A new method for separation of 2D incident and reflected waves by the Morlet wavelet transform

A new method based on the Morlet wavelet transform for separating a 2D wave field into incident and reflected waves is proposed in this paper. The principle of this method, first, is derived for constant depths. Then, using the linear shoaling theory, the method is extended to an arbitrary sloping bathymetry. Owing to the time-frequency characteristic of wavelet transform, the present method can separate waves in the real time domain and is not confined by the stationary assumption of waves. The efficiency and accuracy of this method are demonstrated using numerical simulated data.     

斜向不规则波入、反射波分离的实验研究

斜向入射的不规则波在海岸结构物前发生反射形成入、反射波共存的波浪场,对这种物理场的入、反射波的分离是海岸工程研究的一个重要课题.改进了一种可用于斜向入射的不规则波分离的两点法,使得测波阵列的两波高仪可布置在结构物前任何方向上.将此方法应用于三维波浪水池的物理模型试验研究,试验了不同的两波高仪的组合、不同的基床高度、不同的入射方向和不同的波浪要素等各种条件对分离结果的影响,结果表明,各种情况在满足非奇异条件下可得到较好的分离结果.该方法计算简便,可以给出较准确的反射系数和入、反射波的频谱.     

斜向入射波与反射波的分离

提出了一种分离斜向入射波和反射波的方法,波浪可以是规则波、不规则波,波向可以任意.在一定的限制条件下,采用两点浪高仪的波浪信号就可将斜向入射波和反射波分离.     

Reply to “Discussion of wave setup and setdown generated by obliquely incident waves” by F. Shi and J.T. Kirby

The authors are grateful to the derivation and correction addressed by Shi and Kirby (2008) for the calculation of the wave setup and setdown induced by obliquely incident waves. The mathematical equations for the expression of setup and setdown are rederived in which the velocity potential is expanded to the second-order on the still water lever. The correct form of setdown presented by Shi and Kirby is confirmed in the present paper.     

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.     

A model for obliquely incident wave interacting with a multi-layered object

This paper presents an analytical solution for scattering of oblique incident, small amplitude, monochromatic wave trains by a stationary rigid multi-layered objects with rectangular cross-section. The object is infinite long and consists of multilayers, which can be either solid or permeable. This paper extends the previous work by Hu and Liu [1] from normal incident wave condition with a special object configuration to oblique incident waves with multi-layered object. The present model is validated with several existing solutions for normal/oblique waves interacting with a single object; excellent agreement is observed. New numerical results are presented to investigate the effects of incidence angle on reflection, transmission and energy loss coefficients for a combined floating and bottom-mounted permeable breakwater. A new floating board-cage breakwater is developed from the present model and its solutions are discussed in detail. A computer program, AWAS-P, has been updated so that it is applicable for both oblique and normal incident waves, while the object is multi-layered.     

Tests and applications of an approach to absorbing reflected waves towards incident boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.     

Separation of incident and reflected waves in wave–current flumes

A technique is developed to separate the incident and reflected waves propagating on a known current in a laboratory wave–current flume by analyzing wave records measured at two or more locations using a least squares method. It can be applied to both regular and irregular waves. To examine its performance, numerical tests are made for waves propagating on quiescent or flowing water. In some cases, to represent the signal noise and measurement error, white noise is superimposed on the numerically generated wave signal. For all the cases, good agreement is observed between target and estimation.     

Discussion of “Wave setup and setdown generated by obliquely incident waves” by T.-W. Hsu et al., Coastal Engineering, 53, 865–877, 2006

In the recent paper by Tai-Wen Hsu, John R.-C. Hsu, Wen-Kai Weng, Swun-Kwang Wang, and Shan-Hwei Ou (Coastal Engineering, 53, 865–877, 2006), the authors derived theoretical formulations for calculating the wave setup and setdown induced by obliquely incident waves on a beach. The derivation of an expression for setdown contains errors which would lead to an imbalance in longshore momentum flux outside the surfzone. We correct their derivation and give results in terms of the radiation stress concept in a general case including an oblique wave incidence. We also point out that the correct form of wave setdown is important to describe the zero-net force in the momentum balance outside the surfzone.     

直立堤前海床的局部冲刷

对不规则波作用下直立堤前海床的局部冲刷进行了研究。研究了由于波浪作用导致床面的底沙运动,从而造成提前海床的局部冲刷,即所谓的“相对粒沙”的情况。报导了;(1)堤前海床面为水平、堤下无基床情况下的堤前局部冲刷,以及堤下有明基床时基床尺度对堤前局部冲刷的影响;(2)堤前海床面为斜坡面时堤前的局部冲刷,以及当堤下有明基床时基床尺度对堤前局部冲刷的影响;(3)从波浪作用下床面边界层的理论分析出发,对于在不规则波作用下,离堤面愈远处的冲刷坑深度愈小的事实给出了解释。     

Scattering of obliquely incident water waves by partially reflecting non-transmitting breakwaters

In the present paper, analytic solutions are derived for scattering of water waves obliquely incident to a partially reflecting semi-infinite breakwater or breakwater gap. In order to examine the correctness of the derived solutions, they are compared with the solutions derived by McIver (1999) and Bowen and McIver (2002) for a semi-infinite breakwater and a breakwater gap, respectively, in the case of perfect reflection. The derived analytic solutions are used to investigate the effect of reflection coefficient of the breakwater and wave incident angle upon the tranquility at harbor entrance. The tranquility is deteriorated by the reflected waves as the reflection coefficient increases and as waves are incident more obliquely.     

Separation of incident and reflected waves over sloping bathymetry

An existing 2D method for separating incident and reflected waves over a horizontal bed [Frigaard, P., Brorsen, M., 1995. A time domain method for separating incident and reflected irregular waves. Coastal Eng., 24, 205–215.] is modified to account for normally incident linear waves propagating over a bed with arbitrary 2D bathymetry. Linear shoaling is used to determine the amplitude and phase change between two measurement positions; thereafter the existing technique can be applied. Comparisons between the existing and modified methods are made using numerically simulated data. Errors in the reflection coefficient are found to be small for large reflection coefficients, but may become large if reflection is low. However, if an accurate assessment of the amplitude of the incident and reflected wave trains is required, the bathymetry must be accounted for in order to avoid significant errors (up to 90% for cases considered).     

Wave profile measurement by wavelet transform

A new technique for measuring wave profiles by wavelet transform using the Mexican Hat wavelet as the mother wavelet is introduced. This technique has the potential to provide low cost, high resolution field measurements of wave profiles in the laboratory. The experiments to capture the video image of the wave profile were carried out in a wave flume. Then, the Mexican Hat wavelet was adopted to trace out the exact profiles of the waves from the captured video images. The series of tests on numerical data and video images show promise as means of detecting two-dimensional profiles of waves.     

Near-optimal control of a wave energy device in irregular waves with deterministic-model driven incident wave prediction

This paper investigates wave-by-wave control of a wave energy converter using incident wave prediction based on up-wave surface elevation measurement. The goal of control is to approach the hydrodynamically optimum velocity leading to optimum power absorption. This work aims to study the gains in energy conversion from a deterministic wave propagation model that accounts for a range of group velocities in deriving the prediction. The up-wave measurement distance is assumed to be small enough to allow a deterministic propagation model, and further, both wave propagation and device response are assumed to be linear. For deep water conditions and long-crested waves, the propagation process is also described using an impulse response function (e.g. [1]). Approximate low and high frequency limits for realistic band-limited spectra are used to compute the corresponding group velocity limits. The prediction time into the future is based on the device impulse response function needed for the evaluation of the control force. The up-wave distance and the duration of measurement are then determined using the group velocity limits above.A 2-body axisymmetric heaving device is considered, for which power capture is through the relative heave oscillation between the two co-axial bodies. The power take-off is assumed to be linear and ideal as well as capable of applying the necessary resistive and reactive load components on the relative heave oscillation. The predicted wave profile is used along with device impulse response functions to compute the actuator force components at each instant. Calculations are carried out in irregular waves generated using a number of uni-modal wave spectra over a range of energy periods and significant wave heights. Results are compared with previous studies based on the use of instantaneous up-wave wave-profile measurements, both without and with oscillation constraints imposed. Considerable improvements in power capture are observed with the present approach over the range of wave conditions studied.     

The reflection of oblique waves by an infinite number of partially perforated caissons

This study examines the reflection of obliquely incident waves by an infinite array of partially perforated caissons. Based on the linear potential theory, an analytical solution of the present problem was developed by means of the matched eigenfunction expansion method. The solution was obtained in a single strip consisting of the semi-infinite narrow region in front of a caisson and the fluid domain inside this caisson. It was then extended to the whole fluid domain by using the periodicities of the structure and the incident waves along the length of the caissons. The present model was validated by comparing the reflection coefficients of several limiting cases with the corresponding results obtained by previous researchers. Numerical experiments were also conducted to examine the variations of the reflection coefficient versus its main effect factors. The numerical results indicate the differences between the present model and the previous limiting cases, and some helpful results are recommended for practical engineering.     

Numerical modelling of a point-absorbing wave energy converter in irregular and extreme waves

Based on the Navier-Stokes (RANS) equations, a three-dimensional (3-D) mathematical model for the hydrodynamics and structural dynamics of a floating point-absorbing wave energy converter (WEC) with a stroke control system in irregular and extreme waves is presented. The model is validated by a comparison of the numerical results with the wave tank experiment results of other researchers. The validated model is then utilized to examine the effect of wave height on structure displacements and connection rope tension. In the examined cases, the differences in WEC’s performance exhibited by an inviscid fluid and a viscous fluid can be neglected. Our results also reveal that the differences in behavior predicted by boundary element method (BEM) and the RANS-based method can be significant and vary considerably, depending on wave height.     

基于小波变换法定义的波群参数

通过小波变换分析的波能过程定义了两个描述波浪群性的参数,由数值模拟波浪和实测波浪资料对其与常用的波群参数进行对比分析,结果表明基于小波波能过程定义的群性参数是有效的,从而展示了小波变换用于在时频域上分析波群的能力。详细探讨了波浪记录长度对群性参数稳定性的影响,分析结果表明,波浪观测长度对于波群参数的影响较大,在考虑波浪群性的波浪模拟及分析时,建议模拟时间长度应在400~500个波以上。     

Wave parameters and functions in wavelet analysis

A preliminary study of wave parameters and functions in wavelet analysis is conducted in this paper. The Morlet wavelet transform is used to calculate the time–frequency wavelet energy density function, its volume (i.e. the total energy), its frequency-integral (i.e. the wavelet smoothed instantaneous wave energy history), its time-integral (i.e. the wavelet spectral density function), and two non-dimensional wave indices (NIF, NIT). The processing of the measured wave data obtained from the Chi-Gu coastal observation tower during the period August 2000 to July 2001 indicates that the inter-comparison of wavelet smoothed instantaneous wave energy history and smoothed instantaneous wave energy history (SIWEH) as defined by Funke and Mansard (Proc 17th Int Conf on Ocean Eng, 1980) can reveal the noise structure of the wave signal. The wave data with index NIF greater than 2 is always accompanied with noise, therefore NIF can be used as one of the data quality criteria. The index NIT is linearly correlated with the significant wave period and with the significant wave height, therefore NIT can be used to study the wave growth and decaying phenomena.     

Cross-shore variations of wave groupiness by wavelet transform

This paper proposes a new definition of groupiness factor (GF) based on the local wavelet energy density of the wave time series to describe the groupiness degree of waves. The main advantage of this new GF is that the effect of the operational definition on it is smaller than that on SIWEH-based GF or envelop-based GF. Then, the new GF is used to study the groupiness variations of mechanically generated irregular waves in a wave flume propagating on a slope of 1:45. The results of present study show that the decrease of groupiness in the coast is triggered by breaking. And energy distribution along the record time for the first harmonics of waves in the surf zone, which becomes more uniform than that out the surf zone, is the main reason causing the decrease of groupiness.     

基于小波变换和HIS变换的海冰SAR与光学遥感影像融合方法研究

Sea ice as a disaster has recently attracted a great deal of attention in China. Its monitoring has become a routine task for the maritime sector. Remote sensing, which depends mainly on SAR and optical sensors, has become the primary means for sea-ice research. Optical images contain abundant sea-ice multi-spectral information, whereas SAR images contain rich sea-ice texture information. If the characteristic advantages of SAR and optical images could be combined for sea-ice study, the ability of sea-ice monitoring would be improved. In this study, in accordance with the characteristics of sea-ice SAR and optical images, the transformation and fusion methods for these images were chosen. Also, a fusion method of optical and SAR images was proposed in order to improve sea-ice identification. Texture information can play an important role in sea-ice classification. Haar wavelet transformation was found to be suitable for the sea-ice SAR images, and the texture information of the sea-ice SAR image from Advanced Synthetic Aperture Radar(ASAR) loaded on ENVISAT was documented. The results of our studies showed that, the optical images in the hue-intensity-saturation(HIS) space could reflect the spectral characteristics of the sea-ice types more efficiently than in the red-green-blue(RGB) space, and the optical image from the China-Brazil Earth Resources Satellite(CBERS-02B) was transferred from the RGB space to the HIS space. The principal component analysis(PCA) method could potentially contain the maximum information of the sea-ice images by fusing the HIS and texture images. The fusion image was obtained by a PCA method, which included the advantages of both the sea-ice SAR image and the optical image. To validate the fusion method, three methods were used to evaluate the fused image, i.e., objective, subjective, and comprehensive evaluations. It was concluded that the fusion method proposed could improve the ability of image interpretation and sea-ice identification.