Comparison of experimental irregular water wave elevation and kinematic data with new hybrid wave model predictions

Surface water wave elevations and kinematics from four unidirectional irregular wave trains, with a Pierson and Moskowitz or JONSWAP random wave spectrum, were measured in the laboratory using resistance wave probes and a laser Doppler anemometer. The wave elevation data, velocity time series, extreme (largest) wave horizontal velocity profiles and extreme wave acceleration fields are compared with the predictions of a new wave kinematics model, named the hybrid wave model. Irregular waves are commonly viewed as the summation of many linear wave components of different frequencies, but more accurate predictions of downstream surface elevations (wave evolution) and wave kinematics are attained by considering the non-linear interactions among wave components. The hybrid wave model incorporates these non-linear wave component interactions, and its wave evolution predictions and kinematics estimates are compared with laboratory measurements in this study. Linear random wave theory, Wheeler stretching and linear extrapolation wave kinematic prediction techniques are also compared. Comparisons between measurements and hybrid wave model estimates demonstrate its improved capability to predict velocity and acceleration fields and wave evolution in two-dimensional irregular waves.     

Measurement of water particle velocities in waves

Water surface profiles and horizontal and vertical water particle velocity components have been measured to investigate the properties of intermediate depth waves generated in the laboratory. The data has been compared with linear wave theory. It was found that linear theory predicted the attenuation of velocity field with depth successfully and that it overestimates both components of velocity slightly.     

Interactions between nonlinear water waves and non-wall-sided 3D structures

Interactions between water waves and non-wall-sided cylinders are analyzed based on velocity potential theory with fully nonlinear boundary conditions on the free surface and the body surface. The finite element method (FEM) is adopted together with a 3D mesh generated through an extension of a 2D Delaunay grid on a horizontal plane along the depth. The linear matrix equation for the velocity potential is constructed by imposing the governing equation and boundary conditions through the Galerkin method and is solved through an iterative method. By imposing the gradient of the potential equal to the velocity, the Galerkin method is used again to obtain the velocity field in the fluid domain. Simulations are made for bottom mounted and truncated cylinders with flare in a numerical tank. Periodic waves and wave groups are generated by a piston type wave maker mounted on one end of the tank. Results are obtained for forces, wave profiles and wave runups. Further simulations are made for a cylinder with flare subjected to forced motion in otherwise still open water. Results are provided for surge and heave motion in different amplitudes, and for a body moving in a circular path in the horizontal plane. Comparisons are made in several cases with the results obtained from the second order solution in the time domain.     

Characteristics of breaking irregular wave forces on a monopile

The substructures of offshore wind turbines are subjected to extreme breaking irregular wave forces. The present study is focused on investigating breaking irregular wave forces on a monopile using a computational fluid dynamics (CFD) based numerical model. The breaking irregular wave forces on a monopile mounted on a slope are investigated with a numerical wave tank. The experimental and numerical irregular free surface elevations are compared in the frequency-domain for the different locations in the vicinity of the cylinder. A numerical analysis is performed for different wave steepness cases to understand the influence of wave steepness on the breaking irregular wave loads. The wave height transformation and energy level evolution during the wave shoaling and wave breaking processes is investigated. The higher-frequency components generated during the wave breaking process are observed to play a significant role in initiating the secondary force peaks. The free surface elevation skewness and spectral bandwidth during the wave transformation process are analysed and an investigation is performed to establish a correlation of these parameters with the breaking irregular wave forces. The role of the horizontal wave-induced water particle velocity at the free surface and free surface pressure in determining the breaking wave loads is highlighted. The higher-frequency components in the velocity and pressure spectrum are observed to be significant in influencing the secondary peaks in the breaking wave force spectrum.     

Measurements of higher harmonic wave forces on a vertical truncated circular cylinder

Wave forces on a vertical truncated circular cylinder in Stokes waves with the wave slopes ranging from 0.06 to 0.24, are measured in a wave tank. The higher harmonic wave forces are compared with the available values from theories of the FNV (Faltisen–Newman–Vinje) model and Varyani solution. The first harmonic horizontal forces measured are much larger than the theoretical values from the FNV model, while the first harmonic vertical forces are well predicted by the Varyani theory. It was also found that the FNV model significantly overpredicts the second harmonic horizontal forces in high frequency waves, but under predicts the third harmonic forces. The differences between the actual measurement and the theory, in the second and third harmonic horizontal forces, become smaller at low wave frequencies as the wave slope increases. In addition, the transverse instabilities in the incoming waves with high wave slope were observed, which is due to the nonlinear modulation. Measurements were, thus, carried out before the instability occurred.     

Nonlinear wave interaction with a vertical circular cylinder: wave forces

Second-order wave forces on a large diameter vertical circular cylinder, computed according to a semi-analytic nonlinear diffraction theory, are compared to results of 22 laboratory experiments with regular waves. In general, predicted forces agree quite well with measured forces. In most tests, both measured and predicted maximum forces exceeded linear theory by 5 to 15%. In a few cases, however, the measured forces were less than those predicted by linear theory, in contrast to the second-order predictions. It is shown that these results are related to the phasing of various linear and nonlinear wave force components, and are consistent with those obtained by other investigators.     

The limiting wave height in wind-induced wave trains

The vertical acceleration threshold concept has been applied to evaluate the limiting wave height in the train of wind-induced waves propagated over a horizontal bottom. This concept yields very simple computation of the probability of breaking for stochastic sea in deep and finite water depths. The computations confirmed the available field and laboratory observations that the limiting wave steepness in the deep water is lower than the steepness predicted by Stokes. For shallow water depth, the limiting wave height is smaller than 0.55h. This conclusion is consistent with field as well as wave tank observations.     

Radar backscatter from mechanically generated transient breakingwaves. I. Angle of incidence dependence and high resolution surfacemorphology

This paper describes the results of an experimental investigation of the microwave backscatter from several laboratory generated transient breaking waves. The breaking waves were generated mechanically in a 35 m×0.7 m×1.14 m deep wave tank, utilizing chirped wave packets spanning the frequency range 0.8-2.0 Hz. Backscatter measurements, were taken by a X/K-band (10.525 GHz, 24.125 GHz) continuous wave Doppler radar at 30°, 45°, and 60° angles of incidence, and at azimuth angles of 0° and 180° relative to the direction of wave propagation. Surface profiles were measured with a high-speed video camera and laser sheet technique. Specular facets were detected by imaging the surface from the perspective of the radar. The maximum radar backscatter occurred in the upwave direction prior to wave breaking, was nearly polarization independent and corresponded to the detection of specular facets on the steepened wave face. This peak radar backscatter was predicted through a finite conductivity corrected physical optics technique over the measured surface wave profiles. Post break backscatter was predicted using a roughness corrected physical optics technique and the small perturbation method, which was found to predict the returns for vertical polarization, but to under predict the horizontal returns     

Green water overtopping analyzed with a SPH model

Wave overtopping on the decks of offshore platforms and ships can cause severe damage due to the high forces generated by the water. This phenomenon is analyzed within the framework of the Smoothed Particle Hydrodynamics (SPH) method. The presence of a fixed horizontal deck above the mean water level modifies strongly the wave kinematics. In particular, the flow in the wave crest is split into two, showing a different behavior above and below the deck. Numerical results generated by the SPH method are compared to laboratory experiments. The formation of a jet in the rear of the deck after overtopping is observed under extreme conditions.     

Experimental and numerical investigation of viscous effects on solitary wave propagation in a wave tank

Two-dimensional depth-averaged Boussinesq-type equations were presented with the consideration of slowly varying bathymetry and effects of bottom viscous boundary layer. These Boussinesq-type equations were written in terms of the horizontal velocity components evaluated at an arbitrary elevation in the water depth and the free surface displacement. The leading order effects of the bottom boundary layer were represented by a convolution integral in the depth-integrated continuity equation. To test the validity of the theory, a set of laboratory experiments was performed to measure the viscous damping and shoaling of a solitary wave propagating in a wave tank. The time histories of the free surface profiles were measured at several locations along the centerline of the flume. To compare these laboratory data with theoretical results, the two-dimensional Boussinesq-type equations were integrated across the wave tank, resulting in a set of one-dimensional equations, while the side-wall boundary layers were properly considered. The agreement between the experimental data and numerical results was very good. The bottom shear stress formula was also given and its impact on the sediment transport rate was discussed.     

SPH方法的孤立波与部分淹没结构物相互作用数值计算研究

为研究孤立波作用下结构物周围流场特征,基于无网格SPH方法,建立孤立波与海洋结构物相互作用模型,对不同波幅孤立波作用下部分淹没矩形结构物周围波面、流速、涡量及结构受力特征进行计算分析,探索了相对波高对非淹没结构物周围流场的影响规律。结果表明:流场特征与相对波高密切相关,相对波高较小时,波面、流速、涡量及结构荷载均较为光滑,相对波高在0.2以上时,波峰爬升至结构物顶部并在越过结构物后与水槽内水体碰撞造成流场波动,波面、流速、涡量及结构荷载的波动幅度随着相对波高增大而增大,流场更加复杂,结构物水平和垂向负压也越大,且结构物周围涡分布逐渐向深度方向和下游方向发展。     

Wake II model for hydrodynamic forces on marine pipelines including waves and currents

The Wake II model for the determination of the hydrodynamic forces on marine pipelines is extended to include currents and waves. There are two main differences between the Wake II and the traditional model. First, in the Wake II model the velocity is modified to include the pipe's encounter with the wake flow when the velocity reverses. Second, the model uses time dependent drag and lift coefficients. The flow field is assumed to be the linear superposition of regular waves and uniform current and is treated as wave only but in two different phases. The model requires eight empirical parameters that are obtained from comparisons with field data for various Keulegan–Carpenter numbers and current to wave ratios. The effective velocity and the force predictions are compared with field data from Exxon Production Research Company and with the conventional model. The model gives satisfactory results and predicts lift forces that in shape, magnitude and phase relative to the velocity are in very close agreement with measured forces. For the horizontal forces the results are very accurate. A substantial improvement is obtained over the predictions with the conventional model. This work is applicable to the design of submarine pipelines laying on the sea bottom in water depths where waves or waves and currents contribute to the hydrodynamic forces.     

Quantification of changes in current intensities induced by wave overtopping around low-crested structures

The phenomenon of overtopping is traditionally studied for well-emerged harbour structures and often focuses on safety and stability. In this paper laboratory tests are presented and analysed to sharpen the hypothesis that overtopping is capable of changing the horizontal circulation pattern around low-crested structures. A unique data set from laboratory experiments was acquired in the wave basin at Delft University of Technology. The experiments were performed using an emerged impermeable low-crested structure (three freeboards and three different wave conditions for each freeboard) and yielded nine different combinations of set-up and overtopping driving forces. Using this information it was possible to quantify the changes in cross-shore and longshore velocity induced by the overtopping and the set-up changes under the different freeboard and wave conditions described. It is found that overtopping enhances the outgoing flows (longshore velocities parallel to the structure) away from the lee side of the structure and dampens the water level gradient driven flow towards the structure.     

Laboratory observations of green water overtopping a fixed deck

A small-scale laboratory experiment was conducted to quantify a transient wave overtopping a horizontal, deck fixed above the free surface. Detailed free surface and velocity measurements were made for two cases with and without the deck structure to quantify the effect of the deck on the wave kinematics. The study showed that the structure increased the free surface above the leading edge of the deck by 20%. The velocity profile at the leading edge was fairly uniform, and the maximum horizontal velocity was similar to the maximum crest velocity measured without the deck. Immediately below the deck, the maximum velocity was 2.5 times greater than the corresponding velocity without the deck and 2.1 times greater than the maximum crest velocity without the deck. On the deck, the wave collapsed into a thin bore with velocities that exceeded 2.4 times the maximum crest velocity measured without the deck.     

Wave Currents Generated by a Moving Load in a Liquid Covered with Ice

We study horizontal wave currents generated in a liquid of finite depth by a load of constant intensity moving over the floating ice cover and analyze the dependences of the space structure of the field of wave velocities on the characteristics of the ice cover and the velocity of motion of the load. It is shown that the velocity of wave currents caused by flexural waves can increase with the velocity of motion of the load, whereas the wave currents caused by the gravity waves decay monotonically. The ice compression increases the velocity of horizontal wave currents.     

On dynamic coupling effects between a spar and its mooring lines

The responses of a spar constrained by slack mooring lines to steep ocean waves and tensions in the mooring lines are simulated using two different numerical schemes: a quasi-static approach (SMACOS) and a coupled dynamic approach (COUPLE). The two approaches are the same in computing wave loads on the structure. Their difference is in modeling dynamic forces of mooring lines; that is the dynamic forces are included in the computation of COUPLE but neglected in SMACOS. The numerical simulation is examined against the laboratory measurements of the JIP Spar in a water depth of 318 m. The dynamic coupling effects between the JIP Spar and its mooring lines in different water depths (318, 618 and 1018 m) are investigated by the comparison of numerical simulations obtained using the quasi-static and coupled dynamic approaches. It is found that the damping of mooring lines reduces the slow-drift surge and pitch of the Spar, especially in deep water. The reduction in the amplitude of slow-drift surge can reach about 10% in a water depth of 1018 m. The tension in mooring lines may greatly increase in the wave frequency range when dynamic forces in mooring lines are considered. The mooring-line tension in the wave frequency range predicted by the coupled dynamic approach can be eight times as great as the corresponding prediction by the quasi-static approach in a water depth of 1018 m. This finding may have important implications for the estimation of the fatigue strength and life span of the mooring lines deployed in deep water oceans.     

The FUNWAVE model application and its validation using laboratory data

In this paper, the performance of a well known and widespread Boussinesq model is evaluated for its ability to predict deep waters and shoaling zone velocity and elevation, comparing them with laboratory data. The model evaluation places emphasis on the parameters of the wave field that could be used for the prediction of coastal phenomena. It was found that the model proved its ability to predict regular wave velocity and elevation both in deep waters and shoaling zones right up to the breaking region. In contrast to previous works found in literature, the comparisons in this case are not limited to modelled and measured wave elevations, but also involve horizontal velocities. As a result, experimental and computed time series of wave elevations and horizontal velocities and their corresponding phase-averaged values are investigated along the wave channel, showing a good performance of the model.     

Field investigation on the results of non-linear shallow water equations in the Swash Zone

For the study of the cross-shore wave-induced hydrodynamics in the swash zone, a numerical model is developed based on the one-dimensional non-linear shallow water (NSW) equations for prediction of hydrodynamic parameters in the swash zone. In order to evaluate the accuracy of the outputs of the numerical model, the model's predictions in terms of water surface elevations and cross-shore velocities, are compared to field data from full-scale experiments conducted on three sites with different beach slope; mild and steep, several bed particle sizes and under various incident wave conditions. The quantitative and qualitative comparison of the results of the numerical model and the full-scale data reveals that the model can generally predict many aspects of the flow in the surf and swash zone on both types of beach. The accuracy is adequate for application in a sediment transport study. Considering the time-history and probability distribution of water surface elevation, the model is generally more accurate on steep beaches than on the mild beach. The model can adequately simulate the dominant frequency across the beach and saturation of higher frequencies on both mild and steep beaches for various incident wave energy characteristics. With regard to the horizontal (cross-shore) velocity, the sawtooth shape of time-history and negative acceleration of water are well predicted by the model for both mild and steep beaches. Due to the uncertainties in maximum and minimum values of velocity data, clear judgement about the accuracy of the numerical model in this matter was not possible. However, the comparison of the minimum velocities (offshore direction) revealed that the application of friction factors below the range which is suggested by literature best match the data.     

Extreme value prediction of inundation drag force with and without current

This paper deals with drag forces due to irregular waves on a vertical slender structure in the splash zone, i.e. in the vicinity of still-water free surface, by considering the inundation effect due to instantaneous wave elevation. The force turns out to be a third-order quantity with respect to wave elevation. The focus of this paper is however limited to extreme value prediction of this force in stochastic waves. Based upon a transformation of random variables and use of the Rice formula, the mean up-crossing rate of inundation drag force is obtained in the frequency domain both by direct numerical integration and asymptotic evaluation for high levels using the Laplace method. The extreme value distribution of this force is then established by the Poisson probability law assuming independent up-crossing events. The proposed method agrees very well with time-domain simulations both for the mean up-crossing rate and the extreme value prediction. The effect of correlation between wave elevation and horizontal water particle velocity and the presence of current have been studied.     

Velocity predictions for shoaling and breaking waves with a Boussinesq-type model

In this paper, the performance of a 1-D Boussinesq model is evaluated against laboratory data for its ability to predict surf zone velocity moments. Wave evolution over a plane beach and a complex bathymetry both extending into the surf-zone is examined for six cases. For the plane beach, these comprise two cases, a spilling and a plunging cnoidal wave. For the complex bathymetry, these comprise four cases of longer and short wavelengths (spilling and plunging breakers), with regular and irregular periodicity. The model evaluation places emphasis on parameters of the wave field that could be used for the prediction of sediment transport; orbital velocity, undertow, velocity skewness, kurtosis and asymmetry. It is found that, despite an overestimation of the depth-averaged horizontal velocity in the regular waves cases, the predicted higher order velocity moments and undertow are in good agreement with the laboratory data. A bispectral analysis demonstrates that the nonlinear transfers of energy amongst the low order harmonics are well reproduced, but energy exchanges with the higher harmonics are less well predicted. As a result, the model handles velocity moments better in the shorter wave tests than in the long wave cases where triad interactions are stronger. Of the four parameters describing wave breaking, the model behaviour is most sensitive to the critical wave front slope φ_B, especially with regard to velocity skewness and kurtosis predictions. It is also found that increasing the thickness of the surface roller for the case of plunging breakers improves the model's performance.