Laboratory evidence of freak waves provoked by non-uniform bathymetry

Abstract

We show experimental evidence that as relatively long unidirectional waves propagate over a sloping bottom, from a deeper to a shallower domain, there can be a local maximum of kurtosis and skewness close to the shallower side of the slope. We also show evidence that the probability of large wave envelope has a local maximum near the shallower side of the slope. We therefore anticipate that the probability of freak waves can have a local maximum near the shallower side of a slope for relatively long unidirectional waves.

Numerical modeling of rogue waves in coastal waters

“…Zeng and Trulsen (2012) considered a "deeper" regime (kh > 1.2) of wave evolution compared to numerical simulations by Sergeeva et al (2011) (kh < 0.4) and exposed the reduced kurtosis and skewness for the shallower region of transformation. Laboratory experiments of Trulsen et al (2012) embrace the "transitional" zone when the waves travel from an intermediate depth to the shallow water with kh down to 0.54. An increase of large wave likelihood and kurtosis was observed for the smallest dimensionless depth kh = 0.54 in the experiment.…”

“…An important feature of the measured time series, which are in the focus of the present paper, is variable bathymetry: the sea is considered as a finite-depth basin, and the depth variation is essential. The complicated picture of changes in nonlinear waves when they travel from deep to shallow water was revealed by Sergeeva et al (2011), Zeng and Trulsen (2012), and Trulsen et al (2012). Though nonlinear wave interactions in constant-depth water are believed to trigger more rogue waves than predicted by the linear quasiGaussian statistics, these publications proved that variabledepth conditions were able to further increase the probability of rogue waves.…”

Anomalous wave statistics induced by abrupt depth change

“…Inspired by this line of thought, we perform laboratory experiments to examine the statistics of unidirectional waves propagating over a 1D, variable bottom, in the shallow-to-moderate depth regime (outside the influence of the BF instability). Unlike previous experiments which featured gradual slopes of 1:20 [30], we focus on abrupt depth transitions. In particular, we consider waves propagating over a step in bottom topography-much like the step potentials considered in quantum mechanics that helped lay the foundation of scattering theory.…”

Experimental Study of Statistics of Random Waves Propagating Over a Bar

“…In deep water, the occurrence of freak waves is closely related to wave statistics, such as kurtosis and skewness, such as kurtosis and skewness (Mori and Janssen, 2006). However, recent studies Trulsen et al, 2012;Sergeeva et al, 2011) found that, when waves propagate over a slope bottom, the skewness and kurtosis can reach to a maximum value near the shallower side of a slope and extreme waves can be formed. Kashima et al (2013) also pointed out freak waves can be generated by the shoaling effect.…”