多向聚集极限波浪的模拟研究
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摘要
极限波浪是波浪的一种极限情况，它会对海上船只和结构物产生极强的破坏力，目前受到了普遍的重视，大量的研究结果表明，波能聚焦是产生极限波浪的重要机理之一。因此，本文通过物理模拟和数值模拟两种方法对由波能聚焦产生的极限波浪及其破碎波进行了研究。
本文首先给出了聚焦极限波浪的产生方法，即波能聚焦法。并且通过线性理论分析了聚焦波浪的影响因素，得出影响聚焦波浪特征的主要参数应包括：聚焦波高、中心频率、频率宽度、频谱类型、方向分布宽度及水深等。
同时，采用波能聚焦的方法在三维水池中成功地产生了极限波浪和破碎波浪，通过物模实验对多向聚焦极限波浪的特性进行了研究。实验考虑了不同聚焦波高、频谱类型、水深对极限波浪和破碎波浪的影响，较系统地分析了波浪聚焦和破碎过程中的波面特性、破碎指标、频谱变化及能量损失等问题。研究结果表明了聚焦波高、频谱类型、水深以及方向分布都将影响到波浪的聚焦及破碎，其中波高越大、水深越浅波浪越容易破碎，在相同水深的情况下，等波幅分布的波浪较等波陡分布的波浪更容易破碎。同时对几种常用的破碎指标进行了分析研究。
除了物理模拟实验，本文还采用了数值模拟的方法，对聚焦波浪进行了分析研究。首先，建立了能够模拟完全非线性波浪的数值模型，考虑到计算三维水波问题需很大的计算量，所以采用了高阶谱方法，在这种方法中采用快速傅立叶变换求解偏微分方程，具有较高的计算效率和精度。但是这种方法要求计算域具有周期性，为了能够模拟波浪的产生，在谱方法的基础上，引入造波边界，建立了完整的数值模拟水池。并采用典型的算例对模型进行了验证。
同时利用所建立的数值模型对二维和三维聚焦极限波浪进行了系统的模拟分析。考虑了聚焦波浪的各种影响因素，研究了聚焦波面，最大波峰值、聚焦点的偏移、波面的几何参数，聚焦过程中的频谱变化及聚焦波浪的水动力特性。研究结果表明假定聚焦波高的大小、频率宽度、中心频率、方向分布和水深等对波浪的聚焦特性有较大影响，研究成果对聚焦波浪的应用具有重要的参考价值。
最后，对高阶谱方法做了进一步的扩展，建立了能够模拟波浪在规则地形上传播的数学模型，通过与实验结果比较，两者吻合较好，说明建立的模型是有效的。
本文通过物理实验模拟和数值模拟两种方法，研究了聚焦极限波浪，对其特性有了一定的了解，对今后进一步研究聚焦波浪对结构物的作用打下了基础。
The extreme wave is one kind of limited wave, which imposes large or extreme forces on ship and offshore structures. Recently, it has been paid a considerable attention to. A lot of research indicated that wave focusing is one of the most important mechanisms that contributed to the extreme wave. In this paper, the extreme waves generated by wave focusing method are studied by physical experiment and numerical simulation.
At the beginning of this paper, the method of focusing wave generation was introduced. The influencing factors are discussed through linear theory, such as, assumed amplitude, central frequency, frequency band, spectral distribution, directional distributional band and water depth.
In the third chapter, the extreme and breaking waves were generated using focusing wave method in three-dimensional wave basin, considering effects of different assumed amplitudes, spectral distributions, water depth and directional distributions. The focusing wave surface characteristics, breaking criteria, the change of spectrum and energy loss are discussed. The results show that wave focusing and breaking are strongly affected by assumed focusing amplitude, frequency spectra, water depth and directional distribution. The waves with larger amplitude and shallower water depth are easier to break. For the same water depth, the waves with constant wave amplitude are easier to break than those of constant wave steepness.
In the following chapters, the numerical model was developed based on the high-order spectral (HOS) method. The method has the properties of fast convergence and low computational costs, owing to using the fast Fourier transformation (FFT) method to solve the differential equations. It permits the fully-nonlinear simulation of gravity-wave evolution within periodic unbounded 3-D domains. But the original surface and velocity potential should be given.. In order to simulate the generation of focusing waves, the model is developed by introducing wave maker boundary.
In the sixth chapter, the 2-Dand 3-D focusing waves were numerically studied using the developed numerical model, considering different parameters. The characteristics of the focusing wave including surface elevations, maximum crest, the shift of focusing point, surface parameters and the change of frequency spectra are discussed. The results indicate that the nonlinearity of the focusing wave becomes obviously with the increase of assumed
focusing amplitude and central frequency, the decrease of directional distribution and water depth.
Finally, the numerical model was developed to simulate the wave propagation over regular bottom. The numerical results were compared with experimental results. The comparisons show that the model is available.
The extreme waves are studied through experimental and numerical method. The results lay the foundation for the study of interaction between wave and structures.
本文首先给出了聚焦极限波浪的产生方法，即波能聚焦法。并且通过线性理论分析了聚焦波浪的影响因素，得出影响聚焦波浪特征的主要参数应包括：聚焦波高、中心频率、频率宽度、频谱类型、方向分布宽度及水深等。
同时，采用波能聚焦的方法在三维水池中成功地产生了极限波浪和破碎波浪，通过物模实验对多向聚焦极限波浪的特性进行了研究。实验考虑了不同聚焦波高、频谱类型、水深对极限波浪和破碎波浪的影响，较系统地分析了波浪聚焦和破碎过程中的波面特性、破碎指标、频谱变化及能量损失等问题。研究结果表明了聚焦波高、频谱类型、水深以及方向分布都将影响到波浪的聚焦及破碎，其中波高越大、水深越浅波浪越容易破碎，在相同水深的情况下，等波幅分布的波浪较等波陡分布的波浪更容易破碎。同时对几种常用的破碎指标进行了分析研究。
除了物理模拟实验，本文还采用了数值模拟的方法，对聚焦波浪进行了分析研究。首先，建立了能够模拟完全非线性波浪的数值模型，考虑到计算三维水波问题需很大的计算量，所以采用了高阶谱方法，在这种方法中采用快速傅立叶变换求解偏微分方程，具有较高的计算效率和精度。但是这种方法要求计算域具有周期性，为了能够模拟波浪的产生，在谱方法的基础上，引入造波边界，建立了完整的数值模拟水池。并采用典型的算例对模型进行了验证。
同时利用所建立的数值模型对二维和三维聚焦极限波浪进行了系统的模拟分析。考虑了聚焦波浪的各种影响因素，研究了聚焦波面，最大波峰值、聚焦点的偏移、波面的几何参数，聚焦过程中的频谱变化及聚焦波浪的水动力特性。研究结果表明假定聚焦波高的大小、频率宽度、中心频率、方向分布和水深等对波浪的聚焦特性有较大影响，研究成果对聚焦波浪的应用具有重要的参考价值。
最后，对高阶谱方法做了进一步的扩展，建立了能够模拟波浪在规则地形上传播的数学模型，通过与实验结果比较，两者吻合较好，说明建立的模型是有效的。
本文通过物理实验模拟和数值模拟两种方法，研究了聚焦极限波浪，对其特性有了一定的了解，对今后进一步研究聚焦波浪对结构物的作用打下了基础。
The extreme wave is one kind of limited wave, which imposes large or extreme forces on ship and offshore structures. Recently, it has been paid a considerable attention to. A lot of research indicated that wave focusing is one of the most important mechanisms that contributed to the extreme wave. In this paper, the extreme waves generated by wave focusing method are studied by physical experiment and numerical simulation.
At the beginning of this paper, the method of focusing wave generation was introduced. The influencing factors are discussed through linear theory, such as, assumed amplitude, central frequency, frequency band, spectral distribution, directional distributional band and water depth.
In the third chapter, the extreme and breaking waves were generated using focusing wave method in three-dimensional wave basin, considering effects of different assumed amplitudes, spectral distributions, water depth and directional distributions. The focusing wave surface characteristics, breaking criteria, the change of spectrum and energy loss are discussed. The results show that wave focusing and breaking are strongly affected by assumed focusing amplitude, frequency spectra, water depth and directional distribution. The waves with larger amplitude and shallower water depth are easier to break. For the same water depth, the waves with constant wave amplitude are easier to break than those of constant wave steepness.
In the following chapters, the numerical model was developed based on the high-order spectral (HOS) method. The method has the properties of fast convergence and low computational costs, owing to using the fast Fourier transformation (FFT) method to solve the differential equations. It permits the fully-nonlinear simulation of gravity-wave evolution within periodic unbounded 3-D domains. But the original surface and velocity potential should be given.. In order to simulate the generation of focusing waves, the model is developed by introducing wave maker boundary.
In the sixth chapter, the 2-Dand 3-D focusing waves were numerically studied using the developed numerical model, considering different parameters. The characteristics of the focusing wave including surface elevations, maximum crest, the shift of focusing point, surface parameters and the change of frequency spectra are discussed. The results indicate that the nonlinearity of the focusing wave becomes obviously with the increase of assumed
focusing amplitude and central frequency, the decrease of directional distribution and water depth.
Finally, the numerical model was developed to simulate the wave propagation over regular bottom. The numerical results were compared with experimental results. The comparisons show that the model is available.
The extreme waves are studied through experimental and numerical method. The results lay the foundation for the study of interaction between wave and structures.
引文
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[2] Davis M, Zarnick. Testing ship models in transient waves. Proc. Fifth Symp. on Naval Hydrodynamic, Washington, PC, Office of Naval Research, 1964:509-540.
[3] Rapp R J, Melville WK. Laboratory study of steep and breaking waves. Transactions Philosophical of the Royal Society of London, 1990, A331: 735-800.
[4] Kway H L, Lob Y S, Chan, E S. Laboratory study of deep-water breaking waves. Ocean Engineering, 1998,25(8):657-676.
[5] Baldock T, Swan C, Taylor P. A laboratory study of nonlinear surface waves on water. Philos. Roy. Soc. London, 1996,452A: 649-676.
[6] Baldock T.E. Nonlinear transient water waves:[ PhD dissertation].London: University of London, 1996.
[7] She K, Greated CA, Easson WJ. Experimental study of three-dimensional wave breaking. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE, 1994,120(1): 20-36.
[8] She K, Greated CA, Easson WJ. Experimental study of three-dimensional wave kinematics. Applied Ocean Research, 1997,19: 329-343.
[9] Johannessen TB. The effect of directionality on the nonlinear behavior of extreme transient ocean waves:[PhD dissertation].London: University of London, 1997.
[10] Wu CH, Nepf HM. Breaking criteria and energy losses for three-dimensional wave breaking, Journal of Geophysical Research, 2002,107(C10) 41-1-18.
[11] Hong, K and Liu S. The directional characteristics of breaking waves generated by the directional focusing in a wave basin, Proceedings of 21st International Conference on Offshore Mechanics and Arctic Engineering, Oslo, Norway, 2002.
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