风浪破碎和波群统计特征的研究
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摘要
海浪的破碎和群性是重要的海洋现象。风浪破碎率和白浪覆盖率是波浪破碎的基本统计特征量,是计算波浪破碎其它统计特征量(如平均破碎强度和平均破碎经历时间等)和计算水雾、气泡分布与浓度的基本参量,从而在上层海洋动力学、海一气交换、海洋遥感、海洋工程和海洋噪声等方面的研究中有直接意义,因此,有必要对二者的统计模式进行深入的研究。而波群对于波浪与建筑物的作用、海洋灾害及海洋结构物的设计等都有明显的影响,研究波群特征量的统计分布同样具有重要的科学意义和广泛的应用价值。
本文基于Xu et al.(2000)的结果推出新的白浪覆盖率与风浪破碎概率理论计算模式,将风浪破碎统计特征量与海上观测更易获得的参量(如波周期、海面风速、摩擦风速)联系起来,避免了风区长度的计算,具有形式简单、实用性强的特点;风浪的破碎特征与海浪成长状态关系密切,且海浪的理论研究中常会涉及到海浪的状态参量波龄c /U ,因此本文将W与B发展成一种形式简单的波龄的函数,得到不同海浪状态下的风浪破碎统计特征。
现存的波群统计特征的分布大多假定海浪是窄谱的且波面位移服从正态分布。考虑到实际海浪的随机性和复杂性,本文将信息熵的概念引入到推导波群特征量统计分布的研究中,基于最大熵原理在无任何假定的基础上推出波群统计特征量的最大熵分布,使其不仅能够很好的拟合已有观测数据,而且对未知数据的分布保持最大的不确定性(最大熵),即此分布可使作为随机变量的波群统计特征量的信息熵最大。为检验该分布与实际符合的情况,分别采用实验室数据与观测资料验证了该分布的合理性,并与至今仍被广泛应用的Longuet-Higgins (1984)的分布相比较验证其可靠性与实用性。
为验证推导出的风浪破碎与波群理论模型的有效性,采用自行设计并搭建的声学测量系统在不同海域通过水声监测和海面观测相结合的方式进行了两次海上实验。从水声信号中判断破碎信息是获取风浪破碎率的前提,实验中借助于海面观测资料获得基于声谱级水平(SSL)的声学判据,并进一步验证了依赖于波龄的风浪破碎率的理论计算模式的合理性;分析实测资料时采用Xu et al. (2004)提出的快速带通滤波方法作相应处理后得到波群特征量的统计信息,通过最大熵分布与实测资料及Longuet-higgins(1984)推出的分布相比较可知最大熵分布能更好地描述波群统计特征量G、H、l ,并且其相应得最大熵分布f_(n= 0.6)(G )、f_(n=1) ( H)、f n= 0.5(l )拟合效果最好。初步分析同步测得的破碎与波群的实测资料得出风浪破碎与波群统计特征的关系:风浪破碎主要发生在连续且大的浪即群性大的风浪的波峰处。
Breaking and grouping are two important phenomena of sea waves. The breaking probability and whitecap coverage are usually used to evaluate breaking, from which other features of breaking waves (i.e. intensity and duration of breaking waves), as well as distribution and concentration of spray and bubble clouds can be easily calculated, hence play important parts in upper ocean dynamics, air-sea interaction, remote sensing, ocean engineering and sea noise. Thus models of breaking probability and whitecap coverage deserve lucubrating. While wave groups have great influence on wave-structure interaction, marine disasters and design of offshore structures. It would be not only of major scientific interest but also of practical significance to study the statistical properties of wave group parameters.
In this paper, the models of Xu et al.(2000) for breaking probability and whitecap coverage are developed into new forms. To avoid the complex estimation of dimensionless fetch, the new models are expressed in terms of average wave period and wind speed, which are relatively easy to measure in field. Considering that wave age has been widely used to parameterize spectral models of ocean waves and air-sea fluxes, the derived models are further developed into simple functions of wave age, respectively.
The conventional distribution of wave group statistics is derived by taking records of the sea surface elevation as a random Gaussian process, which ignores the nonlinear effect of sea waves. Thus another aim of this paper is to derive a new distribution for statistical properties of wave groups based on the maximum entropy principle. Such a distribution is desirable, because its acquisition is under the maximum uncertainty, i.e., free of a Gaussian hypothesis. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins (1984) with the laboratory wind-wave data show that the former gives a better fit.
To further test the validation of the above models, two measurements were conducted on Bohai Sea to provide real sea data of different conditions. Hydrophones and pressure sensor were adopted to record the wave breaking events and wave elevation, respectively. Instead of the acceleration criterion, the breaking criterion in terms of Sound Spectrum Level (SSL) is definitely employed to help detect wave breaking from the ambient sound signals. With the wave elevation and wind speed data observed, the wave age dependent model of wave breaking probability is reanalyzed. The result shows the new model is competent for breaking probability prediction. By use of the FFT filtering method proposed by Xu et al.(2004), the maximum entropy probability density function of wave records are plotted with comparison to the PDFs of Longuet-Higgins(1984). It has been shown that f_(n= 0.6)(G ), f_(n=1) ( H), and f n= 0.5(l ) have rather good agreements with the field data. Furthermore, tentatively examination of correlations between wave groups and breaking suggests that breaking occurs most commonly in the center of a group, which accords with the earlier findings.
本文基于Xu et al.(2000)的结果推出新的白浪覆盖率与风浪破碎概率理论计算模式,将风浪破碎统计特征量与海上观测更易获得的参量(如波周期、海面风速、摩擦风速)联系起来,避免了风区长度的计算,具有形式简单、实用性强的特点;风浪的破碎特征与海浪成长状态关系密切,且海浪的理论研究中常会涉及到海浪的状态参量波龄c /U ,因此本文将W与B发展成一种形式简单的波龄的函数,得到不同海浪状态下的风浪破碎统计特征。
现存的波群统计特征的分布大多假定海浪是窄谱的且波面位移服从正态分布。考虑到实际海浪的随机性和复杂性,本文将信息熵的概念引入到推导波群特征量统计分布的研究中,基于最大熵原理在无任何假定的基础上推出波群统计特征量的最大熵分布,使其不仅能够很好的拟合已有观测数据,而且对未知数据的分布保持最大的不确定性(最大熵),即此分布可使作为随机变量的波群统计特征量的信息熵最大。为检验该分布与实际符合的情况,分别采用实验室数据与观测资料验证了该分布的合理性,并与至今仍被广泛应用的Longuet-Higgins (1984)的分布相比较验证其可靠性与实用性。
为验证推导出的风浪破碎与波群理论模型的有效性,采用自行设计并搭建的声学测量系统在不同海域通过水声监测和海面观测相结合的方式进行了两次海上实验。从水声信号中判断破碎信息是获取风浪破碎率的前提,实验中借助于海面观测资料获得基于声谱级水平(SSL)的声学判据,并进一步验证了依赖于波龄的风浪破碎率的理论计算模式的合理性;分析实测资料时采用Xu et al. (2004)提出的快速带通滤波方法作相应处理后得到波群特征量的统计信息,通过最大熵分布与实测资料及Longuet-higgins(1984)推出的分布相比较可知最大熵分布能更好地描述波群统计特征量G、H、l ,并且其相应得最大熵分布f_(n= 0.6)(G )、f_(n=1) ( H)、f n= 0.5(l )拟合效果最好。初步分析同步测得的破碎与波群的实测资料得出风浪破碎与波群统计特征的关系:风浪破碎主要发生在连续且大的浪即群性大的风浪的波峰处。
Breaking and grouping are two important phenomena of sea waves. The breaking probability and whitecap coverage are usually used to evaluate breaking, from which other features of breaking waves (i.e. intensity and duration of breaking waves), as well as distribution and concentration of spray and bubble clouds can be easily calculated, hence play important parts in upper ocean dynamics, air-sea interaction, remote sensing, ocean engineering and sea noise. Thus models of breaking probability and whitecap coverage deserve lucubrating. While wave groups have great influence on wave-structure interaction, marine disasters and design of offshore structures. It would be not only of major scientific interest but also of practical significance to study the statistical properties of wave group parameters.
In this paper, the models of Xu et al.(2000) for breaking probability and whitecap coverage are developed into new forms. To avoid the complex estimation of dimensionless fetch, the new models are expressed in terms of average wave period and wind speed, which are relatively easy to measure in field. Considering that wave age has been widely used to parameterize spectral models of ocean waves and air-sea fluxes, the derived models are further developed into simple functions of wave age, respectively.
The conventional distribution of wave group statistics is derived by taking records of the sea surface elevation as a random Gaussian process, which ignores the nonlinear effect of sea waves. Thus another aim of this paper is to derive a new distribution for statistical properties of wave groups based on the maximum entropy principle. Such a distribution is desirable, because its acquisition is under the maximum uncertainty, i.e., free of a Gaussian hypothesis. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins (1984) with the laboratory wind-wave data show that the former gives a better fit.
To further test the validation of the above models, two measurements were conducted on Bohai Sea to provide real sea data of different conditions. Hydrophones and pressure sensor were adopted to record the wave breaking events and wave elevation, respectively. Instead of the acceleration criterion, the breaking criterion in terms of Sound Spectrum Level (SSL) is definitely employed to help detect wave breaking from the ambient sound signals. With the wave elevation and wind speed data observed, the wave age dependent model of wave breaking probability is reanalyzed. The result shows the new model is competent for breaking probability prediction. By use of the FFT filtering method proposed by Xu et al.(2004), the maximum entropy probability density function of wave records are plotted with comparison to the PDFs of Longuet-Higgins(1984). It has been shown that f_(n= 0.6)(G ), f_(n=1) ( H), and f n= 0.5(l ) have rather good agreements with the field data. Furthermore, tentatively examination of correlations between wave groups and breaking suggests that breaking occurs most commonly in the center of a group, which accords with the earlier findings.
引文
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