Breaking wave prediction with boundary elements and finite volumes for use with small boat capsize studies: Convergence and resource requirements

The prediction of extreme breaking waves forms the foundation of many fields of research. The authors have recently completed a study in the capsize and re-righting of sailing yachts using breaking wave prediction to enhance experimental results. As breaking wave prediction is only the beginning of any research program a prediction method is required to be both accurate and computationally inexpensive. This paper describes the investigation of two methods varying in computational demand. It has been concluded that a non-linear free surface boundary element method is immediately realisable with application to a research program requiring a large number of predicted waves. A finite volume approach is realisable, but its engineering application across numerous waves is difficult.     

Numerical simulation of ship stability for dynamic environment

The prediction of ship stability during the early stages of design is very important from the point of vessel’s safety. Out of the six motions of a ship, the critical motion leading to capsize of a vessel is the rolling motion. In the present study, particular attention is paid to the performance of a ship in beam sea. The linear ship response in waves is evaluated using strip theory. Critical condition in the rolling motion of a ship is when it is subjected to synchronous beam waves. In this paper, a nonlinear approach has been tried to predict the roll response of a vessel. Various representations of damping and restoring terms found in the literature are investigated. A parametric investigation is undertaken to identify the effect of a number of key parameters like wave amplitude, wave frequency, metacentric height, etc.     

Stability and capsizing analysis of nonlinear ship rolling in wind and stochastic beam seas

Considering the actual seaway condition, stability and capsizing of nonlinear ship rolling system in stochastic beam seas is of significant importance for voyage safety. Safe zone are defined in the phase space plan of the unperturbed Hamilton system to qualitatively distinguish ship motions as capsize and noncapsize. Capsize events are defined by solutions passing out of the safe zone. The probability of such an occurrence is studied by virtue of the random Melnikov function and the concept of phase space flux. In this paper, besides conventional wave excitation, the effect of wind load is also taken into account. The introduction of wind load will lead to asymmetry, in other words, it transforms the symmetric heteroclinic orbits into asymmetric homoclinic orbits. For asymmetric dynamical system, the orbital analytic solutions and its power spectrum are not readily available, and the technique of discrete time Fourier transformation (DTFT) is used. In the end, as verification of theoretical critical significant wave height, capsizing probability contour diagram is generated by means of numerical simulation. The contour diagram shows that these analytical methods provide reliable and predictive results about the likelihood of a vessel capsizing in a given seaway condition.     

Wave resistance for high-speed catamarans

The object of this study was to investigate the wave resistance component for high-speed catamarans. Two methods were applied: the slender-body theory proposed by Michell [Philos. Mag. 45(5) (1898) 106] and a 3D method used by Shipflow^™ (FLOWTECH, Shipflow^™ 2.4, User Manual, 1988) software.Results were obtained for different types of twin hulls and attention was given to the effects of catamaran hull spacing.The study also included the effects of shallow water on the wave resistance component.Special attention was given to the height of waves generated by the craft to ascertain effects on river banks.     

On the design of a longitudinal motion control system of a fully-submerged hydrofoil craft based on the optimal preview servo system

The current control system of a fully-submerged hydrofoil craft based on optimal feedback control has several problems: it has no good performance of contouring waves and it cannot reduce the effect of wave disturbance. In this paper, we apply the optimal preview servo system to the longitudinal control system of a fully-submerged hydrofoil craft in order to settle the problems of current control system. The control system based on optimal preview servo system is composed of feedback controller and feedforward controller. Also in order to design the control system, the necessary prediction range of future information, the weight function in performance index, the future reference input and wave disturbance are determined. Finally, the validity of the proposed control system in this paper is confirmed by simulation. The simulation results show that the control system has good performance of contouring waves in following seas and is effective to settle the problems of current control system of a fully-submerged hydrofoil craft.     

Multiple criteria optimization applied to high speed catamaran preliminary design

The demand for high-speed craft (mainly catamarans) used as passenger vessel has increased significantly in the recent years. Looking towards the future and trying to respond to the increasing requirement, high-speed crafts international market is passing through deep changes. Different types of high-speed crafts are being used for passenger transport. However, catamarans and monohulls have been the main choice not only for passenger vessel but also as ferryboat.Generally speaking, the efficient hydrodynamic hull shapes, engine improvements, and lighter hull structures using aluminum and composite materials make possible the increase in cruising speed.The high demand for catamarans are due to its proven performance in calm waters, large deck area compared to monohull crafts and higher speed efficiency using less power. Although the advantages aforementioned, the performance of catamaran vessels in wave conditions still needs to be improved.The high-speed crafts (HSC) market is demanding different HSC designs and a wide range of dimensions focusing on lower resistance and power for higher speed. Therefore, the hull resistance optimization is a key element for a high-speed hull success.In addition to that, trade-off high-speed catamaran (HSCat) design has been improved to achieve main characteristics and hull geometry. This paper presents a contribution to HSCat preliminary design phase. The HSCat preliminary design problem is raised and one solution is attained by multiple criteria optimization technique.The mathematical model was developed considering: hull arrangement (area and volume), lightweight material application (aluminum hull), hull resistance evaluation (using a slender body theory), as well as wave interference effect between hulls, calculated with 3D theory application. Goal programming optimization system was applied to solve the HSCat preliminary design.Finally this paper includes an illustrative example showing the mathematical model and the optimization solution. An HSCat passenger inland transport in Amazon area preliminary design was used as case study. The problem is presented, the main constrains analyzed and the optimum solution shown. Trade off graphs was also included to highlight the mathematical model convergence process.     

Dynamic properties of green water event in the overtopping of extreme waves on a fixed dock

A statistical model is developed to predict wave overtopping volume and rate of extreme waves on a fixed deck. The probability density function for the volume and rate of overtopping water are formulated based on the truncated Weibull distribution with the assumption of local sinusoidal profile for small amplitude waves. Sensitivity to the wave nonlinearity parameter and deck clearance is discussed. The statistical model is compared to laboratory data of the instantaneous free surface elevation measured in front of a fixed deck, and overtopping volume and overtopping rate measured at the leading edge of the deck. The statistical theory compared well with the measured exceedance probability seaward of the deck. The model prediction of the exceedance probability of deck overtopping gave qualitatively good agreement for large overtopping values.     

瘫船稳性第二层薄弱性衡准研究

基于IMO第二代完整稳性草案中瘫船稳性第二层薄弱性衡准的有关研究,分析草案提出的简化计算方法,采用一个单自由度船舶横摇运动微分方程,利用例船CEHIPAR2792数据,编译相应程序,求得不规则横风横浪作用下瘫船横摇运动相应特征,进而计算特定海况下的倾覆概率及特定海区的平均倾覆指数,并与草案值进行对比。分析不同拟合扶正力臂曲线方法和剩余稳性高对计算结果的影响,并对瘫船稳性第二层薄弱性衡准方法进行修改。     

The role of offshore boundary conditions in the uncertainty of numerical prediction of wave overtopping using non-linear shallow water equations

The paper examines the variability of wave overtopping parameters predicted by numerical models based on non-linear shallow water equations, due to the boundary conditions obtained from wave energy density spectra. Free surface elevation time series at the boundary are generated using the principle of linear superposition of the spectral components. The components' phases are assumed to be random, making it possible to generate an infinite number of offshore boundary conditions from only one spectrum.A reference case was provided by carrying out overtopping tests on a simple concrete structure in a wave flume. Numerical tests using the measured free surface elevation at the toe of the structure were carried out. Three parameters were analysed throughout the paper: the overtopping discharge, the probability of overtopping and the maximum overtopping volume. These showed very good agreement between the numerical solver prediction and the overtopping measurements. Subsequently, the measured spectra at the toe were used to generate a population of reconstructed offshore boundary time series for each test, following a Monte Carlo approach. A sensitivity analysis determined that 500 tests were suitable to perform a statistical analysis on the predicted overtopping parameters. Results of these tests show that the variability in the predicted parameters is higher for the smaller number of overtopping waves in the modelled range and decreases significantly as overtopping becomes more frequent. The characteristics of the distributions of the predictions have been studied. The average value of the three parameters has been compared with the measurements. Although the accuracy is lower than that achieved by the model when the measured time series are used at the boundary, the prediction is still fairly accurate above all for the highest overtopping discharges. The distribution of the modelled probability of overtopping was found to follow a normal distribution, while the maximum value follows a GEV one. The overtopping discharge shows a more complex behaviour, values in the middle of the tested range follow a Weibull distribution, while a normal distribution describes the top end of the range better.Results indicate that when the probability of overtopping is smaller than 5%, a sensitivity analysis on the seeding of the offshore boundary conditions is recommended.     

Parametric model identification of high-speed craft dynamics

Parametric models of heave, pitch and roll dynamics of a high-speed craft have been estimated for different wave incidence angles in the frequency domain. Several issues that make the identification problem interesting are the following: type of parameterization, starting values, non-quadratic functions, excitation signals and short data record. The method employed guarantees a fine linear approximation of the nonlinear dynamics of a fast ship for the ultimate goal of stabilization control to reduce motion sickness associated with heave, pitch and roll accelerations. In addition, the approach achieves high-quality starting values and avoids non-quadratic terms in the cost function, which results in less computational load and significantly more accurate models when compared with a previous method employed for the same problem.     

An investigation on the vertical motion sickness characteristics of a high-speed catamaran ferry

Low frequent motions of vessel may cause motion sickness in rough seas. These undesirable effects induce fatigue of crews during the navigation. The motion sickness is always an important criterion for the high-speed craft design. Modern ferry designs have been marketed with a great emphasis on the seakeeping performance. This research has been carried out by investigating the results on the vertical motion sickness incidence (MSI) study for a 40 m wave-piecing catamaran at seas. The primary purpose of this research is to investigate the vertical motion sickness characteristics of a high-speed catamaran ferry. Two mathematical models, three-dimensional translating–pulsating source distribution technique and three-dimensional pulsating source distribution technique, are used for predicting the vertical acceleration responses of the wave-piecing catamaran in oblique waves. The comparison between numerical predictions and experimental data shows a good agreement except that around the pitch resonance region in FP vertical acceleration motions. Based on the experimental observation, the discrepancies may be caused by the nonlinear effects of centre bow during large pitch motions in waves. The comfort assessments are based on the ISO-2631/1997 standard with the hydrodynamic analysis for determining the acceleration levels in different locations on the vessel. The effects of seating location, wave heading and duration of motion exposure on seasickness are discussed.     

On the capsize performance of a discus buoy in deep sea breakers

The mode of capsize of a discus buoy in breaking waves is discussed. The results of model tests are given; these show that a judicious choice of mooring design can substantially reduce the chance of capsize. A comparison is made with the performance of the buoy on station.     

Probabilistic Models for the Probability of Wave Breaking and Whitecap Coverage Based on Kinematic Breaking Criterion

More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact moders the models either for the probability of wave breaking B or for the whitecap coverage W based on these criteria difficult to apply. In this paper and the one which follows we seek to develop models for the prediction of both B and W based on the kinematical criterion. First, several joint probabihstic distribution functions (PDFs) of wave characteristics are derived, based on which the breaking properties B and W are estimated. The estimation is made on the assumption that a wave breaks ff the horizontal velocity of water particles at its crest exceeds the local wave celerity, and whitecapping occurs in regions of fluid where water particles travel faster than the waves. The consequent B and W depend on wave spectral moments of orders 0 to 4.Then the JONSWAP spectrum is used to represent the fetch-limited sea waves in deep water, so as to relate the probahility of wave breaking and the whitecap coverage with wind parameters. To this end, the time-averaging technique proposed by Glazman (1986) is applied to the estimation of the spectral moments involved, and furthermore, the theoretical models are compared with available observations collected from published literature. From the comparison, the averaging time scale is determined. The final models show that the probability of wave breaking as well as the whitecap coverage depends on the dimensionless fetch. The agreement between these models and the database is reasonable.     

The nonlinear rolling response of a vessel including chaotic motions leading to capsize in regular seas

The rolling motion of a ship has been successfully modelled using a semi-empirical nonlinear differential equation by a number of researchers. Experimental data has been used to model nonlinear damping and righting lever characteristics and comparison with observed behaviour has been reasonably good. The present article describes a numerical, phenomenological approach to analyse this type of behaviour. The stability of the periodic motion, and in particular the possibility of capsize, is explored with reference to qualitative prediction techniques. The appearance of chaotic motions in regular beam seas is a new feature which should be of interest to designers. The inability of traditional quantitative methods, such as the perturbation technique, to detect chaos is a further justification for using numerical simulation guided by dynamical systems theory.     

Supercritical planning hulls

This paper gives an overview of the development of the supercritical planing hull concept during the last two decades. Our starting point was the body of theoretical and tank testing work on supercritical displacement ships which was completed by Lewis and others by 1960. In 1964 we launched a manned model small waterplane twin hull (SWATH) craft having a very low pitch stiffness, and thus very little pitching motion at wave encounter frequencies above resonance. A second craft was launched the following year, after which we changed the emphasis of our program to the higher speeds associated with planning craft. Planning catamarans occupied us between 1967 and 1971, when the first Sea Knife monohull supercritical planning hull was launched. The most recent Sea Knife is 34 ft L.O.A., displaces 16,000 lb with full fuel and crew, has been timed at 80 mph in sea state 3, and (from model tests) can do the same in sea state 4 with a comfortable ride. We conclude that supercritical planing hulls are very suitable for high speed ferries, patrol craft and crewboats, and that the technology is now mature.     

A simplified 3-D human body–seat interaction model and its applications to the vibration isolation design of high-speed marine craft

High-speed boats experience a harsh vibration environment and human response to this environment is of increasing interest to naval architects who wish to mitigate the effects of vibration and shocks. Based on published experiment data, a three-dimensional human body model with one degree-of-freedom in each direction is established. This model is combined with a simple seat model to construct a simplified 3-D human body–seat interaction model for naval architects to investigate the integrated interaction system when subjected to ship motions. The governing equations describing the dynamics of the human body–seat interactions are formulated and their theoretical solutions are derived. This model, in association with the experimental data recorded on board a high-speed marine craft, is used to study seat isolation system designs. The spring coefficient of the seat isolation system is chosen to avoid any resonance of the human–seat interaction system excited by sea waves. The damping coefficient of the seat isolation system is determined to attenuate motions at the most common excitation frequencies. The designed system is further checked by considering its response to an individual slam impact where the designed system is compared with typical existing seats to illustrate the potential advantages of the proposed approach. In addition the designed seat is compared with existing seats excited by actual boat loads. The study provides a simplified, effective approach for high-speed craft seat design in reducing the shock and vibration level experienced by the crew.     

Towing dynamics of a liferaft and fast rescue craft in a surface wave

The equations of motion for the coupled dynamics of a small liferaft and fast rescue craft in a surface wave are formulated in two dimensions using the methods of Kane and Levinson [1985. Dynamics: Theory and Applications. McGraw-Hill Inc., New York]. It is assumed that the motion normal to the wave surface is small and can be neglected, i.e. the bodies move along the propagating wave profile. The bodies are small so that wave diffraction and reflection are negligible. A Stokes second order wave is used and the wave forces are applied using Morison's equation for a body in accelerated flow. Wind loads are similarly modelled using drag coefficients. The equations are solved numerically using the Runge–Kutta routine “ode45” of MATLAB^®. The numerical model provides guidelines for predicting the tow loads and motions of small craft in severe sea states.     

Wave run-up on bermed coastal structures

Reliable estimation of wave run-up is required for the effective and efficient design of coastal structures when flooding or wave overtopping volumes are an important consideration in the design process. In this study, a unified formula for the wave run-up on bermed structures has been developed using collected and existing data. As data on berm breakwaters was highly limited, physical model tests were conducted and the run-up was measured. Conventional governing parameters and influencing factors were then used to predict the dimensionless run-up level with 2% exceedance probability. The developed formula includes the effect of water depth which is required in understanding the influence of sea level rise and consequent changes of wave height to water depth ratio on the future hydraulic performance of the structures. The accuracy measures such as RMSE and Bias indicated that the developed formula is more accurate than the existing formulas. Additionally, the new formula was validated using field measurements and its superiority was observed when compared to the existing prediction formulas. Finally, the new design formula incorporating the partial safety factor was introduced as a design tool for engineers.     

岬间海滩泥沙输运趋势与剖面分形研究

根据1999年7月实测的粤东岬间海滩沉积与地形变化资料,采用沉积物输运概率模式(McLaren模型)对海滩沿岸泥沙运移趋势进行探讨。结果表明,在常波况条件下海滩沿岸泥沙向偏南方向运移,在高能条件下可能出现与常波况条件下相反运动的趋势。进一步利用分形分布模型研究了海滩剖面的分形性质,提出了岬间海滩剖面地形变化的短期分形预测模型。