畸形波生成、演化及内部结构研究
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摘要
畸形波是一种波高极大,持续时间很短,能量高度集中的灾难性波浪,能对船舶和海上工程结构等造成严重的危害。目前,其发生机理和生成概率等基本问题还没有统一的结论。主要是因为畸形波破坏力极大,发生前没有征兆,实测资料十分有限等方面原因,导致畸形波的研究工作开展的还不够深入。本文针对畸形波生成、演化过程,内部结构及内、外部结构之联系等问题开展研究,取得了以下研究成果：
实现了畸形波的物理模拟和数值模拟。数值模型是通过有限差分法求解雷诺时均N-S方程,以k-ε双方程模型封闭,使用VOF方法捕捉自由表面建立的。通过将孤立波、不规则波、畸形波的数值模拟结果与物理试验结果比较,验证了数值模型模拟畸形波波面及水质点速度的有效性。为研究畸形波生成、演化及内部结构等提供了基础工具。
基于复演天然实测及数值模拟畸形波(或深谷),对比分析了天然畸形波和数值模拟畸形波的生成和演变规律。研究发现,畸形波的生成、演化过程可归纳为：从连续大波(大波群)→深谷→准畸形波→畸形波→准畸形波→深谷→连续大波。该过程中,最大波浪并不是一直以自由水面形态向前传播,会发生大峰波与深谷相互转化、深谷与畸形波相互转化,相邻的波浪间,能量和波面传播速度不同步使最大波发生“突变”。由此可见,畸形波并非独立的异常波浪现象,常与深谷和连续大波等异常波浪现象相伴发生。
基于284组物理模拟畸形波和64组数值模拟畸形波传播速度的计算结果,使用回归分析方法给出了畸形波传播速度的半经验、半理论计算公式。并对比分析了畸形波与3阶Stokes波传播速度中的非线性成分,发现非线性对畸形波传播速度的影响远远大于3阶Stokes波,并且随着广义波陡的增加,两者之间的差距越明显。
使用小波分析方法定量分析了畸形波生成、演化过程中出现的特征大波(大峰波、深谷、准畸形波和畸形波)的时频能量谱特征(能量集中度,能量集中区域在时域和频域的分布范围),并与常规不规则波列(不包含异常大波的不规则波列)中的最大波浪进行对比。研究发现,畸形波生成、演化过程中出现的特征大波的能量集中度远大于常规不规则波列中的最大波浪。定义满足aE三6的大波浪为“广义畸形波”。aE是描述波浪能量集中程度的参数,与畸形波外部特征参数α1显著线性相关。
广义畸形波水质点速度、加速度的最大值均发生在自由表面附近。波峰(波谷)两侧速度场、加速度场的分布均不对称,与规则波有明显的区别。尽管广义畸形波的波高很大,但其远未达到波浪的运动学、动力学破碎指标。波峰高度、周期完全相同的条件下,比较畸形波与5阶Stokes波波峰位置水质点水平速度得知,静水面以上,畸形波水质点水平速度较大,静水面以下,情况相反；畸形波水质点水平速度沿水深变化比5阶Stokes波快。有限的计算结果显示,畸形波内部结构参量与畸形波外部特征参数ηc/Lp,α1和α4的关系较为密切,对此还需进一步的研究。
斜坡和曲线地形的存在对于畸形波外部特征参数的影响未表现出显著的规律。但当坡度(或曲线高度)连续变化时,特征参数a4存在一个谷值。斜坡和曲线地形的存在对于畸形波内部结构的影响主要表现在：当地形特征变化显著时,可使得时频能量集中区在时域的分布范围减小,同时显著增加时频能量的高频成分,但对能量集中度αE、时频能量集中区在频域的分布范围的影响不显著。
Freak wave is a type of large and short-lived water wave. Such wave has high energy density, which can bring serious damages to vessels, maritime structures and other facilities in the ocean. So far, its physical mechanics and probability of occurrence are still unclear. The further study on freak waves cannot be carried out smoothly due to the insufficient in-situ data, devastating force and unexpected occurrence. This work aims to conduct a systematic investigation on the generation, evolution, internal structure and the relationship between internal and external features. The thesis work can be described as the following6major parts.
Both numerical and experimental simulations of freak waves are realized. The numerical model is built by solving for the variables from a finite-difference approximation of the Reynolds time-averaged N-S equations, the k-ε model is for the turbulence closure, and the volume of fluid (VOF) method is used for free surface tracking. The simulated results of the fission phenomenon of a solitary wave over a change of water depth through a bottom slope, a conventional random wave train, the wave profile and velocity of a freak wave show good agreement with the experimental results, which indicates the model's capability to resolve the wave profiles and velocities of freak waves. The numerical and experimental simulations are effective tools for the study of the generation, evolution and internal structure of freak waves.
The present numerical model is implemented to reproduce3in-situ random wave trains containing a freak wave (or a deep trough), and to simulate5non-designed freak waves. Analysis of the simulated results attests that the generation and evolution of freak waves can be summarized as:large wave sequence→deep trough→quasi-freak wave→freak wave→quasi-freak wave→deep trough→large wave sequence. During that process, the maximum wave is not always in the form of free surface propagation, there are transformations between the wave with high crest and deep trough, between the deep trough and freak wave. The difference between propagation speeds of energy and free surface results in sudden change of the maximum wave. It can be seen that freak waves do not come alone, always accompanied by other abnormal events such as successive large waves and deep troughs.
On the basis of the calculation results of the speeds of284experimental freak waves and64supplementary numerical freak waves, a semi-theoretical and semi-empirical formula is proposed to predict the freak wave speed by using regression analysis method. Through analyzing the difference between the nonlinearity effects on the speeds of freak waves and3rd-order Stokes waves, it is found that the nonlinearity effect on the freak wave speed is much greater than on the3rd-order Stokes wave speed, and that the increase of the modified wave steepness enhances the difference between the nonlinearity effects on the speeds of freak waves and3rd-order Stokes waves.
Quantitative analysis of the time-frequency energy spectrum characteristics (transient energy density and the ranges of focused energy distribution in both time and frequency domains) of the abnormal waves occurring during the generation and evolution of freak waves (wave with high crest, deep trough, quasi-freak wave and freak wave) is performed by wavelet analysis method. Comparison of the time-frequency energy structure characteristics of abnormal waves and the maximum wave in a conventional random wave train (a random wave train contains no abnormal wave) attests that the energy densities of abnormal waves are much higher than the maximum wave in a conventional random wave train. It is suggested that the abnormal wave with energy parameter αE≥6is considered as the "general freak waves". The energy parameter αE is presented to describe the transient energy densities of waves, which is correlated linearly with the external characteristic parameter α1.
The maximal velocity and acceleration of general freak waves appear close to the free surface. The velocity and acceleration fields of the general freak waves exhibit strong front/back asymmetry, which is different from regular wave. Although the general freak wave has a height to significant wave height ratio more than2, the kinematic and dynamic wave-breaking criteria are not met. Comparison of the horizontal velocity profiles below wave crest of general freak wave and5th-order Stokes wave (identical crest height and period) attests that the horizontal velocity of general freak wave is larger than5th-order Stokes wave close to the free surface and smaller below the still water level, and that the vertical variation of the horizontal velocity of general freak wave is more obvious than5th-order Stokes wave. Present numerical results show that the internal structure parameters of general freak waves have relation with the external characteristic parameters ηc/Lp, α1and α4. Further studies are needed to thoroughly analyze the relationship between the internal and external characteristic parameters.
As the characteristic altitudes of the uneven topographies (slope topography and curved topography) increase, the external characteristic parameters show no obvious trend except a valley value for α4. For internal structure, the increase of the characteristic altitudes of the uneven topographies results in the decrease of the range of the focused energy distribution in time domain, the increase of the high-frequency energy, no obvious trend for αE and the range of the focused energy distribution in frequency domain.
实现了畸形波的物理模拟和数值模拟。数值模型是通过有限差分法求解雷诺时均N-S方程,以k-ε双方程模型封闭,使用VOF方法捕捉自由表面建立的。通过将孤立波、不规则波、畸形波的数值模拟结果与物理试验结果比较,验证了数值模型模拟畸形波波面及水质点速度的有效性。为研究畸形波生成、演化及内部结构等提供了基础工具。
基于复演天然实测及数值模拟畸形波(或深谷),对比分析了天然畸形波和数值模拟畸形波的生成和演变规律。研究发现,畸形波的生成、演化过程可归纳为：从连续大波(大波群)→深谷→准畸形波→畸形波→准畸形波→深谷→连续大波。该过程中,最大波浪并不是一直以自由水面形态向前传播,会发生大峰波与深谷相互转化、深谷与畸形波相互转化,相邻的波浪间,能量和波面传播速度不同步使最大波发生“突变”。由此可见,畸形波并非独立的异常波浪现象,常与深谷和连续大波等异常波浪现象相伴发生。
基于284组物理模拟畸形波和64组数值模拟畸形波传播速度的计算结果,使用回归分析方法给出了畸形波传播速度的半经验、半理论计算公式。并对比分析了畸形波与3阶Stokes波传播速度中的非线性成分,发现非线性对畸形波传播速度的影响远远大于3阶Stokes波,并且随着广义波陡的增加,两者之间的差距越明显。
使用小波分析方法定量分析了畸形波生成、演化过程中出现的特征大波(大峰波、深谷、准畸形波和畸形波)的时频能量谱特征(能量集中度,能量集中区域在时域和频域的分布范围),并与常规不规则波列(不包含异常大波的不规则波列)中的最大波浪进行对比。研究发现,畸形波生成、演化过程中出现的特征大波的能量集中度远大于常规不规则波列中的最大波浪。定义满足aE三6的大波浪为“广义畸形波”。aE是描述波浪能量集中程度的参数,与畸形波外部特征参数α1显著线性相关。
广义畸形波水质点速度、加速度的最大值均发生在自由表面附近。波峰(波谷)两侧速度场、加速度场的分布均不对称,与规则波有明显的区别。尽管广义畸形波的波高很大,但其远未达到波浪的运动学、动力学破碎指标。波峰高度、周期完全相同的条件下,比较畸形波与5阶Stokes波波峰位置水质点水平速度得知,静水面以上,畸形波水质点水平速度较大,静水面以下,情况相反；畸形波水质点水平速度沿水深变化比5阶Stokes波快。有限的计算结果显示,畸形波内部结构参量与畸形波外部特征参数ηc/Lp,α1和α4的关系较为密切,对此还需进一步的研究。
斜坡和曲线地形的存在对于畸形波外部特征参数的影响未表现出显著的规律。但当坡度(或曲线高度)连续变化时,特征参数a4存在一个谷值。斜坡和曲线地形的存在对于畸形波内部结构的影响主要表现在：当地形特征变化显著时,可使得时频能量集中区在时域的分布范围减小,同时显著增加时频能量的高频成分,但对能量集中度αE、时频能量集中区在频域的分布范围的影响不显著。
Freak wave is a type of large and short-lived water wave. Such wave has high energy density, which can bring serious damages to vessels, maritime structures and other facilities in the ocean. So far, its physical mechanics and probability of occurrence are still unclear. The further study on freak waves cannot be carried out smoothly due to the insufficient in-situ data, devastating force and unexpected occurrence. This work aims to conduct a systematic investigation on the generation, evolution, internal structure and the relationship between internal and external features. The thesis work can be described as the following6major parts.
Both numerical and experimental simulations of freak waves are realized. The numerical model is built by solving for the variables from a finite-difference approximation of the Reynolds time-averaged N-S equations, the k-ε model is for the turbulence closure, and the volume of fluid (VOF) method is used for free surface tracking. The simulated results of the fission phenomenon of a solitary wave over a change of water depth through a bottom slope, a conventional random wave train, the wave profile and velocity of a freak wave show good agreement with the experimental results, which indicates the model's capability to resolve the wave profiles and velocities of freak waves. The numerical and experimental simulations are effective tools for the study of the generation, evolution and internal structure of freak waves.
The present numerical model is implemented to reproduce3in-situ random wave trains containing a freak wave (or a deep trough), and to simulate5non-designed freak waves. Analysis of the simulated results attests that the generation and evolution of freak waves can be summarized as:large wave sequence→deep trough→quasi-freak wave→freak wave→quasi-freak wave→deep trough→large wave sequence. During that process, the maximum wave is not always in the form of free surface propagation, there are transformations between the wave with high crest and deep trough, between the deep trough and freak wave. The difference between propagation speeds of energy and free surface results in sudden change of the maximum wave. It can be seen that freak waves do not come alone, always accompanied by other abnormal events such as successive large waves and deep troughs.
On the basis of the calculation results of the speeds of284experimental freak waves and64supplementary numerical freak waves, a semi-theoretical and semi-empirical formula is proposed to predict the freak wave speed by using regression analysis method. Through analyzing the difference between the nonlinearity effects on the speeds of freak waves and3rd-order Stokes waves, it is found that the nonlinearity effect on the freak wave speed is much greater than on the3rd-order Stokes wave speed, and that the increase of the modified wave steepness enhances the difference between the nonlinearity effects on the speeds of freak waves and3rd-order Stokes waves.
Quantitative analysis of the time-frequency energy spectrum characteristics (transient energy density and the ranges of focused energy distribution in both time and frequency domains) of the abnormal waves occurring during the generation and evolution of freak waves (wave with high crest, deep trough, quasi-freak wave and freak wave) is performed by wavelet analysis method. Comparison of the time-frequency energy structure characteristics of abnormal waves and the maximum wave in a conventional random wave train (a random wave train contains no abnormal wave) attests that the energy densities of abnormal waves are much higher than the maximum wave in a conventional random wave train. It is suggested that the abnormal wave with energy parameter αE≥6is considered as the "general freak waves". The energy parameter αE is presented to describe the transient energy densities of waves, which is correlated linearly with the external characteristic parameter α1.
The maximal velocity and acceleration of general freak waves appear close to the free surface. The velocity and acceleration fields of the general freak waves exhibit strong front/back asymmetry, which is different from regular wave. Although the general freak wave has a height to significant wave height ratio more than2, the kinematic and dynamic wave-breaking criteria are not met. Comparison of the horizontal velocity profiles below wave crest of general freak wave and5th-order Stokes wave (identical crest height and period) attests that the horizontal velocity of general freak wave is larger than5th-order Stokes wave close to the free surface and smaller below the still water level, and that the vertical variation of the horizontal velocity of general freak wave is more obvious than5th-order Stokes wave. Present numerical results show that the internal structure parameters of general freak waves have relation with the external characteristic parameters ηc/Lp, α1and α4. Further studies are needed to thoroughly analyze the relationship between the internal and external characteristic parameters.
As the characteristic altitudes of the uneven topographies (slope topography and curved topography) increase, the external characteristic parameters show no obvious trend except a valley value for α4. For internal structure, the increase of the characteristic altitudes of the uneven topographies results in the decrease of the range of the focused energy distribution in time domain, the increase of the high-frequency energy, no obvious trend for αE and the range of the focused energy distribution in frequency domain.
引文
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