber and h denotes the water depth) was performed in Zhang et al (2019), who studied the triad wave–wave non-linear interactions in the case of long records of JONSWAP irregular waves (1200 Tp, where Tp is the peak period) using a Fourier-based bispectral analysis They found that the phase coupling is strong near the end of the slope, where second and third harmonics become more important.
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