An efficient focusing model for generation of freak waves
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An efficient focusing model for generation of freak waves LIU Zanqiang1∗ , ZHANG Ningchuan1 , YU Yuxiu1 1
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China
Received 13 April 2010; accepted 11 April 2011 ©The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2011
Abstract Based on the Longuet-Higgins wave model theory, the previews studies have shown that freak waves can be generated in finite space and time successfully. However, as to generating high nonlinear freak waves, the simulation results will be unrealistic. Therefore, a modified phase modulation method for simulating high nonlinear freak waves was developed. The surface elevations of some wave components at certain time and place are positive by modulating the corresponding random initial phases, then the total surface elevation at the focused point is enhanced and furthermore a freak wave event is generated. The new method can not only make the freak wave occur at certain time and place, but also make the simulated wave surface time series satisfy statistical properties of the realistic sea state and keep identical with the target wave spectrum. This numerical approach is of good precision and high efficiency by the comparisons of the simulated freak waves and the recorded freak waves. Key words: Longuet-Higgins wave model, modified phase modulation method, freak waves, wave focusing
tory seems to be particularly important. In the laboratory, if a freak wave is simulated using a realistic wave spectrum (e.g., JONSWAP spectrum) with a random phase approach, this rare event would happen only once in approximately 3000 waves according to a Rayleigh wave height distribution. Therefore this method is not often adopted for freak wave laboratory experiments. Alternatively, spatialtemporal focusing of a wave group has been widely used to generate extreme or breaking waves in the laboratory (Ning et al., 2009; Sun et al., 2009; Li et al., 2008; Liu and Hong, 2004; Baldock et al., 1996; Rapp and Melville, 1990). However, based on the LonguetHiggins (1952) wave model, Kriebel (2000) proposed an efficient procedure for the generation of freak waves by embedding an extreme transient wave within a random sea; Pei (2007) discussed the relationship between the parameter Hj /Hs and the energy percentage within the combined wave model (Kriebel, 2000); Zhao (2009) summarized four wave focusing models for the generation of freak waves: extreme wave model plus random wave model and extreme wave model plus regular wave model (the same as Kriebel’s in essence), focusing model of phase interval modulation and wave model with initial asymmetrical phases which are ref-
1 Introduction Freak waves, alternatively called rogue waves or giant waves, are characterized by a single, steep crest and giving severe damage to offshore structures and ships (Dysthe et al., 2008; Didenkulova et al., 2006; Kharif and Pelinovsky, 2003). Up to now, there is no definitive consensus about their definition. The definition based
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