Numerical Simulation And Evolution Of Freak Wave In Shallow Water And Finite-depth Water

Freak waves are waves with short life,great crests and highly focusing energy,which can occur in shallow water and finite-depth water.It has attracted people's attention because of many accidents at sea.Since freak waves occur temporally and occasionally,the data of freak wave in situation is insufficient.So far,the mechanism and influencing factors are still unclear,and research work remains to be supplemented.In this paper,the generation and evolution of freak waves in shallow water and finite depth are studied.The research work of the thesis is as follows.In this paper,a two-dimensional numerical tank is constructed.Regular wave,freak wave with gauss envelopes and first-order Peregrine breather solution are simulated.The validity of the numerical wave tank is examined by making comparison against numerical and theoretical solutions.At the same time,the suitable mesh density and upwind coefficient have been chosen in consideration of computational stability and accuracy.Based on the comparison between the numerical solution of the solitary wave and the theoretical solution,the waveform invariance of the solitary wave,and the analysis of the separation stability of the solitary wave,the accuracy of the numerical solution of the KdV equation is verified.The generation and evolution of shallow water freak wave and freak wave with Gauss-shape envelopes are studied under the framework of KdV equation.The time-frequency energy characteristics of freak wave are analyzed by wavelet transform(CWT).The research shows that the ordinary wave train given initial conditions can be evolved into freak wave.The disappearance and appearance of freak wave is accidental.Freak wave with Gauss-shape envelopes has collision separation stability in KdV equation.When the wave number of freak wave with Gauss-shape envelopes decreases,the asymmetry of freak wave will be enhanced.When the freak wave is generated,the concentration of wave energy increases.When the freak wave disappears,the energy decreases.Based on the comparison between the numerical solution and theoretical solution of first-order solitary wave and second-order solitary wave,the accuracy of the numerical solution of the nonlinear Schr?dinger(NLS)equation is verified.The generation and evolution of the finite water depth freak wave are studied under the framework of the NLS equation.The time-frequency energy characteristics of freak wave are analyzed by wavelet transform.Studies show that when the freak wave occurs,it is often accompanied by large peaks and deep valleys.The generation and disappearance of freak waves are accidental.When the Peregrine breather appears,the energy spectrum shows that the wave spectrum sideband is widened,the sideband energy is increased.When the freak wave disappears,the sideband energy dissipates.On the condition of the finite water depth,the dispersion of Gauss envelope will occur,and the shallower the water depth,the slower the dispersion process.When the initial amplitude of Gauss envelope increases,the dispersion effect slows down,and the evolution of the Gauss envelope exhibits the characteristics of the soliton.Based on the constructed 2D numerical wave tank,Peregrine breather of the third-order nonlinear Schr?dinger equation is chosen as the nonlinear model of freak waves to simulate the evolution of freak waves.Square obstacles of different sizes are arranged at the bottom to simulate the evolution of freak waves.Furthermore,analysis of the time-frequency energy spectrum of freak waves is performed with wavelet transformation,and the impact of bottom obstacles on the evolution of freak waves is investigated.Studies have shown that when the height of the obstacle increases,the energy of the freak wave increases in front of the obstacle,and the energy of the freak wave above and behind the obstacle decreases,but the nonlinearity increases.When the ratio of the wavelength to the length of the obstacle increases,the dissipating effect of the freak wave energy is weakened,the depth of the freak wave trough is increased above and at the front of the obstacle,and the peak-to-valley asymmetry of the freak wave behind the obstacle is significantly enhanced.