Radar Investigation of the Structure of Wind Waves

Radar data from three experiments are analysed. Scatter characteristics of 50 cm wind-generated waves have been investigated with a C-band radar in a large wind-wave tank. Evidence of wave groups in sea clutter from the west coast of Scotland in the Sound of Sleat is also presented. The spectrum of the waves in the sound is narrow-banded and the waves are young, like the wind-wave spectrum in the laboratory. Clutter measurements, collected on the English south coast at Portland, of more ocean-like waves with broad band spectra also suggest the presence of wave groups. Evidence of the presence of wave groups is demonstrated in range-time images, as well as in the Fourier domain. Some ad hoc processing schemes, the normalised variance and binary threshold techniques, were successfully applied to enhance the appearance of the wave groups. The wind waves change frequency with fetch in the wave tank and the downshifting process is investigated using range-frequency maps of the radar data. The waves appear to change frequency in discrete steps that are associated with wave breaking events. The difference in wave period before and after breaking could be measured, and a wave crest was shown to be lost to compensate for the change in period, as expected. Some downshifting could also be measured in the Sound of Sleat. The ratio of wave group frequency and wave frequency is inaccordance with Benjamin-Fier sideband instability theory, as it is for the data measured at Portland. This revised version was published online in July 2006 with corrections to the Cover Date.     

Investigation of the space structure of the free-surface profile of forced circular waves in a bounded basin of variable depth

We perform the numerical analysis of the influence of variations of the geometric characteristics of an annular basin of variable depth on the space structure of wave motions generated by the oscillations of atmospheric pressure periodic as functions of time. Within the framework of the linear theory of long waves, we determine (with regard for the action of the Coriolis force) the ranges of periods inside which the free surface of liquid has a fixed number of nodes. The dependence of these ranges on the parameters of the basin is established and the shapes of the free-surface profiles are compared for circular and axisymmetric waves.Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 14–23, September–October, 2004.This revised version was published online in May 2005 with corrections to cover date.     

Comparison of Linear Level I Green-Naghdi Theory with Linear Wave Theory for Prediction of Hydroelastic Responses of VLFS

Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate estimation of their hydroelastic responses to waves is very important for the design. Recently, an efficient numerical algorithm was developed by Ertekin and Kim (1999). However, in their analysis, the linear Level I Green-Naghdi (GN) theory is employed to describe fluid dynamics instead of the conventional linear wave (LW) theory of finite water depth. They claimed that this linear level I GN theory provided betler predictions of the hydroelastic responses of VLFS than the linear wave theory. In this paper, a detailed derivation is given in the conventional linear wave theory framework with the same quantity as used in the linear level I GN theory framework. This allows a critical comparison between the linear wave theory and the linear level I GN theory. it is found that the linear level     

Internal Wave Generation by Tidal Flow over a Continental Shelf Slope

The generation process of internal waves by strong tidal flow over a continental shelf slope is reproduced using a multi-level numerical model. On the basis of the numerical results, the crucial role of the tidal advection effect in the generation process of internal waves is demonstrated. The close relation between the resulting internal waveform and the strength of the tidal advection effect is also examined. The barotropic forcing on the internal wave actually works within a relatively small horizontal scale over the top of the continental shelf slope. When the maximum internal Froude number at the shelf break (Fr_m) is less than about 0.6, the amplitude of the resulting internal wave is almost proportional to F_rm. When F_rm is more than about 0.6, however, the amplitude of the resulting internal wave becomes larger than predicted by linear theory. In particular, when F_rm is more than unity, the time period during which the shoreward propagating internal wave stays in the barotropic forcing region becomes much longer. Consequently, the internal wave is significantly amplified with the horizontal scale approaching that of the barotropic forcing, which concentrates in a relatively small region over the top of the continental shelf slope. This revised version was published online in July 2006 with corrections to the Cover Date.     

Second-order wave maker theory using force-feedback control. Part II: An experimental verification of regular wave generation

This paper provides an experimental verification of the new wave maker theory outlined by Spinneken and Swan [2009. Second-order wave maker theory using forcefeedback control. Part I. A new theory for regular wave generation. Ocean Engineering, in press, doi:10.1016/j.oceaneng.2009.01.019]. This theory concerns the generation of regular waves by a flap-type wave maker using force-feedback control, providing the first quantitative evidence of the inherent advantages of this latter approach. When the wave maker is controlled by a first-order force command signal, comparisons between the theory and experimental observations confirm two key points: (i) The first-order behaviour is crucial for the absorption characteristics of the machine. (ii) The second-order behaviour leads to a spurious, or unwanted, freely propagating second harmonic that is substantially smaller in amplitude when compared to an identical wave paddle operating with first-order position control. Both aspects of this work, effective absorption and reduced second-order spurious wave generation, are investigated over a broad range of wave frequencies and shown to be widely applicable. Furthermore, the theory also provides a force command signal correct to second order. This is introduced in a separate set of experiments and shown to provide further improvement in the quality of the wave generation.     

Wave force on vertically submerged circular thin plate in shallow water

The paper presented is a solution of shallow water wave force, using small amplitude linear wave theory on two-dimensional vertically submerged circular thin plates under three different configurations: (1) a surface-piercing circular thin plate, (2) a submerged circular thin plate, and (3) a bottom-standing circular thin plate. Finally Morison's equation is used for the determination of wave force which is based on the linear wave theory. The plate is submerged in water near the shore on uniformly sloping bottom. The solution method is confined in a finite domain, which contains both the region of different depth of water and the plate. Laplace's equation and boundary value problems are solved in a finite domain, by the method of separation of variables and the small amplitude linear wave theory. The variation of horizontal force by single particle, total horizontal force and moment with respect to the wave amplitude are obtained at different depth of water and at different wave period. It is observed that the force and moment are converging with the increase of wave period and the gradients of force and moment with respect to the wave amplitude are extremely high for lower wave period.     

Seasat altimeter sensor file algorithms

The Seasat altimeter is designed to measure three parameters important to oceanography: height of the spacecraft above the ocean surface (h), significant wave height (H_{1/3}), and ocean backscatter coefficient (sigmadeg) from which surface winds may be inferred. Since the measurement process is indirect, and the measurement environment is complicated by many factors affecting the instrument readings, corrections to the raw data are needed before they are used to compute geophysical parameters. These corrections are accomplished by the Seasat altimeter sensor file algorithms. The purpose of this paper is to describe these algorithms, why they are needed, how they are implemented, and their evaluation using in-flight data.     

Spectral wave data assimilation for the prediction of waves in the North Sea

Spectral observations from pitch-and-roll buoys have been assimilated in a North Sea wave model, in order to study their impact on the wave analysis and forecast. The assimilation is based on Optimal Interpolation (OI) of a limited number of characteristic spectral parameters. In a case study, the propagation of the corrections through the model domain is followed, and it is clarified for which wave conditions the data assimilation has the largest influence on the forecast: this is especially the case for swell waves with long travel times between the assimilation site and the location where validation is carried out. A 1-year test has been carried out in which an analysis and subsequent forecast were produced four times a day. From a statistical analysis of the results a modest but systematic improvement of the 12-h forecast is found. When only swell cases are selected, the impact is more pronounced. It is argued that for shelf seas like the North Sea, more progress is to be expected from extension of the ‘conventional' observations network (buoys and wave radars) than from satellite measurements.     

Nonlinear Wave Force on Pier Group in Shallow Water

Based on the 1st order cnoidal wave theory, the wave diffraction around the pier group inshallow water is studied in this paper. The formulas for calculating the nonlinear wave forces are also presented here. In order to verify the theoretical results, model tests are conducted in the wave flume in The State Key Laboratory of Coastal and Offshore Engineering located in Dalian University of Technology. The range of the wave parameters in the experiments is characteristic wave period T g/d~(1/2) = 8.08- 22.86, characteristic wave height H/ d= 0.1 ~ 0.45. The results obtained from the experiments agree with the theoretical results quite well. It is shown that, in shallow water the nonlinear wave forces acting on a pier group are greater than those calculated by linear wave theory, the value of increment in wave force increases with the increases of the nonlinearity of the wave. In the wave range studied in this paper, the nonlinear wave force can reach over 4 times the force calculatecd by linear wave theory. Thus, it is suggested that, when Tg / d~(1/2)> 8, the wave force on the piers in the pier group in shallow water should be calculated by using the cnoidal wave theory.     

Transformation of a strongly nonlinear wave in a shallow-water basin

The transformation of a nonlinear wave in shallow water is investigated analytically and numerically within the framework of long-wave theory. It is shown that the nonlinearity parameter (the Mach number), which is defined as the ratio of the particle velocity in the wave to the propagation velocity, can be well above unity in a deep trough and that a jump appears initially in the trough. It is demonstrated that shockwave amplitudes at large times change in accordance with the prediction of weakly nonlinear theory. The shock front generates a reflected wave, which, in turn, transforms into a shock wave if the initial amplitude is large enough. The amplitude of the reflected wave is proportional to the cube of the initial amplitude (as predicted by weakly nonlinear theory) over a wide range of amplitudes except for the case of anomalously strong nonlinearity. When there is a sign-variable sufficiently intense initial perturbation, the basic wave transforms into a positive shock pulse (crest) and the reflected wave turns into a negative pulse (trough).     

Local model approximation in the real time wave forecasting

The notion of data assimilation is common in most wave predictions. This typically means nudging of wave observations into numerical predictions so as to drive the predictions towards the observations. In this approach, the predicted wave climate is corrected at each time of the observation. However, the corrections would diminish soon in the absence of future observations. To drive the model state predictions towards real time climatology, the updating has to be carried out in the forecasting horizon too. This could be achieved if the wave forecasting at the observational network is made available. The present study addresses a wave forecasting technique for a discrete observation station using local models. Embedding theorem based on the time-lagged embedded vector is the basis for the local model. It is a powerful tool for time series forecasting. The efficiency of the forecasting model as an error correction tool (by combining the model predictions with the measurements) has been brought up in a forecasting horizon from few hours to 24 h. The parameters driving the local model are optimised using evolutionary algorithms.     

Second-order wavemaker theory for irregular waves

Through the last decade the theory for second-order irregular wave generation was developed within the framework of Stokes wave theory. This pioneering work, however, is not fully consistent. Furthermore, due to the extensive algebra involved, the derived transfer functions appear in an unnecessarily complicated form. The present paper develops the full second-order wavemaker theory (including superharmonics as well as subharmonics) valid for rotational as well as translatory wave board motion. The primary goal is to obtain the second-order motion of the wave paddle required in order to get a spatially homogeneous wave field correct to second order, i.e. in order to suppress spurious free-wave generation. In addition to the transfer functions developed in the line of references on which the present work is based, some new terms evolve. These are related to the first-order evanescent modes and accordingly they are significant when the wave board motion makes a poor fit to the velocity profile of the desired progressive wave component. This is, for example, the case for the high-frequency part of a primary wave spectrum when using a piston-type wavemaker. The transfer functions are given in a relatively simple form by which the computational effort is reduced substantially. This enhances the practical computation of second-order wavemaker control signals for irregular waves, and no narrow band assumption is needed. The software is conveniently included in a PC-based wave generation system—the DHI Wave Synthesizer. The validity of the theory is demonstrated for a piston type wavemaker in a number of laboratory wave experiments for regular waves, wave groups and irregular waves.     

A Spectral Approach for Determining Altimeter Wind Speed Model Functions

We propose a new analytical algorithm for the estimation of wind speeds from altimeter data using the mean square slope of the ocean surface, which is obtained by integration of a widely accepted wind-wave spectrum including the gravity-capillary wave range. It indicates that the normalized radar cross section depends not only on the wind speed but also on the wave age. The wave state effect on the altimeter radar return becomes remarkable with increasing wind speed and cannot be neglected at high wind speeds. A relationship between wave age and nondimensional wave height based on buoy observational data is applied to compute the wave age using the significant wave height of ocean waves, which could be simultaneously obtained from altimeter data. Comparison with actual data shows that this new algorithm produces more reliable wind speeds than do empirical algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Relative Trough Froude Number for initiation of wave breaking: Theory,experiments and numerical model confirmation

It is important to accurately locate the wave breaking region for the calculation of nearshore hydrodynamics. Energy from breaking waves drives hydrodynamic phenomena such as wave set-up, set-down, wave run-up, longshore currents, rip currents, and nearshore circulation. Numerous studies have been undertaken to describe when and where wave breakings occurs. Recent development of computer resources permits the use of phase-resolving numerical models for the study of wave propagation, transformation, and nearshore hydrodynamics. This requires new types of wave breaking criteria for the numerical model. The Relative Trough Froude Number (RTFN) is a new wave breaking criterion. This model is based on the moving hydraulic jump concept, therefore it satisfies properly posed boundary-value conditions. It has been experimentally proved that a critical RTFN at the initiation of wave breaking is consistent with and without the presence of an opposing current, but previous efforts did not investigate the theory for the critical value. This paper provides a theoretical analysis and a numerical analysis to demonstrate why the RTFN theory works as a wave breaking initiation (trigger) index. The theoretical analysis provides a universal constant for the initiation of wave breaking for all water depths assuming the Miche formula properly describes the wave breaking condition. A subroutine for wave breaking in a numerical model, FUNWAVE was modified to include the RTFN trigger. The numerical model was calibrated with data from wave tank experiments, and it was found that the critical condition is very close to the theoretical number, CTFN = 1.45. A second paper (in preparation) provides details of the theory and experiments for a second criterion for termination of wave breaking. The time scale for the establishment of the breaking region i.e., between the initiation position and termination position, depends upon the additional momentum present under turbulent condition within the breaking wave. This subject is not considered herein.     

Stability of planetary waves in a two-layer system

A stability of planetary waves on an infinite beta-plane is investigated in an idealized two-layer fluid system for the large local Rossby numberM. When a primary wave is barotropic, two kinds of barotropic instability modes are found. One of them was previously discussed byGill (1974). When a primary wave is baroclinic, two different kinds of modes that enable barotropic and baroclinic energy transfers are found. The one that has the larger growth rate gains its energy mainly from the mean shear of the primary wave when the internal rotational Froude numberF is smaller than 1/2. WhenF is larger than 1/2, however, the available energy conversion of the primary wave is dominant. This mode has a fairly large part of its energy in the barotropic motion although the primary wave is purely baroclinic.The effect ofO(M ^–2) corrections is found to have a stabilizing influence on all symmetrical modes. The geophysical applications of the present analysis are suggested in the context.     

An intercomparison of GEOSAT, TOPEX and ERS1 measurements of wind speed and wave height

Mean monthly values of altimeter wind speed and wave height are compared with data from NDBC buoys. As a result of these comparisons, corrections are made to the raw data products available from these satellites. Data from the GEOSAT, TOPEX and ERS1 missions corrected in this fashion are used to show that there have been no measurable changes in the global wind and wave climate during the 10 years spanned by these various missions. It is proposed that the corrected values of wind speed and wave height provide the basis for the formation of a long-term global data base which spans the periods of these multiple missions.     

空波包理论在海浪群性研究中的应用

用 Monte Carlo方法数值模拟海浪 ,研究其波包曲线跨某参考水平的波包中空波包所占的平均比例 ,并与 Ditlevsen和 L indgren关于空波包的理论相比较。结果表明 ,在二阶近似下该理论近似适用于海浪。在此基础上对 Longuet- Higgins的群性波包理论进行修正。修正后的理论与数值结果的比较表明本文所做的修正是十分有效的。修正后的群性波包理论克服了原理论的某些固有缺陷     

Long-Term Validation of Wave Height Measurements from Altimeters

Since July 1991, six altimeter missions have been launched successfully, and they have provided almost continuous wave height measurements for more than 12 years. Long-term series of wave height measurements are of major interest for climatology and oceanic wave modeling. Before using such data, the measurements have to be validated, and the homogeneity of the data from various satellites has to be checked. Significant wave height measurements from ERS, TOPEX/Poseidon, GEOSAT Follow-on, Jason-1 and ENVISAT altimeters are validated using cross-altimeter and buoy comparisons. Emphasis is put on the two recent missions Jason-1 and ENVISAT. Corrections for biases and trends are proposed for the six altimeters, allowing the generation of consistent and homogeneous data. Tests of these corrections are performed over global ocean simple statistics.     

The Nonlinear Wave Force on a Circular Cylinder in Shallow Water

Based on the 1st order cnoidal wave theory, the nonlinear wave diffraction around a circular cylinder in shallow water is studied in this paper. The equation of the wave surface around the cylinder is formulated and by using this formula the wave surface elevation on the cylinder surface can be obtained. In this paper, the formula for calculating the cnoidal wave force on a circular cylinder is also derived. For the wave conditions which are often encountered in practical engineering designs, the ratios of the nonlinear wave forces to the linear wave forces are calculated, and the results are plotted in this paper for design purposes. In order to verify the theoretical results, model tests are conducted. After comparing the test results with the theoretical ones, it is concluded that, in shallow water, for the case of T g / d~(1/2) > 8-10 and H / d > 0.3, the cnoidal wave theory should be used to calculate the wave action on a cylindrical pier.