Abstract
The occurrence probabilities of Rogue Waves in different nonlinear states are investigated based on high-order spectral method (HOSM), which is a direct phase-resolved numerical method. The focus is given to the occurrence probability of Rogue Waves in the nonlinear evolution stage where the Benjamin-Feir Instability is not the dominate mechanism due to the quartet resonance interactions for wave fields with a broad range in frequencies. The initial wave trains are generated from Stokes waves and two sidebands. Based on the simulation, we find that the Kurtosis evolves distinctly at three nonlinear stages and shows a weak relation to the probabilities of the Rouge Waves. We also introduce a simple Entropy formula, turning out to close a stable value.
Highlights
The concept of Rouge Wave was first put forward by Draper (1965) to describe exceptionally high waves surprisingly appearing on the sea surface, which may cause disastrous damages to offshore structures and surface vessels
If a wave train can propagate in a large scale distance, or a sea state can evolve for a long time, such as the ocean in the monsoon seasons, the nonlinearity may grow to a stage beyond the Benjamin-Feir Instability can control, since the quartet resonance interactions for wave fields with a broad range in frequencies and directions
The relationship between probability of Rouge Waves and extreme wave heights is obscure, which means higher Rouge Waves and high probabilities may not occur together, while the probabilities weakly related to the Kurtosis, which means the probabilities have a trend to increase with high nonlinearity
Summary
The concept of Rouge Wave was first put forward by Draper (1965) to describe exceptionally high waves surprisingly appearing on the sea surface, which may cause disastrous damages to offshore structures and surface vessels. One of The latest studies for the probability of Rogue Waves has been performed by Bithner-Gregersen & Toffoli (2012), focusing on the design practice One of their results is that ‘the extreme crest considerably increases for prolonged sea state durations’. Considering the concept, which indicates that there are different kinds of Rogue Waves according to their intrinsic nonlinear mechanisms, shown by Liu (2006) based on field data and Tao(2011, 2012a, 2012b) via numerical simulations. It does need carry out some studies to understand the characteristics of the Rouge Waves in a long time evolved wave state, including the occurrence of them. As shown in the picture, it has smooth evolution process, assuring the numerical results
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