Research On The Mechanisms In The Generation And Nonlinear Evolution Of The Rogue Waves In Deep Ocean

A rogue wave is a type of very rare and extremely large wave that possesses powerful concentrated energy,strong nonlinear dynamics and can be enormously devastating.When it interacts with deep-sea structures,the structure's integrity will suffer a potentially serious threat,its stability and orientation will be severely challenged and it may even cause significant harm to the on-board staff and valuable property.Studies on the mechanisms of rogue waves are thus of great significance to the vessel and platform design and their security.It is also one of the current key issues on wave mechanics within hydrodynamic studies.In recent years,as the result of an increasing number of accidents that are believed to have happened due to encounters with rogue waves,the physical mechanics of this phenomenon has attracted much research and academic interest.The formation of rogue waves,also known as freak waves,monster waves,killer waves,extreme waves,and abnormal waves,seems to appear from nowhere and quickly disappear without a trace.Thus there is little useful at-sea evidence except for visual sighting and chance photographic records.They may appear on a relatively calm sea surface and are potentially very destructive to ships and offshore structures due to their lethality and unexpectedness.Among the various physical mechanics that have been employed in order to explain the occurrence of rogue waves in deep oceans,the focusing due to dispersion(spatio-temporal focusing)of wave packets and the focusing due to modulational instability(nonlinear self-focusing)are currently the most popular physical mechanisms to describe the high concentration of wave energy in a small local area of an open sea field.In this study,the behaviour of the Peregrine breather-type rogue waves is numerically studied based on the fourth order nonlinear Schr?dinger equation.The generation and evolution of 1st~5th order super-rogue waves were simulated by solving the mNLS equation numerically.The 4th order split-step pseudo-spectral method was used during the integral process in order to obtain more accurate results.The wavelet analysis method was adopted in order to analyses the time-frequency energy distribution during the generation and evolution of the super rogue wave up to 5th order.Here we have only studied the limited case of 2D wave propagation.It is found that the huge wave crest suddenly appears from nowhere and similarly quickly disappears without a trace,which coincides with the recognised short-lived property of rogue wave.The fourth-order terms in the mNLS equation should not be ignored in numerically simulating the evolution of the rogue wave formation.The rogue wave event appears at a distance different from the expected location due to the higher-order nonlinear effects.Compared with the results based on the NLS equation,the computational results obtained in the framework of the mNLS equation demonstrates a stronger asymmetry property between the crest and the trough.In the time-frequency spectrum,we find that a strong energy density surges instantaneously and that it is seemingly carried over to the high frequency components at the instant that the large,rogue,wave occurs.The energy of the sideband frequency in the frequency spectrum mainly comes from the contribution of the rogue wave.Thus,the breather-type rogue wave is considered to be the result of the transient energy transfer from the fundamental frequency to the sideband frequency.The shifts of the fundamental frequency of the first-to fifth-order super rogue waves consistently occur at positions where maximum or minimum amplitudes appear.The energy of the sideband frequency in the frequency spectrum primarily comes from the contribution of the carrier waves near the super rogue waves.Longer durations during wave energy transfer seem to be associated with the generation of higher-order super rogue waves.Wave energy transfers in the form of wave groups and shows considerable asymmetry before and after the appearance of super rogue waves.Super-rogue waves are determined to be the consequence of the superposition of waves in the time domain and nonlinear focusing in which the transient energy transfer between the fundamental frequency and the sideband frequency.Moreover,the generation and evolution of the rogue wave in the random wave field is investigated based on the mNLS equation.The lag effects of focusing position and focusing time of the rogue wave become stronger with the increasing significant wave height used in the numerical simulation due to the growing nonlinearity.Additionally,the increasing nonlinearity may lead to the changes of the wave spectrum of the rogue wave.