The patterns of surface capillary-gravity short-crested waves with uniform current fields in coastal waters

A fully three-dimensional surface gravitycapillary short-crested wave system is studied as two progressive wave-trains of equal amplitude and frequency, which are collinear with uniform currents and doubly-periodic in the horizontal plane, are propagating at an angle to each other. The first- and second-order asymptotic analytical solutions of the short-crested wave system are obtained via a perturbation expansion in a small parameter associated with the wave steepness, therefore depicting a series of typical three-dimensional wave patterns involving currents, shallow and deep water, and surface capillary waves, and comparing them with each other.

Portable Dynamic Positioning Control System on A Barge in Short-Crested Waves Using the Neural Network Algorithm

This paper develops a nonlinear mathematical model to simulate the dynamic motion behavior of the barge equipped with the portable outboard Dynamic Positioning （DP） system in short-crested waves. The self-tuning Proportional- Derivative （PD） controller based on the neural network algorithm is applied to control the thrusters for optimal adjustment of the barge position in waves. In addition to the wave, the current, the wind and the nonlinear drift force are also considered in the calculations. The time domain simulations for the six-degree-of-freedom motions of the barge with the DP system are solved by the 4th order Runge-Kutta method which can compromise the efficiency and the accuracy of the simulations. The technique of the portable alternative DP system developed here can serve as a practical tool to assist those ships without being equipped with the DP facility while the dynamic positioning missions are needed.

Laboratory Research on Effective Test Area of Short-Crested Waves Generated by Two-Sided Segmented Wavemakers

The size and shape of the effective test area are crucial to consider when short-crested waves are created by segmented wavemakers. The range of the effective test area of short-crested waves simulated by two-sided segmented wavemakers is analyzed in this paper. The experimental investigation on the wave field distribution of short-crested waves generated by two-sided segmented wavemakers is conducted by using an array of wave gauges. Wave spectra and directional spreading function are analyzed and the results show that when the main direction is at a certain angle with the normal line of wave generators, the wave field of 3D short-crested waves generated by two-sided segmented wavemakers has good spatial uniformity within the model test area. The effective test area can provide good wave environments for seakeeping model tests of various ocean engineering structures in the deep ocean engineering basin.

Short-Crested Waves Interaction with A Concentric Porous Cylinder System with Partially Porous Outer Cylinder

In this paper, based on the linear wave theory, the interaction of short-crested waves with a concentric dual cylindrical system with a partially porous outer cylinder is studied by using the scaled boundary finite element method （SBFEM）, which is a novel semi-analytical method with the advantages of combining the finite element method （FEM） with the boundary element method （BEM）. The whole solution domain is divided into one unbounded sub-domain and one bounded sub-domain by the exterior cylinder. By weakening the governing differential equation in the circumferential direction, the SBFEM equations for both domains can be solved analytically in the radial direction. Only the boundary on the circumference of the exterior porous cylinder is discretized with curved surface finite elements. Meanwhile, by introducing a variable porous-effect parameter G, non-homogeneous materials caused by the complex configuration of the exterior cylinder are modeled without additional efforts. Comparisons clearly demonstrate the excellent accuracy and computational efficiency associated with the present SBFEM. The effects of the wide range wave parameters and the structure configuration are examined. This parametric study will help determine the various hydrodynamic effects of the concentric porous cylindrical structure.

Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity.However,the path that the rays travel along in media with irregular interfaces is not clear.Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements（SEMO） that can accurately evaluate waves traveling along an irregular interface.Consequently,the head waves are separated from interface waves by a time window.Thus,their energy and arrival time changes can be analyzed independently.These analyses demonstrate that,contrary to the case for head waves propagating along a flat interface,there are two mechanisms for head waves traveling along an irregular interface：a refraction mechanism and transmission mechanism.That is,the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media.Such knowledge will be helpful in constructing a more accurate inversion method,such as head wave travel-time tomography,and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas,such as the Tibetan Plateau.

An Irregular Wave Generating Approach Based on naoe-FOAM-SJTU Solver

In this paper,a wave generating approach for long-crest irregular waves in a numerical tank by our in-house solver naoe-FOAM-SJTU is presented.The naoe-FOAM-SJTU solver is developed using an open source tool kit,Open FOAM.Reynolds-averaged Navier？Stokes（RANS） equations are chosen as governing equations and the volume of fluid（VOF） is employed to capture the two phases interface.Incoming wave group is generated by imposing the boundary conditions of the tank inlet.A spectrum based correction procedure is developed to make the measured spectrum approaching to the target spectrum.This procedure can automatically adjust the wave generation signal based on the measured wave elevation by wave height probe in numerical wave tank.After 3 to 4 iterations,the measured spectrum agrees well with the target one.In order to validate this method,several wave spectra are chosen and validated in the numerical wave tank,with comparison between the final measured and target spectra.In order to investigate a practical situation,a modified Wigley hull is placed in the wave tank with incoming irregular waves.The wave-induced heave and pitch motions are treated by Fourier analysis to obtain motion responses,showing good agreements with the measurements.

Experimental Researches on Reflective and Transmitting Performances of Quarter Circular Breakwater Under Regular and Irregular Waves

A series of regular and irregular wave experiments are conducted to study the reflective and transmitting performances of quarter circular breakwater （QCB） in comparison with those of semi-circular breakwater （SCB）. Based on regular wave tests, the reflection and transmission characteristics of QCB are analyzed and a few influencing factors are investigated. Then, the wave energy dissipation as wave passing over the breakwater is discussed based on the hydraulic coefficients of QCB and SCB. In irregular wave experiments, the reflection coefficients of QCB and their spectrums are studied. Finally, the comparisons between the experimental results and numerical simulations for QCB under regular and irregular wave conditions are presented.

Effect of Berm Width and Elevation on Irregular Wave Run-Up

This paper discusses the effect of berm width and elevation of composite slope on irregular wave run-up. Based on the data obtained from model tests, the formula and distribution of irregular wave run-up on composite slope are derived. The changing of wind speed, width and elevation of the berm are considered comprehensively. The wave run-up with various exceedance probability can be es-timated utilizing the distribution curves of irregular wave run-up.

Numerical Simulation of Irregular Wave Overtopping Against A Smooth Sea Dike

Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model, a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes. Simulations of fully nonlinear standing wave and regular wave＇s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules. To model stationary ergodic stochastic processes, several cases with different random seeds are computed for each specified irregular wave spectrum. It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas, other numerical results and experimental data.

An Irregular Wave Maker of Active Absorption with VOF Method

A numerical irregular wave flume with active absorption of re-reflected waves is simulated by use of volume of fluid （VOF） method. An active ＇absorbing wave-maker based on linear wave theory is set on the left boundary of the wave flume. The progressive waves and the absorbing waves are generated simultaneously at the active wave generating-absorbing boundary. The absorbing waves are generated to eliminate the waves coming back to the generating boundary due to reflection from the outflow boundary and the structures. SIRW method proposed by Frigaard and Brorsen （1995） is used to separate the incident waves and reflected waves. The digital filters are designed based on the surface elevation signals of the two wave gauges. The corrected velocity of the wave-maker paddle is the output from the digital filter in real time. The numerical results of regular and irregular waves by the active absorbing-generating boundary are compared with the numerical results by the ordinary generating boundary to verify the performance of the active absorbing-generator boundary. The differences between the initial incident waves and the estimated incident waves are analyzed.

Experimental Study on Local Scour Around A Large Circular Cylinder Under Irregular Waves

A series of physical model tests are conducted for local scour around a circular cylinder of a relatively large diameter (0 15< D/L <0.5) under the action of irregular waves. The laws of change of the topography around the cylinder are systematically studied. The effects of wave height, wave period, water depth, sediment grain size and cylinder diameter are taken into account. The mechanism of formation of the topography around the cylinder is analyzed. A detailed analysis is given to bed sediment grain size, and it is considered that the depth of scour around the cylinder under wave action is not inversely proportional to the sediment grain diameter. On such a basis, an equation is proposed for calculation of the maximum depth of scour around a cylinder as well as its position under the action of irregular waves.

Experimental Investigation of Irregular Wave Uplift Force on Deck of Exposed High-Pile Jetties

A laboratory setup was developed to investigate irregular wave uplift loads on exposed high-pile jetties. It is shown that the dimensionless uplift load increases to the maximum with an increasing relative clearance and then decreases. The relative clearance corresponding to the peak force is linked to a range from 0.4 to 0.8. When the relative clearance exceeds a certain value, the wave can not reach the underside of the deck and the force becomes zero. Distinct trends of dimensionless force with a relative width of deck show that the force tends to decrease as the relative deck width increases, and then the decrease slows down after the relative deck width increases or decreases to a certain value. The pressure distribution length associated with the maximum uplift force is equivalent to the wave contact width x. When x is larger than the width of deck B, it is taken as B. The statistical distribution of loads obeys the Weibull distribution. The results from the analyses of the real data suggest a new dimensionless prediction model on wave-in-deck uplift loads and the conversion ratio between wave loads at different exceedance probabilities. A comparison is made between the new prediction model and the existing widely used three prediction models. These results are used as useful references for structural design of the jetty.

Parametric Resonance Analyses for Spar Platform in Irregular Waves

The parametric instability of a spar platform in irregular waves is analyzed. Parametric resonance is a phenomenon that may occur when a mechanical system parameter varies over time. When it occurs, a spar platform will have excessive pitch motion and may capsize. Therefore, avoiding parametric resonance is an important design requirement. The traditional methodology includes only a prediction of the Mathieu stability with harmonic excitation in regular waves. However, real sea conditions are irregular, and it has been observed that parametric resonance also occurs in non-harmonic excitations. Thus, it is imperative to predict the parametric resonance of a spar platform in irregular waves. A Hill equation is derived in this work, which can be used to analyze the parametric resonance under multi-frequency excitations. The derived Hill equation for predicting the instability of a spar can include non-harmonic excitation and random phases. The stability charts for multi-frequency excitation in irregular waves are given and compared with that for single frequency excitation in regular waves. Simulations of the pitch dynamic responses are carried out to check the stability. Three-dimensional stability charts with various damping coefficients for irregular waves are also investigated. The results show that the stability property in irregular waves has notable differences compared with that in case of regular waves. In addition, using the Hill equation to obtain the stability chart is an effective method to predict the parametric instability of spar platforms. Moreover, some suggestions for designing spar platforms to avoid parametric resonance are presented, such as increasing the damping coefficient, using an appropriate RAO and increasing the metacentric height.

The reflection of regular and irregular waves by a partially perforated caisson breakwater on a step bed

This study examines the reflection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the linear potential theory, an analytical solution is developed to calculate the reflection coefficient of the structure subjected to regular waves. The matched eigenfunction expansion method is used for the solution. The regular wave method is also extended to irregular waves using a linear transfer function. The calculated results obtained for limiting cases are exactly the same as corresponding results given by the previous researchers. The present predictions also agree well with experimental data in the published literatures. Numerical experiments are conducted to examine the variations of the reflection coefficient versus its main effect factors, and some interesting results are presented.

Ince-Strutt Stability Charts for Ship Parametric Roll Resonance in Irregular Waves

Ince-Strutt stability chart of ship parametric roll resonance in irregular waves is conducted and utilized for the exploration of the parametric roll resonance in irregular waves. Ship parametric roll resonance will lead to large amplitude roll motion and even wreck. Firstly, the equation describing the parametric roll resonance in irregular waves is derived according to Grim’s effective theory and the corresponding Ince-Strutt stability charts are obtained. Secondly, the differences of stability charts for the parametric roll resonance in irregular and regular waves are compared. Thirdly, wave phases and peak periods are taken into consideration to obtain a more realistic sea condition. The influence of random wave phases should be taken into consideration when the analyzed points are located near the instability boundary. Stability charts for different wave peak periods are various. Stability charts are helpful for the parameter determination in design stage to better adapt to sailing condition. Last, ship variables are analyzed according to stability charts by a statistical approach. The increase of the metacentric height will help improve ship stability.

Numerical Study of the Impact of Climate Change on Irregular Wave Run-up Over Reef-Fringed Coasts

Wave hydrodynamics over fringing reefs is largely controlled by the reef surface roughness and hydrodynamic forcing.It is believed that climate change will result in a net increase in the water depth over the reef flat,a degrading of the surface roughness of coral reefs and changes in extreme incident wave heights.For an accurate assessment of how climate change affects the safety of reef-fringed coasts,a numerical study of the impact of climate change on irregular wave run-up over reef-fringed coasts was carried out based on a Boussinesq wave model,FUNWAVE-TVD.Validated with experimental data,the present model shows reasonable prediction of irregular wave evolution and run-up height over fringing reefs.Numerical experiments were then implemented based on the anticipated effects of climate change and carried out to investigate the effects of sea level rise,degrading of the reef surface roughness and increase of extreme incident wave height on the irregular wave run-up height over the backreef beach respectively.Variations of run-up components(i.e.,spectral characteristics of run-up and mean water level)were examined specifically and discussed to better understand the influencing mechanism of each climate change-related effect on the run-up.

Interaction of Irregular Waves with Vertical Breakwater and Characteristics of Secondary Wave Generated by Overtopping

This study investigated the interaction between irregular waves and vertical breakwater.The main goal was to determine the wave force on the breakwater for different depths,along with the evolution of the secondary wave generated by overtopping.The open source code DualSPHysics was used in the simulation.Wavelet transform was employed to remove the acoustic components from the weakly compressible smoothed particle hydrodynamics pressure solution.The results of the experiments and simulations showed that although the wave height at the low water level(case 2 was smaller than that at the high water level(case 1,the horizontal and uplifting force of case 2 was higher than that of case 1.In case 2,a large impact pressure occurred because of the plunging wave and wave breaking effects.As the water level was close to the breakwater top in case 1,the secondary wave generated by overtopping was studied.Results indicated that wave and breakwater interactions transfer wave energy from the leading wave component to higher harmonics.Two main harmonics were identified in the secondary wave.The first harmonic was the incident peak frequency,which was still the dominant component.During the wave propagation behind the breakwater,the frequencies of harmonics remained unchanged,but the amplitude of the first harmonic showed an obvious change.Under the same wave condition,the first and second harmonics did not change with depth.

Numerical simulation of the propagation of electromagnetic waves in ionospheric irregularities

The characteristics of high-frequency(HF)electromagnetic(EM)wave propagation can be affected when EM waves propagate in the ionosphere.When ionospheric irregularities appear in the ionosphere,they can have a serious impact on the propagation of HF EM waves.In this study,the propagation of HF EM waves in ionospheric irregularities was investigated by numerical simulation.First,a twodimensional model of plasma bubbles was used to produce ionospheric irregularities in the ionosphere.A ray-tracing method was then utilized to simulate the propagation of HF radio waves in these ionospheric irregularities.Results showed that the propagation of HF radio waves in the ionosphere was more complex in ionospheric irregularities than without ionospheric irregularities.In addition,corresponding ionograms were synthesized by radio rays propagated in the ionosphere with these irregularities.The synthesized ionograms were then compared with the experimental ionograms recorded by an ionosonde.Results showed that spread F could be simulated on the ionograms when ionospheric irregularities occurred in the ionosphere.This result was consistent with the ionosonde observations.

Reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core

The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.

Laboratory Study of the Nonlinear Transformation of Irregular Waves over A Mild Slope

This paper considers the nonlinear transformation of irregular waves propagating over a mild slope （1：40）. Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.