Viscous drift forces in regular and irregular waves

A method to compute wave- and current-induced viscous drift forces and moments on floating platforms in regular and random waves is presented. The relative velocity drag term of Morison's equation is used in conjunction with frequency domain first-order motion transfer functions to compute the drift forces and moments. Mean viscous drift forces and moments in regular waves in all six degrees-of-freedom of a tension leg platform are computed. The relative importance of the free-surface force integration, steady current, wave-current interaction and platform motions on the computed drift forces and moments are discussed. The results from this method, in the frequency domain, are used to compute the drift forces and responses in irregular waves using existing methods developed for potential drift computations. Comparisons with results from time-domain computations are also presented and good agreement between the frequency-domain and time-domain results is found. Some comparisons with experimental data are also made. The frequency-domain method is found to be an efficient and useful tool for the analysis of semi-submersible and tension leg platforms during the preliminary design stage in which extensive parametric studies need to be undertaken.     

不规则波下船舶运动响应特征数值分析

针对不规则波浪作用下Wigley型船的运动响应问题进行了系统的研究,采用统计学方法深入探讨了船舶不规则运动幅值和响应周期的分布规律,并通过傅里叶变换对船舶运动响应进行了频谱特征分析。结果表明,船舶横摇方向与升沉和纵摇方向随机运动的响应特征有显著差异。在升沉与纵摇方向,波浪谱峰频率远离自振频率,前十分之一大振幅运动对应周期离散性较小,基本稳定在波浪谱峰周期附近,但小振幅运动周期分布离散性较大,频谱分析指出船舶升沉与纵摇运动响应频谱在波浪谱峰频率附近出现明显峰值。而在横摇方向,波浪谱峰频率与自振频率相耦合,不同振幅的横摇运动响应周期均稳定在自振周期附近,且周期离散性较小,频谱分析也表明横摇运动响应频谱主要集中于船舶运动自振频率附近。     

Reproduction of higher harmonics in irregular waves

The basic features of higher harmonic waves were originally presented by Stokes in 1847 who showed that a 2nd-order regular wave would attain a higher, sharper crest and a flatter trough than the basic linear one. In this paper, these characteristics are investigated for an irregular wave train. This was done to make it possible to reproduce in a laboratory flume a wave train which has the correct profile and rms according to 2nd-order theory. The 2nd-order wave heights and the overall horizontal asymmetries of the wave train were calculated for a 1st-order PM and a Jonswap spectrum. The theoretical predictions show that the traditional wave generation in a laboratory flume which is based on linear theory produces free 2nd-order waves in addition to the bound 2nd-order waves described by Stokes. These free, parasitic waves incorrectly distort the shape of the waves and produce a varying rms as a function of distance from the wave paddle. In the 2nd-order theory presented in this paper, these free (parasitic) waves are calculated for the entire spectrum. Knowing these, they can be eliminated by compensating for them by using a 2nd-order control signal on the wave paddle. This is verified by a series of model tests which show that realistic wave profiles can be generated only by means of 2nd-order control signals. The theory and corresponding paddle control are presented for any type of translating, rotating or combined wave generator.     

多向不规则波浪的确定性模拟

波浪波动时间过程及波列的模拟,对于开展实际波浪对于工程建筑物的作用具有重要的意义。本文采用线性叠加的单叠加模型,建立了多向不规则波浪的确定性模拟方法。基于理论模拟的规则波、单向不规则波和多向不规则波,验证了波浪确定性模拟方法的有效性。定性地对比分析了模拟波列和已知波列的一致性;定量地研究了模拟波浪在空间范围rr/L_s的误差分布情况(rr表示指定位置与给定位置的空间距离,L_s为有效波长)。并且建议,采用本文方法进行波浪确定性模拟时,最佳的浪高仪间距应小于0.12L_s。     

Efficient primary energy conversion in irregular waves

This paper studies reactive control of wave-energy devices in irregular waves. Estimates of future velocity of the primary energy converter are based on a time history of past velocity measurements, and prediction of incident waves is not attempted. Time–domain computations for a single-degree-of-freedom oscillating water column in irregular waves reveal that control is not optimal; but would enhance efficiency at low peak frequencies where energy-rich swells predominate, and allow appreciably smaller devices to fulfill a given power requirement.     

Seakeeping performance of fishing vessels in irregular waves

A study of the seakeeping performance of a set of fishing vessels is carried out aiming to identify the seakeeping criteria, and vessel conditions that limit the operability of the fishing vessels in certain sea states. Ship motions and derived responses are obtained in fully developed sea states using the transfer functions of the hull forms. Those responses are assessed against the prescribed values, for the chosen criteria, to determine the vessels operational conditions that might result in hazards or seasickness. For the purpose of this study, each fishing vessel is considered operating in sea states 5 and 6, with different Froude numbers and heading angles, and their short term responses are assessed against the most relevant criteria related with the absolute and relative motions, accelerations, slamming and green water on deck. The results obtained show that roll and pitch criteria are most critical for seakeeping performance, and there is a significant influence of the transverse metacentric height, GMt, and the location of the reference checking points in the seakeeping performance of these fishing vessels.     

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.     

Numerical calculation of drift current in wind waves

-Drift current induced by wind and waves is investigated with phase-averaged Navier-Stokes equation in which the Reynolds stress is closed by k-ε model. The governing equations are solved by the finite volume method in a system of nonorthogonal coordinates which is fitted to the phase-averaged wave surface. The predicted drift current is fairly reasonable and the drag coefficient of sea-surface predicted with the newly developed interface conditions shows good agreement with previous measurements when breaking waves do not exist.     

不规则波中半潜式平台及其系泊系统动力响应分析

采用时域分析方法,研究某半潜式平台在不规则波作用下的动力响应特性。重点分析在不同浪向角情况下,平台系统有1根锚链缆发生断裂时,其运动谱与锚链缆张力谱的变化特性。研究表明,在该半潜平台遭遇恶劣海况时,一旦有某1根锚链缆发生断裂,则对整个平台系统的动力响应特性将是有很大影响的。     

Active heave compensation on drill-ships in irregular waves

This paper investigates a possible method for heave compensation on board deep-water drill-ships subjected to irregular-wave excitation. The proposed system exploits favorable interaction of coupled oscillators to achieve the desired results. This study examines an actively controlled compensator which performs well over a large wave-frequency bandwidth. Performance under certain operating conditions is investigated using a dynamic model. Simple mathematical arguments and frequency-domain computations in an irregular wave spectrum show the proposed heave compensation system to be effective within the bounds of linearity.     

Exact distributions for apparent waves in irregular seas

We discuss the long-run distributions of several characteristics for the apparent waves in a Gaussian sea. Three types of one-dimensional wave records are considered: 1) the seaway in time at a fixed position; 2) the instantaneous profile along a horizontal line; 3) the encountered seaway. Exact integral forms of the joint long run distributions are derived for the apparent periods, lengths, and heights. Results of numerical approximations of these distributions are presented in examples. For the computations we considered, as the input spectra, empirical estimates of the frequency spectra as well as JONSWAP type spectra. Effective algorithms are discussed and utilized in the form of a comprehensive computer package of numerical routines.     

On a near-optimal control approach for a wave energy converter in irregular waves

Real-time smooth reactive control and optimal damping of wave energy converters in irregular waves is difficult in part because the radiation impulse response function is real and causal, which constrains the frequency-dependent added mass and radiation damping according to the Kramers–Kronig relations. Optimal control for maximum energy conversion requires independent synthesis of the impulse response functions corresponding to these two quantities. Since both are non-causal (one being odd and other even), full cancellation of reactive forces and matching of radiation damping requires knowledge or estimation of device velocity into the future. To address this difficulty and the non-causality of the exciting force impulse response function, this paper investigates the use of propagating-wave surface elevation up-wave of the device to synthesize the necessary forces. Long-crested waves are assumed, and the approach is based on the formulations of Naito and Nakamura [2] and Falnes [22]. A predominantly heaving submerged device comprised of three vertically stacked discs driving a linear power take-off is studied. The overall formulation leads to smooth control that is near-optimal, given the approximations involved in the time-shifting of the non-causal impulse response functions and the consequent up-wave distances at which wave surface elevation is required. Absorbed power performance with the near-optimal approach is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Simulation results for wave spectra over a range of energy periods and significant wave heights are compared for the three situations studied. While practical implementation presents engineering challenges, in terms of time-averaged absorbed power, unconstrained near-optimal control is found to perform significantly better than single-frequency tuning in the spectra with longer energy periods (>10 s for the present device), and somewhat better in the spectra with shorter energy periods (here ≤10 s).     

Inline forces on vertical pile in irregular waves

The total inline wave forces, the irregular wave forces in particular, on an isolated pile are investigated by experiment. The relationships between force coefficients Cd and CM including in Morison's Eq. . and KC number or Reynolds number Re, and the variation of Cd and Cm in frequency domain are analysed with the method of least-squares in time domain and that of cross-spectral analysis. The plots of C4and Cmversus KCare given for both regular and irregular waves and those for irregular waves are used for numerical simulation of the irregular wave forces on the vertical pile and the results are in fairly good agreement with the test data. Based on the experimental results , the applicability of the spectral analysis method for calculating irregular wave forces on an isolated pile is investigated with the coherency γ between wave and wave forces and with KC number.     

直立堤前海床的局部冲刷

对不规则波作用下直立堤前海床的局部冲刷进行了研究。研究了由于波浪作用导致床面的底沙运动,从而造成提前海床的局部冲刷,即所谓的“相对粒沙”的情况。报导了;(1)堤前海床面为水平、堤下无基床情况下的堤前局部冲刷,以及堤下有明基床时基床尺度对堤前局部冲刷的影响;(2)堤前海床面为斜坡面时堤前的局部冲刷,以及当堤下有明基床时基床尺度对堤前局部冲刷的影响;(3)从波浪作用下床面边界层的理论分析出发,对于在不规则波作用下,离堤面愈远处的冲刷坑深度愈小的事实给出了解释。     

Linear and nonlinear irregular waves and forces in a numerical wave tank

A time-domain higher-order boundary element scheme was utilized to simulate the linear and nonlinear irregular waves and diffractions due to a structure. Upon the second-order irregular waves with four Airy wave components being fed through the inflow boundary, the fully nonlinear boundary problem was solved in a time-marching scheme. The open boundary was modeled by combining an absorbing beach and the stretching technique. The proposed numerical scheme was verified by simulating the linear regular and irregular waves. The scheme was further applied to compute the linear and nonlinear irregular wave diffraction forces acting on a vertical truncated circular cylinder. The nonlinear results were also verified by checking the accuracy of the nonlinear simulation.     

Wave-induced drift of small floating objects in regular waves

Water waves induce a slow drift of an object floating on the water surface. In this study, we examined, by a series of laboratory experiments, the drift motion of small rigid floating objects driven by regular waves in deep water. Different shapes of planar objects, including square, circular and elliptical, were investigated for two different submergences, and their drift motions in waves were determined using an infrared motion monitoring system. The corresponding measurements enabled the quantification of the drift characteristics with respect to the wave characteristics and object shapes. Numerical simulations based on an existing theory were presented and comparisons between the experimental data and the predictions by the existing theory were performed.     

Numerical analysis on ship maneuvering coupled with ship motion in waves

This paper considers a numerical analysis of ship maneuvering performance in the presence of incident waves and resultant ship motion responses. To this end, a time-domain ship motion program is developed to solve the wave–body interaction problem with the ship slip speed and rotation, and it is coupled with a modular-type 4-DOF maneuvering problem. In this coupled problem, the second-order mean drift force, which can play an important role in the ship maneuvering trajectory, is estimated by using a direct pressure integration method. The developed method is validated by observing the second-order mean drift force, and planar trajectories in maneuvering tests with and without the presence of incident waves. The comparisons are made for two ship models, Series 60 with block coefficient 0.7 and the S-175 containership, with existing experimental data. The maneuvering tests observed in this study include a zig-zag test in calm water, and turning tests in calm water and in regular waves. The present results show a fair agreement of overall tendency in maneuvering trajectories.