Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework

Abstract

Abstract. The transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model. The skewness and kurtosis are computed, and it is shown that they increase when the depth decreases, and simultaneously the wave state deviates from the Gaussian. The probability of large-amplitude (rogue) waves increases within the transition zone. The characteristics of this process depend on the wave steepness, which is characterized in terms of the Ursell parameter. The results obtained show that the number of rogue waves may deviate significantly from the value expected for a flat bottom of a given depth. If the random wave field is represented as a soliton gas, the probabilities of soliton amplitudes increase to a high-amplitude range and the number of large-amplitude (rogue) solitons increases when the water shallows.

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.…”

Outcomes of the Special Issue on Extreme and Rogue Waves

“…A rogue wave quickly changes its shape from a high ridge to a deep depression. Sergeeva et al (2011) studied the appearance of freak waves in shallow water of variable depth in the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model.…”

A preliminary investigation of rogue waves off the Jiangsu coast, China

“…It could be discerned from the above that the majority of the studies on the rogue waves based on in situ measurements merely concentrates on the open seas rather than nearshore areas, although the rogue waves in shallow water have also attracted attention (Sergeeva et al, 2011;Didenkulova et al, 2006;Didenkulova and Pelinovsky, 2011;. Chien et al (2002) once reported about 140 freak wave events in the coastal zone of Taiwan in the past 50 years , which claims the existence of freak waves off the deep water areas.…”