Numerical And Experimental Study On The Strongly Nonlinear Breaking Waves Based On The High Level Irrotational Green-Naghdi Equations

The strongly nonlinear characteristics and wave breaking effect of ocean waves under high sea conditions play an important role on the wave loads and safety evaluation of offshore structures.However,it is still deficient in the consideration of wave nonlinear effect and wave breaking in industry.Taking the evaluation of the short-term wave statistics as an example,the Rayleigh distribution based on linear wave theory and the forristall distribution based on second-order nonlinear wave theory is far underestimated the occurrence probability of strongly nonlinear waves.Moreover,the both statistical distributions mentioned above do not consider the effec of wave breaking,which leads to the energy dissipation of waves and greatly affect the accurate evaluation of short-term wave statistics in industry.Due to the scarcity of field observations,experimental studies on strongly nonlinear waves are usually carried out in physical tanks.However,compared with the rapidly developing of the wave model,there are still many deficiencies in the experimental works in wave basin,especially for the quantitative analysis on the strongly nonlinear wave propagation with wave breaking.Therefore,it is necessary to carry out numerical and experimental investigation on strongly nonlinear waves.Firstly,the governing equations,boundary conditions,dispersion relations and numerical algorithms of the strongly nonlinear and strongly dispersive High-Level Irrotational Green-Naghdi(HLIGN)equations are briefly introduced.In order to deal with wave breaking,the wave breaking model is added into the HLIGN equations,and the HLIGN equations is thus developed with the wave breaking effect.Secondly,the numerical simulation of the non-breaking focused wave in deep water is carried out in this research.The wave profile and velocity field of the deep-water focused wave are compared with the physical experiments,and the influence of water depth on the focused wave is studied.In addition,the wave breaking and evolution of regular wave trains are studied by physical experiments and numerical simulations.The quantitative analysis of time history,geometric characteristics,spectrum and energy dissipation of regular wave trains with different initial wave steepness and initial group length are provided.Finally,the short-term distribution of the long crest waves is also studied by physical experiments and numerical simulation.The statistical distributions of wave crest and wave height under the sea states with different significant wave heights,peak periods and peak imhancement factors are provided.An empirical formula for the short-term distribution of the long crest waves,considering wave nonlinearity and wave breaking,is proposed,which is verified by comparing with the measurments of physical experiments.Based on the research in this thesis,the HLIGN equations considering wave breaking can be used to accurately and efficiently simulate the strongly nonlinear waves with wave breaking.The effect of water depth variation on the wave profile and velocity field of the focused wave can be obtained.The influence of wave breaking can be achieved on the evolved regular wave trains with different wave steepness.According to the initial characteristic parameters of a given sea state,the short-term distribution considering wave breaking and wave nonlinearity of the long crest waves can be obtained.It provides a reliable theoretical support for the design and safety evaluation of offshore structures under high sea conditions.