Numerical Simulation And Evolution Characteristics Of Higher Order Freak Waves

Freak waves are catastrophic waves with highly focusing energy.It has the characteristics of large wave height,large wave steepness,no warning,and short duration.Its huge destructive power poses a serious threat to the navigational safety of ships and the safe operation of marine structures.Because there are many difficulties in the measurement of freak waves at sea,people mainly rely on experiment and numerical simulation to study the freak waves.Compared with experiment,numerical simulation can simulate more complex and larger-scale waves,and has the advantages of high economy and small error.Therefore,this paper conducts relevant research on the generation and evolution of higher order freak waves and their interactions.The research work of the thesis is as follows.In this paper,the Korteweg-de Vries(KdV)equation is solved by pseudo-spectral method,which provides a reference for the study of evolution characteristics of the Gaussian pulse type freak wave solution.Taking the JONSWAP spectrum as the target spectrum,based on linear cosine wave and cnoidal wave respectively,the random wave is simulated by superposition ideas,numerically solved the evolution characteristics of Gaussian pulse type freak wave in random wave field.To analyze the wave number and energy distribution of the freak wave during the evolution,the CMOR wavelet transform are used.When the freak wave is generated,the simulation results reflect the characteristics of energy concentration and high-frequency energy transfer.The curve fitting results show the duration and propagation distance of the freak wave have a quadratic function relationship with the amplitude and width of the Gaussian pulse under different wave conditions.The existing method for constructing the initial value function of freak waves interaction is improved,and a new method for constructing the initial value function of interaction is proposed.The improved piecewise function method completely preserves the shape of the initial wave functions,and has continuous smoothness.The evolution characteristics of the first to third order rational solution within the modified Korteweg-de Vries(mKdV)equation are studied.The study shows that the higher order rational solutional can focus and form freak waves while having certain soliton properties.the mKdV equation is solved by pseudo-spectral method,which provides a reference for interaction study of the higher order rational solution.The analysis found that after the interaction of rational solutional is stable,it will keep the sum of solitons wave numbers that are stable when each order rational solution evolves to propagate.With the order of rational solutions increasing,freak waves will appear during the evolution of the interaction.The evolution characteristics of the first to third-order breather solutions of the nonlinear Schr?dinger(NLS)equation are studied.The research shows that the first to third-order breather solutions of the NLS equation have typical characteristics of freak wave,and occur unpredictably.The initial value function of the breather solution interaction is constructed,and the NLS equation is numerically solved by pseudo-spectral method.The research shows that the results of the interactions of the breather solutions have some common characteristics.In the early stage of the interaction,the wave train gradually changes from a freak wave to a normal stationary wave train,and then the energy is focused to generate the first quasi Peregrine breather solution.Eventually,the height of each wave peak will gradually decrease,and the wave train will return to a normal stationary wave train,which is consistent with the actual freak wave evolution and reflects the conservation of wave train energy.