Studies Of 2-D Focusing Wave And Interactions With A Vertical Cylinder

The extreme wave is one kind of limited wave, which has strong devastation on the ocean engineering. How to estimate the occurrence and transformation of the extreme wave in the sea field rightly is becoming a more and more important task. A lot of researches indicated that wave focusing is one of the most important mechanisms that contributed to the extreme wave. So it is convenient to simulate extreme wave in the lab to study the interactions between waves and structures using focusing wave. In this paper, the characteristics of extreme waves and the interactions with vertical cylinder are experimently studied. Also numerical methodes are introduced to simulate the transformation of extreme waves and the underling kinematics.At the beginning of this paper, the method of focusing wave generation is introduced. The focusing waves with different wave factors are generated in 2-D flume using JONSWAP spectrum. The transformations of wave surfaces and corresponding amplitude spectra are studied. The method of addition and subtraction of the wave crest and trough focusing wave is used to analyse the speciality of the harmonic waves. The results show that because of the interaction of the component waves, the lower and higher harmonics can be generated. The energy of each order at the focusing point changes little obviously in the focusing process. Wave factors, especially the inputted amplitude and the peak frequency have important effects on the wave surfaces and the energy of harmonics. Also the relationship and difference of the crest focusing and trough focusing wave are presented.In the following chapters, numerical models are modified to simulate the focusing wave surfaces and the kinematics. Based on one wave surface, Local Fourier series model focuses on a Fourier series expansion in a somewhat larger segment of the wave surface record which can include more wave informations. The combinations of two boundary conditions are solved using the least square method. The horizontal and vertical kinematics under the wave crest can be directly predicted. Good agreement between the numerical results and the theoretical Stokes waves and the laboratory focusing wave groups verify the validity of the numerical model. However, this numerical model can not simulate the spatial characteristics, and the error is a little bigger with the wave steepnes increasing.In the fourth chapter, another numerical model called Double Fourier series model is studied in detail. Based on one or several wave surfaces, the model expansion in the spatial and the temporal domain is extended to calculate the spatial surface and the corresponding kinematics of the focusing waves. Comparisons of numerical results with Stokes results and laboratory data show that the extended model is available. At the same time, the associated parameter is proposed. This extended model can simulate not only the spatial wave surface, but also the kinematics in space. It is also available for high steepness waves. Finally, further expansion of the Double Fourier series model is introduced. The transformation of the incident and reflected wave can be simulated together. Simulations about theoretical waves and focusing waves with reflected wave further prove the applicability of this model. At the same time, the adopted parameters are well suggested.Based on the veracity and the validity of the Double Fourier series model, in the fifth chapter, the characteristics of the focusing wave surfaces and the underling kinematics are analysed using this model. The results show that, the wave parameters have deep effect on the horizontal and vertical velocity, the velocity field and the dynamic pressure of the focusing waves.The interactions between the focusing wave and the vertical circular cylinder are experimentally studied in the sixth chapter. Wave surfaces and corresponding amplitude spectra at the focusing point are much different from that without the cylinder. Each order of the energy increases with the cylinder model in place, especially, the improvement of second order effect is about twice times of first order effect. The effects of wave steepness and relative cylinder sizes on the wave run-up around the cylinder are studied in detail. Results show that, the wave run-up increases with the wave amplitude, the wave steepness and the relative cylinder sizes increasing. The tendency of wave run-up, wave amplitude and amplitude spectrum around the cylinder is different. In this chapter, the wave press and the inline wave force induced by focusing waves are also analysed. Their transfer functions are studied at the same time. The tendency of the time series of wave press and inline force changing with wave parameters is similar with the time series of focusing waves. The transfer functions of wave press at different position of the cylinder are a little different. However the transfer functions of inline wave force increases with the frequency increasing. At the end of this chapter, the higher order of the inline forces is analysed.The characteristics of the focusing waves on the surface, the kinematics, and the interactions with the vertical cylinder are studied experimentally and numerically. These results provide a foundation for further studing the focusing waves and their interactions with structures.