Analytical convolution model for shipping water evolution on a fixed structure

The shipping of water is a problem that affects naval and offshore structures. Estimating its propagation on the decks of these structures by using analytical methods has been a main concern of projects. However, classical approaches disregard the decay tendency of water elevation time series and tend to overestimate the resultant water on deck. This paper is concerned with estimating the evolution of water along the deck of a fixed structure due to shipping water events. An analytical convolution model is proposed to estimate water elevations. The model considers the freeboard exceedance time series and the mean shipping flow velocity as inputs and the frictional effects of the bottom by resistance coefficients, which enables an approximated representation of the water elevation time series over the deck. It was validated with experiments of isolated shipping water events that were generated with the wet dam-break approach. The results obtained with the proposed model captured the experimental results, approximating the peak values and the decay trend of time series. Improvement of the proposed approach over classical models to represent shipping water elevations was demonstrated by comparing the results obtained with those of the dam-break model of Stoker.     

Significant load and green water on deck of offshore units/vessels

In this paper the probability of green water occurrence is investigated by taking into account the threshold of the vertical relative motion exceeding the freeboard. The number of wetting of the unit/vessel is predicted using probabilistic method. This paper compares the significant load, due to shipping of green water with the works of other researchers, and the loads are found to be close with the results presented in this paper. There is no direct relation between the velocities in the waves and the water velocity over the deck. The water velocities around the bow are heavily distributed by the presence of the bow. This scenario makes the flow very complex for schematic modelling.     

Numerical analysis of shipping water impact on a deck using a particle method

The objective of this study is to simulate three-dimensional behavior of shipping water and to predict the impact pressure on the deck using a particle method. An experiment carried out in a two-dimensional wave tank with a fixed deck model was numerically analyzed in three dimensions. The fluid motion, the surface elevation, and the impact pressure on the deck were compared between the experiment and the calculation and good agreement was obtained.     

Numerical prediction of green water incidents

Green water loads on moored or sailing ships occur when an incoming wave significantly exceeds the freeboard and water runs onto the deck. In this paper, a Navier–Stokes solver with a free surface capturing scheme (i.e. the VOF model; [Hirt and Nichols, 1981]) is used to numerically model green water loads on a moored FPSO exposed to head sea waves. Two cases are investigated: first, green water on a fixed vessel has been analysed, where resulting waterheight on deck, and impact pressure on a deck mounted structure have been computed. These results have been compared to experimental data obtained by [Greco, 2001] and show very favourable agreement. Second, a full green water incident, including vessel motions has been modelled. In these computations, the vertical motion has been modelled by the use of transfer functions for heave and pitch, but the rotational contribution from the pitch motion has been neglected. The computed water height on deck has been compared to the experimental data obtained by [Buchner, 1995a] and it also shows very good agreement. The modelling in the second case was performed in both 2-D and 3-D with very similar results, which indicates that 3-D effects are not dominant.     

Experimental investigation of tsunami bore impact pressure on a perforated seawall

Catastrophic failures of many tsunami barriers along the affected coasts during the 2011 Tohoku earthquake tsunami has prompted extensive investigation into improving and revising design codes for tsunami defence structures. To date, researchers and coastal engineers are investigating to understand the failure mechanisms and to find solutions so that the structures merely remain intact in the extreme event such as tsunami. Thus, the present work is motivated to experimentally study tsunami-induced bore pressures exerted on vertical seawalls; a solid vertical wall and a porous vertical seawall that consisted of a perforated front wall and a solid rear wall. Bores with various heights and velocities were generated by using the dam-break method. A porous seawall with 20% porosity of perforated front wall was used in this study. Bore pressures exerted on the solid rear wall and chamber oscillations that occurred in the experiments were also discussed. The experimental results showed that multiple peak pressures were observed during bore run-up phase in the time series of bore impacts. A predictive equation to estimate the maximum bore pressure on a perforated seawall was developed using multiple regression analysis. The proposed equation was also compared with previous empirical formulas.     

Influence of yaw-roll coupling on the behavior of a FPSO: An experimental and numerical investigation

An inconvenience in the experimental set-up of a FPSO in regular waves highlighted occurrence of parametric-roll events promoted by yaw-roll coupling and motivated a combined physical and numerical analysis on the relevance of this phenomenon on the roll resonance, as well as on the water shipping. The model tests examine the ship in head- and bow-sea waves in the zone of the first parametric resonance. Numerically, it is adopted a 3D Domain-Decomposition (DD) strategy combining a weakly-nonlinear potential-flow solver based on the weak-scatterer theory with a shallow-water approximation for the shipped liquid and with a bottom-slamming solution. Detailed comparisons against these and other seakeeping experiments validated the numerical method in its different aspects with global success.At first, a 2-dof equivalent linearized yaw-roll coupled system is examined and the measurements are used to estimate hydrodynamic coefficients required to complete the mathematical model of the problem. Then the DD method is applied to verify the instability occurrence and compared against the experiments. From the analysis, the parametric-roll instability does not occur if all nonlinearities in the roll restoring load are not accounted for. However the amplitude of the resonant roll is affected by the coupling with the other degrees of freedom. Especially the coupling with yaw tends to increase the steady-state roll amplitude. It also affects the water shipping with the trend in reducing its severity for the vessel, this is opposite to the influence of the parametric roll in head-sea waves on the water on deck, as documented in Greco et al. (2014) [4].     

一种基于Roe格式的有限体积法在二维溃坝问题中的应用

溃坝属于典型的非恒定含间断的浅水问题。应用有限体积法离散二维浅水控制方程的守恒型方程组,将基于近似黎曼解的Roe格式用于数值计算溃坝问题,并利用MUSCL方法构造二阶空间积分格式和预测-校正二步法构造二阶时间格式,从而使数值解的整体达到二阶,提高了精度。文中算法在一维溃坝的Stoker问题的数值结果与解析解进行对比,结果证明了此方法的可行性。应用此方法在二维溃坝问题上的结果,说明了此算法可有效模拟溃坝水流的演进过程。     

基于水下光纤应变监测的导管架结构总冰力测量方法

基于测量结构水下光纤应变获取冰力的方法首次应用于渤海JZ20-2NW加锥导管架平台,该方法方便进行零点标定,可获取结构总冰力的绝对信息(包括均值和波动值)。首先介绍了JZ20-2NW平台的现场监测系统,主要包括结构水下应变响应记录冰力信息,甲板上部视频记录同步冰情(冰厚、冰速和来冰方向)信息和拾振器记录结构冰振响应;重点分析了由测点应变向结构总冰力的转化方法,并对总冰力进行了初步分析。将无量纲化实测冰力与5种典型冰力计算模型进行了比较,分析结果表明,锥体宽度与海冰厚度比值(简称"宽厚比")对冰力大小及变化起决定作用。     

Wave-in-deck loads on coastal bridges and the role of air

Recent failures of coastal bridges during extreme storm events have focused attention on the need for research on wave loading of coastal structures suspended above the still water level. This paper presents findings from large-scale experimental work carried out in the wave basin of the Yokohama Port and Airport Technical Investigation Office. Measurements from physical model tests are used to gain insights on the dynamics of wave-loading of coastal bridges and to derive an “ad-hoc” prediction method for both quasi-static and impulsive wave loads. The effect of openings in the bridge deck is also discussed, and guidance derived for design purpose.     

Acceleration of general circulation model convergence by exponential extrapolation

Numerical models of basin-to-global scale ocean circulation generally take thousands of model years to converge to a final steady-state. The long timescale is set by the slow adjustment of the ocean's overall stratification to the classical vertical advective–diffusive balance. During much of this adjustment period, the time evolution of many model variables appears to be an approximately exponential decay to the final state. The adjustment of the model can be accelerated by extrapolating zonal-average temperature and salinity fields forward in time based on this exponential decay. Tests with the GFDL MOM-2, a primitive-equation numerical model, show that the extrapolation does not yield an exact solution, but can shorten integration times by a factor of two to three.     

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.     

A combined wind and wave energy-converter concept in survival mode: Numerical and experimental study in regular waves with a focus on water entry and exit

A combined wind and wave energy converter concept, named STC concept was proposed. Model tests were performed in terms of operational and survival modes. Water entry and exit phenomena as well as green water on deck were observed during the survivability model tests. In this paper, a nonlinear numerical model based on a blended station-keeping potential-flow solver with a local impact solution for bottom slamming events and an approximated model for the water shipped on the deck is proposed to simulate these nonlinear phenomena. Physical investigation of the water entry and exit process was firstly carried out and uncertainty analysis of the model test results were performed. Numerical comparisons between the nonlinear solver and model test results are then performed in terms of mean, wave frequency and double wave frequency motion response components. The slamming and green water involved in the water entry process are specially investigated, in terms of the physical evolution and the effects on the dynamic motion responses. The validation work on the occurrence of slamming and water on deck as well as the slamming pressure are performed.     

Wave interaction with tension leg platforms

The design of deep water offshore platforms requires the analysis of wave-structure interaction phenomena which have not been as critical for shallower water platform designs. In the case of tension leg platforms (TLPs) interaction phenomena such as wave run-up on the vertical legs and the amplification of the waves beneath the deck are major design considerations. The research investigation reported here focuses on a series of small scale wave tank tests on four column TLP models examining these phenomena. The role of vertical leg spacing and comparative tests of the TLP models with and without pontoons was investigated. As the vertical legs were moved closer an increase in wave run-up and a shifting of the incident wave period corresponding to the maximum wave upwelling were noted. Comparisons with wave measurements for single cylinders from previous experimental studies and the TLP configurations used in this study are presented. A design formula for estimating wave run-up on TLPs is suggested based upon these experiments. The wave run-up on a leg directly in the wake of another leg is presented. A comparison of the wave upwelling measurements with previously published numerical results are discussed. A wave uplift force model which allows for the inclusion of the experimentally obtained wave upwelling measurements is presented and discussed with regard to the design specification of platform deck elevation.     

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.     

The behavior of a two-dimensional dual forced plume

The behavior of two plumes ejected into a thin water tank is investigated experimentally. As the time elapses, the plume axes deflect towards each other. Time evolution of this two-dimensional, dual forced plume is found to be similar to that of a two-dimensional, single plume ejected near a vertical wall. The symmetric plane of the two plumes in the former case plays the role of the vertical wall. The time required for the dual plume to attain a quasi-steady state is shorter than that for the single plume. The deflection angles of the plume axes are smaller for the dual plume, and the plume water remains near the free water surface in a quasi-steady state. Water circulation in a triangular region surrounded by the free water surface, the side of the plume and the symmetric plane (or the vertical wall for the single plume case) may account for this difference; the circulation is much more pronounced in the single plume case.     

Vortex braids in the head wave formed as a dam breaks

The formation of flow-backing large vortex braids in a head dam-break wave running over the washed-out soil is revealed experimentally. Vortex dipoles braiding together with the captured soil are formed in the viscous near-bottom layer. Ascending and descending dipoles twist, forming a large near-bottom braid which rises to the water surface and forms a wall consisting of water and soil. The braids hold large soil particles if the flow velocity exceeds the critical value.     

Elucidating the dynamics and mixing agents of a shallow fjord through age tracer modelling

The mixing agents and their role in the dynamics of a shallow fjord are elucidated through an Eulerian implementation of artificial tracers in a three-dimensional hydrodynamic model. The time scales of vertical mixing in this shallow estuary are short, and the artificial tracers are utilized in order to reveal information not detectable in the temperature or salinity fields. The fjord's response to external forcing is investigated through a series of model experiments in which we quantify vertical mixing, transport time scales of fresh water runoff and estuarine circulation in relation to external forcing.Using age tracers released at surface and bottom, we quantify the time scales of downward mixing of surface water and upward mixing of bottom water. Wind is shown to be the major agent for vertical mixing at nearly all depth levels in the fjord, whereas the tide or external sea level forcing is a minor agent and only occasionally more important just close to the bottom. The time scale of vertical mixing of surface water to the bottom or ventilation time scale of bottom water is estimated to be in the range 0.7 h to 9.0 days, with an average age of 2.7 days for the year 2004.The fjord receives fresh water from two streams entering the innermost part of the fjord, and the distribution and age of this water are studied using both ageing and conservative tracers. The salinity variations outside this fjord are large, and in contrast to the salinity, the artificial tracers provide a straight forward analysis of river water content. The ageing tracer is used to estimate transport time scales of river water (i.e. the time elapsed since the water left the river mouth). In May 2004, the typical age of river water leaving the fjord mouth is 5 days. As the major vertical mixing agent is wind, it controls the estuarine circulation and export of river water. When the wind stress is set to zero, the vertical mixing is reduced and the vertical salinity stratification is increased, and the river water can be effectively exported out of the fjord.We also analyse the river tracer fields and salinity field in relation to along estuary winds in order to detect signs of wind-induced straining of the along estuary density gradient. We find that events of down estuary winds are primarily associated with a reduced along estuary salinity gradient due to increased surface salinity in the innermost part of the fjord, and with an overall decrease in vertical stratification and river water content at the surface. Thus, our results show no apparent signs of wind-induced straining in this shallow fjord but instead they indicate increased levels of vertical mixing or upwelling during down estuary wind events.     

Simulation of wave power devices

Classical frequency and time domain models of a single degree of freedom wave power device are presented. In the time domain, a convolution integral is conventionally used to represent the fluid dynamic radiation force, characterised by added mass and damping in the frequency domain. This integral is replaced by an approximate ordinary differential equation (ODE) model which is faster and more convenient in simulations. A time domain model of the fluid dynamics of an oscillating water column (OWC) device is derived to illustrate the technique. Digital simulations of the OWC are used to compare the accuracy of the classical and ODE models. The simulation of the ODE model runs about six times as fast as the classical model based on convolution, yet characterises the fluid dynamics accurately.     

Accurate determination of internal kinematics from numerical wave model results

The internal kinematics for surface waves propagating over a locally constant depth are expressed as convolution integrals. Given the wave kinematics at the still water level (SWL), this provides explicit and exact potential flow expressions for the internal kinematics as convolutions in space with appropriate impulse response functions. These functions are derived in closed form and they are shown to decay exponentially. This effectively reduces the limits of the convolution integral to a horizontal distance of approximately three water depths from the water column of interest. The SWL kinematics must be provided within this region. The source of SWL kinematics may, e.g. be one of the recently developed highly accurate Boussinesq-type formulations. The method is valid for multidirectional, irregular waves of arbitrary nonlinearity at any constant water depth.     

Wave impacts on structures with rectangular geometries: Part 2 decks,baffles and seawalls with impermeable or porous surfaces

This paper considers wave impacts on baffles, on baffles or decks adjacent to a vertical wall, and on porous seawalls and/or sea beds. For seawalls and vertical baffles, impacts can occur in steep waves, whilst a deck can be struck from below by a rising wave crest either in open sea or in a tank with standing waves (sloshing). A simple analytical model for the pressure impulse, P, due to a wave of idealized geometry and dynamics is developed and applied to the following geometries with impermeable surfaces:

• •horizontal wave impact onto a vertical wall with a deck at the waterline,
• •vertical wave impact under a deck in the same configuration (equivalent to vertical water impact of a horizontal plate),
• •horizontal wave impact onto a surface-piercing vertical baffle in open sea,
• •as for 3. but with the baffle in front of a wall,
• •as for 4. but with a deck extending from the vertical wall to the baffle,
• •bottom-mounted baffle in front of a wall with impact occurring on the wall.

We also consider cases that complement part 1 of this paper to include the effect on impacts on a seawall with a porous sea bed and/or sea wall with/without a berm. Finally we reconsider case 3) above but with a porous baffle.The method uses eigenfunction expansions in each of the rectangular regions that satisfy some of the impermeable or porous surface conditions, and a simplified free-surface condition. Their unknown coefficients are determined from the impact boundary condition, impermeable or porous boundary conditions and by matching the solutions, in any two neighbouring rectangles, along their common boundary. Although the fluid motion is treated rather crudely, the method yields the pressure impulse throughout the entire region. Impulses, I, and moment impulses, M, on all or parts of the structure are also presented.