Hilbert Transform Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient.The reflection performance of the physical model can be estimated exactly without calculation of wave height and phasedifference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda‘s method and satisfactory results are obtained.     

Separation of Waves by Interpolation Method

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分离入射波与反射波的解析方法

提出了一种新的分离入射波和反射波的解析方法（AM）。利用两点处的 波高信息，运用Hilbert变换得到波浪信号在复域内的解析表达式，不需要计算合成波高和相位差即可实现信号的分离。根据分离结果，可以精确地估计入射波与反射波的幅值以及反射系数等参数，能够获得入射波与反射波之间的相位信息，并且可方便地用于不规则波的分离。文中通过数值模拟与物理模型实验对AM法进行了检验，所得的结果与实际值非常吻合。     

The application of Hartley transform to ocean engineering

The Hartley transform is a real integral transform based on harmonic functions and hassome characteristics similar to the Fourier transform. Most applications in ocean engineering requiring the Fourier transform can also be performed by the Hartley transform. The fast Hartley transform is twice faster and more convenient to handle than the corresponding fast Fourier transform, so it is a real valued alternative to the complex Fourier transform in many applications. The use of the Hartley transform in ocean engineering is presented in detail in this paper, including wave spectral analysis, separation of waves, cross-correlation in PIV technique and expression of equation in the Hartley domain. The examples in the paper show deeply the advantage and efficiency of the Hartley transform over the Fourier transform.     

Hilbert transform and its application to modulation of capillary gravity waves

INTRODUCFIONlt is well known that the stability and interaction of nonlinear waves lead to modulations ofwavenumber and frequency, as well as arnplitude, with the frequency dePendent on bothwavenumber and arnplitude (Witham, l974; Philips, l98l ). These medulations are not justtheoretical curiossities but have important conSequences in oceanography and meteorology, aswell as naval architecture and ocean engineering (honguer-Higgins, l980).By means of Hilbert transfOrm technique, Melvill…     

Application of Wavelet Algorithm to Spectral Analysis of Oceanic Waves and Offshore Structure Responses

Fourier transform (FT) is a commonly used method in spectral analysis of ocean wave and offshore structure responses,but it is not suitable for records of short length.In this paper another method,wavelet transform (WT),is applied to analyze the data of short length.The Morlet wavelet is employed to calculate the spectral density functions for wave records and simulated Floating Production Storage and Offloading (FPSO) vessels' responses.Computed wave data include simulated wave data based on JONSWAP spectr...     

Analysis and simulation of wave records through fast Hartley transform

The Hartley transform, a real-valued alternative to the complex Fourier transform, is presented as an efficient tool for the analysis and synthesis of ocean surface wave records. Basic theoretical properties of this real-valued transform are briefly reviewed. Similarities and differences between Fourier and Hartley integral transforms, as well as computational benefits and disadvantages between numerical algorithms used to evaluate their discrete versions, are presented. The fast Hartley transform algorithm is used to simulate stationary Gaussian time series of the sea surface elevation and to estimate the spectral density function, the Hilbert transform and the envelope function of wave records.     

浅谈数学变换在海洋技术中的应用

根据以往的工作积累,作者在文中介绍了在海洋技术中得到应用的几种数学变换,包括基于Fourier变换的频谱分析、波浪分离、相关分析及定义的H artley实现,连续M orlet小波变换在波浪信号分析中的应用,以及离散正交小波变换的降噪作用与悬沙图像的特征提取。文中通过公式推导和数据比较,展示了数学变换在海洋技术应用中的科学魅力。     

Relationship Between Mean Length and Mean Period of Wind Waves

1.IntroductionGreat progress has been madeinthe statistics of sea waves based onthe envelopetheory of Gaus-sian processes.Longuet-Higgins(1975,1983)first obtainedthe joint probability distributionfunction(PDF)of wave heights and periods.His work was exten…     

Application of wavelet transform analysis to landslide generated waves

The aim of this paper is to illustrate the results of a preliminary study on aerial landslide-generated waves, which has been mainly intended to establish a method for analyzing water surface records. Some simple physical experiments, reproducing the Scott Russell's wave generator, were carried out in a small two-dimensional wave flume; the Wavelet Transform (WT) is applied to analyze wave measurements and it is shown that useful information can be obtained by means of this technique. The celerity of impulsively generated waves, reflection by an overflow structure and seiching phenomena of the flume are studied. A discussion of the results along with some remarks about ongoing research is also given.     

Hartley变换在海洋工程中的应用研究

Hartley变换是一种基于谐函数的实变换,具有Fourier变换的特性,在海洋工程中使用Fourier变换的大部分应用都可以通过Hartley变换实现,并且快速Hartley变换的计算效率是快速Fourier变换的2倍,并易于实现,所以Hartley变换可以在许多应用中代替Fourier变换。详细介绍了Hartley变换在海洋工程领域的应用,包括:波谱分析、波浪分离、PIV(粒子图像测速法)技术和微分方程的Hartley域变换,举例说明了Hartley变换在节约计算空间和提高计算效率上具备的优越性。     

Bragg Reflection of Waves by Different Shapes of Artificial Bars

Experiments are performed in a wave flume to demonstrate the Bragg reflection of linear gravity waves by artificial bars. Three different artificial bars with rectangular, triangular and rectified cosinoidal shapes are placed discretely on the seabed for measurement of the Bragg reflection. A series of experimental conditions including the number of bars, the pe-riodic bar spacing, the water depth and various wave conditions are tested. Key parameters influencing the Bragg resonances are investigated. The experimental data are compared with the values from both theoretical and numerical models. Some key parameters have proved to be effective in describing the primary resonances. Predictive equations of the charac-teristics for the Bragg reflection are proposed in this paper.     

Analysis of Energy Overshoot of High Frequency Waves with Wavelet Transform

—A study is made on the overshoot phenomena in wind-generated waves.The surface displace-ments of time-growing waves are measured at four fetches in a wind wave channel.The evolution of highfrequency waves is displayed with wavelet transform.The results are compared with Sutherland's. It isfound that high frequency wave components experience much stronger energy overshoot in the evolution.The energy of high frequency waves decreases greatly after overshoot.     

Reflection of Oblique Incident Waves by Breakwaters with Partially-Perforated Wall

The reflection of oblique incident waves from breakwaters with a partially-perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigenfunction expansion method is applied to expand velocity poten-tials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with experimental data. The effect of porosity, the relative chamber width, the relative water depth in the wave absorbing chamber and the water depth in front of the structure are discussed.     

Hilbert变换在海浪波高与周期联合分布函数中的应用

Longuet-Higgins(1983)[1]导出了波高与周期的联合分布函数,此分布函数虽然与实际数据符合良好,但存在很大的缺陷,如:由此分布函数得出的波高分布为形式较为复杂的非Rayleigh分布,很难应用于工程计算中。孙孚(1988a)[2]应用射线理论导出了一种波高与周期联合分布,虽然弥补了Longuet-Higgins的一些缺陷,但推导过程过于复杂。本文在窄谱假定下通过应用Hilbert变换方法得出新的分布函数并与前两者比较,表明Hilbert变换的方法不但简便,而且完全克服Longuet-Higgins的不足,可以方便的应用于工程计算中。本文也为Hilbert变换的方法在工程中的应用提供了理论依据。     

Analytical Study on Transmission and Reflection of Non-Linear Shallow Water Waves

The analytical study is made by using the method of matched asymptotic expansions on the transmission and reflection of solitary waves and cnoidal waves on two-dimensional floating bodies. The solutions give explicitly the variation pattern of the transmitted waves and the characteristics of the reflected waves, including the wave profile, amplitude, phase shift and evolution. The effects of the gap between the body and the sea bottom on the transmission and reflection of those waves are also discussed.     

从航磁资料延拓出海面磁场

因延拓深度有限,现有的位场向下延拓方法不能从航磁资料向下延拓出海面的磁场.位场大深度向下延拓方法——迭代法,可以从航磁资料向下延拓出海面的磁场,得出与航磁同比例尺的海面磁力图,可大大提高海洋磁测成果的综合利用率.介绍了迭代法位场延拓原理.用迭代法对实际资料进行了处理,讨论了误差产生的原因.对比了迭代法与快速傅立叶变换法(FFT)在位场向下延拓中的效果,迭代法显著优于FFT法.     

Comparison of methods for calculation of the wave envelope

Different methods for computing of the Hilbert transform are reviewed and discussed in this work. Statistical characteristics of the wave envelope determined by different methods are compared with the theoretical ones. Field data, collected at the Portuguese coast are used in this comparative analysis. The advantages and shortcomings of the different methods for determination of the wave envelope are shown and discussed.     

Experimental Study of Hydrodynamic Loading on Submarine Composite Pipelines under the Action of Waves and Current

- This article is aimed at the experimental study of the hydrodynamic loading induced by waves and current acting on the JZ 20-2 submarine composite pipelines. The corresponding hydrodynamic coefficients obtained in this experimental study can be applied to engineering projects.     

Modelling of Random Waves over Submerged Breakwaters and Its Application to Reflection Estimation

1.IntroductionGreat efforts have been devoted to the protection of coastal areas over many years by erectingdikes,seawalls,groin systems,and detached breakwaters.The sea walls,jetties,detached breakwa-ters,etc.are traditionally adopted as absorbingfacilit…