Analytical And Terrain Bypass Experimental Study Of The Evolution Of Freak Waves And Internal Solitary Waves

The propagation and evolution of nonlinear waves are very complicated.The typical nonlinear waves such as freak waves and solitary waves can cause damage to the offshore platform and bring huge challenges to research because of its strong nonlinearity,dynamic property and randomness.There are many research methods for nonlinear waves.The analytical method can be used to find solutions of freak waves and solitary waves to nonlinear evolution equations.The analytic expression can show the influence of various parameters on the evolution of nonlinear waves.However,the analytical method has limitations when the complex boundary conditions exist,such as terrain.In this case,model experiment method can be used to obtain the waveform characteristics and evolution rules of over-terrain freak waves and internal solitary waves.In this paper,analytical and experimental methods were adopted.Firstly,the new analytic solutions of the nonlinear Schr(?)dinger equation were obtained based on homotopy analysis method,and it showed that height of freak waves gradually decreased with the time,and the waveform transited from single large crest to symmetric in the waveform of the fifth-order solution curves.The freak waves were generated by near-reef model experiment of irregular waves in the pool.It showed that the analytical results were consistent with the experiment results in vertical asymmetric parameters and horizontal asymmetric parameters.Secondly,the new analytic solutions,such as one-soliton solution,two-soliton solution,freak wave solution,breather soliton solution,ISW solution and Lump soliton solution,were obtained in eKP equation and Ito equation based on Hirota bilinear analysis method.It showed that the projection of two-soliton solution is two intersecting lines in x-y plane,and the waveform width of the larger peak becomes wider at the intersection of the two peaks.The waveform and velocity of ISW were unchanged in the process of propagation.Finally,ISW in a system of two fluids,silicone oil and water,were generated by gravity collapse method.The height of ISW can be obtained by image threshold segmentation method and morphology closing algorithm method,and the flow field of ISW can be obtained by PIV.It is found that the analytical solutions can precisely describe the waveform of ISW by comparing the experimental results with the analytical results above.The wave height,flow field,horizontal induced velocity and vorticity of ISW wave were studied in the model experiment of passing through the upper,lower and concave slopes.It is found that the ISW were not sensitive to the thickness of the lower layer fluid,and the waveform and wave height hardly changed after passing the terrain when the wave height was small.The horizontal induced velocity of ISW changes from positive to negative with depth.It is found that a local vortex has been formed on the leeward side of the terrain when ISW passed through the terrain.The vortices have existed for a long time and their direction of motion was irrelevant to the terrain.In conclusion,the waveform parameters and evolution characteristics of freak waves and ISW were researched in this paper.The research results are helpful to intuitively understand the propagation and evolution of nonlinear waves.The analytical and experimental results can provide the input parameters of load calculation,and guide the design of offshore platform.