Effect of directionality on extreme wave formation during nonlinear shoaling

TL;DR

This study addresses how wave directionality influences depth-induced non-equilibrium dynamics (NED) and extreme-wave formation during nonlinear shoaling. It employs large-scale, multidirectional wave fields in a controlled basin, using Mitsuyasu-type directional spreading and varying incidence angles to quantify non-Gaussian statistics, specifically the skewness $\lambda_3$ and kurtosis $\lambda_4$. The findings show directional spreading has only a modest effect on peak non-Gaussian metrics, while the incidence direction, through the effective bottom slope, significantly modulates the magnitude and location of NED maxima, with kurtosis reaching up to around 4.6 atop the shoal in some configurations. These results provide experimental validation and nuance to prior numerical studies, highlighting the critical role of oblique incidence in coastal extreme-wave dynamics and informing future research and coastal design considerations.

Abstract

Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves. Nevertheless, research on depth-induced NED has been predominantly confined to unidirectional irregular waves, while the role of directionality remains largely unexplored. The scarce studies on multidirectional waves mainly rely on numerical simulations and have yielded conflicting results. In this work, we report on an experimental investigation of wave directionality on the depth-induced non-equilibrium wave statistics. High-order statistical moments, skewness and kurtosis, are used as proxies for the non-equilibrium wave response. Our results indicate that the directional spreading has a minor effect on decreasing the maximum values of these statistical moments. In contrast, the incidence direction plays a significant role in the non-equilibrium wave response, which is attributed to the effective bottom slope.

Figures (7)

• Figure 1: NMEMC wave tank (a); The layout of wave gauge array following Nwogu1989 for the estimation of directional spectrum (b); The experimental wave tank and locations of the wave gauges (c).
• Figure 2: Target directional spectra for the normal incident cases with $s_{\textrm{max}}=10,\, 35,\, 85$ and UNI in panels (a.1--b.1); the corresponding experimental spectra measured offshore (a.2--d.2) and atop of the bar (a.3--d.3).
• Figure 3: Spatial evolution of normalized significant wave height (a), asymmetry parameter (b), skewness (c), and net change of kurtosis (d) of Cases A1--A4 (all with normal incidence, $\theta_{\textrm{inc}}=0$).
• Figure 4: Same as Fig.\ref{['fig:Smax_CasA']}, but for normal incident directional wave cases ($\theta_{\textrm{inc}}=0$) of Cases B1--B4.
• Figure 5: Same as Fig.\ref{['fig:Smax_CasA']}, but for oblique incident unidirectional cases ($s_\textrm{max}=$UNI).