Incident Wave Profile Research Articles

Combination of HOSM and FORM for extreme wave-induced response prediction of a ship in nonlinear waves

This paper proposes a method for predicting the extreme values of linear and nonlinear wave-induced responses of a ship in nonlinear waves. The method is based on a combination of the Higher Order Spectrum Method (HOSM) and First Order Reliability Method (FORM), allowing the most-probable wave episodes for extreme values of interest to be efficiently calculated. The proposed HOSM + FORM approach is first applied to extreme wave crest prediction, and the results are validated through comparisons against Monte Carlo simulations. The HOSM + FORM approach is then used to predict the extreme wave-induced vertical bending moment (VBM) distribution in a container ship. The wave-induced VBM is assumed to be linear with respect to the incident wave profile by leveraging pre-computed VBM transfer functions. Finally, the extreme value distribution of nonlinear roll motion in beam seas is investigated. The proposed HOSM + FORM approach is shown to predict the extreme linear and nonlinear wave-induced responses efficiently and accurately. The effect of wave nonlinearity is found to be significant under circumstances where the VBM is sensitive to high-frequency waves or large roll angles are excited by the wave crests.

Numerical study on hydrodynamic characteristics of coastal bridge deck under joint action of regular waves and wind

In harsh ocean environment, there are complex interactions between extreme surge waves and strong wind during hurricanes. Coastal infrastructures, such as coastal bridges, ineluctably need to withstand the joint action of waves and wind. During past few decades, many researchers have carried out a lot of theoretical, experimental, and numerical simulation work to study the damage mechanism of coastal bridges during extreme weather events. According to the authors’ knowledges, hydrodynamic characteristics of the coastal bridge deck under the joint action of surge waves and onshore wind have been largely ignored in previous researches. As one of the preliminary attempts, a series of numerical simulations have been performed to systematically investigate the hydrodynamic characteristics of coastal bridge deck under joint action of regular waves and onshore wind by considering the effects of prominent factors, such as wind speed, wave height, submersion depth, and water depth. The results indicates that the existence of the onshore wind can significantly distort the incident wave profile, enhance the intensity of wave impacting bridge deck, and generate the suction effects over the bridge deck, which will finally affect the hydrodynamic characteristics of the coastal bridge deck under the impact of regular waves. It is hoped that findings drawn from this study can further enhance our understanding on damage mechanism of coastal bridge decks during extreme weather events.

DETERMINATION OF WAVE SLAMMING LOADS ON HIGH-SPEED CATAMARANS BY HYDROELASTIC SEGMENTED MODEL EXPERIMENTS

A 2.5m hydroelastic segmented catamaran model has been developed based on the 112m INCAT wave-piercer catamaran to simulate the vibration response during the measurement of dynamic slam loads in head seas. Towing tank tests were performed in regular seas to measure the dynamic slam loads acting on the centre bow and vertical bending moments acting in the demihulls of the catamaran model as a function of wave frequency and wave height to establish the operational loads acting on the full-scale 112m INCAT catamaran vessel. Peak slam forces measured on the bow of the model are found to approach the weight of the model, this being similar to the findings of full-scale vessel trials. A review of the motions of the hydroelastic segmented catamaran model found that the heave and pitch motions give a good indication of slamming severity in terms of the dimensionless heave and pitch accelerations. The dynamic wave slam forces are closely related to the relative motion between the bow and the incident wave profile.

A VIRTUAL PISTON-TYPE WAVE MAKER BASED ON OPENFOAM

OpenFOAM is an open source CFD (Computational Fluid Dynamics) toolbox and recently attracts many researchers to develop codes based on it for their own applications. In order to numerically generate waves based on the wave-maker theory for a piston motion, numerical improvements have been done on the base of OpenFOAM by the author. In gen- eral, the present new tool can be employed to simulate wave generation as long as the piston motion is given. This paper presents the related computational procedure and simulations for generating relatively long finite-amplitude waves ac- cording to Madsen’s second-order wave-maker theory. The sensitivities of the computed incident wave profile to grid density and time step are investigated for the case of generating a wave with permanent form. The simulation accuracy is validated by comparison with the analytical solution and available experimental data.

Performance analysis of a point-absorber wave energy converter with a single buoy composed of three rigidly coupled structures

A single-body point absorber system is analysed to improve its power absorption at a finite water depth. The proposed wave energy converter consists of a single floating body coupled to a direct-drive power take-off system placed on the seabed. The structure of a cylindrical buoy with large draft is changed by a single body composed of three structures rigidly coupled, reducing its volume and improving its frequency-dependent hydrostatic parameters that are obtained through a numerical analysis tool called NEMOH. The undamped natural frequency of the oscillating system is tuned to a specified wave period and the performance of the WEC system is obtained assuming a linear Power Take-Off system. In time domain, the performance of the WEC device is carried-out under a regular (sinusoidal) and irregular incident wave profile. Comparing the performance of the WEC system using the cylindrical and the proposed buoy outcomes that the system with the proposed buoy is able to absorb more energy from incident waves with a wider frequency range, whereas the oscillating system is kept as simple as possible.

Experimental study of freak wave impacts on a tension-leg platform

This study investigates the freak wave impinging on a tension-leg platform through wave flume experiments. The freak waves are generated using the focused wave theory. By adjusting the wave focusing location, different incident wave scenarios at the structure location are produced. Simultaneous measurements of wave shape evolutions upon impingement, wave impact pressures on the platform deck, platform motions and tether forces are carried out for synchronized analyses of the wave kinematics/dynamics and structural responses. The variation of these parameters with the incident wave profile is studied. It is found that although applying less intensive local impact pressures as compared to the highly-breaking freak wave, the slightly-breaking or non-breaking freak wave imposes the same level of adverse effect on the platform's global stability in terms of motions and tether forces. In addition, the high-crest freak wave causes violent motions of the floating platform, which are likely to induce snap loads of large amplitude and high occurrence frequency in tethers. The published results would provide useful benchmarks for validating numerical and analytical models.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

Abstract A three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

A Virtual Piston-Type Wave Maker Based on OpenFOAM

OpenFOAM is an open source CFD (Computational Fluid Dynamics) toolbox and recently attracts many researchers to develop codes based on it for their own applications. In order to numerically generate waves based on the wave-maker theory for a piston motion, numerical improvements have been done on the base of OpenFOAM by the author. In gen-eral, the present new tool can be employed to simulate wave generation as long as the piston motion is given. This paper presents the related computational procedure and simulations for generating relatively long finite-amplitude waves ac-cording to Madsen’s second-order wave-maker theory. The sensitivities of the computed incident wave profile to grid density and time step are investigated for the case of generating a wave with permanent form. The simulation accuracy is validated by comparison with the analytical solution and available experimental data.

Bounded inhomogeneous wave profiles for increased surface wave excitation efficiency at fluid-solid interfaces.

Though the ultrasonic excitation of surface waves in solids is generally realized through the use of a contact transducer, remote excitation would enable standoff testing in applications such as the nondestructive evaluation of structures. With respect to the optimal incident wave profile, bounded inhomogeneous waves, which include an exponentially decaying term, have been shown to improve the surface wave excitation efficiency as compared to Gaussian and square waves. The purpose of this work is to investigate the effect of varying the incident wave spatial decay rate, as applied to both lossless fluid-solid interfaces and to solids with viscoelastic losses included. The Fourier method is used to decompose the incident profile and subsequently compute the reflected wave profile. It is shown that inhomogeneous plane wave theory predicts, to a close approximation, the location of the minimum in the local reflection coefficient with respect to the decay rate for bounded incident waves. Moreover, plane wave theory gives a reasonable indication of the decay rate that maximizes the surface wave excitation efficiency.

Wave-by-wave control in irregular waves for a wave energy converter with approximate parameters

This paper investigates wave-by-wave control of a single-mode wave energy converter driven to operate such that the oscillation velocity closely matches the hydrodynamically optimum velocity for best power absorption. Such control typically requires prediction of the incident wave profile, which, for realistic wave spectra may be obtained using up-wave measurements over a duration and at a distance based on a deterministic propagation model and the device dynamics. This work investigates how such control may be attempted when the device inertia, viscous damping, hydrostatic stiffness, frequency-dependent hydrodynamic coefficients, and exciting force are quantified approximately. In particular, this paper studies an implementation of adaptive trajectory-tracking control using on-line estimation of the mechanical and hydrodynamic parameters (i.e. inertia, viscous damping, hydrostatic stiffness, frequency-dependent added mass, frequency-dependent radiation damping, and the exciting force), where a hydrodynamically optimum velocity variation based on approximate parameter estimates provides the reference trajectory. In this study, the rest mass, infinite-frequency added mass, hydrostatic stiffness, a linearized viscous damping coefficient, and two parameters representing the uncertainties in the radiation impulse-response function and the exciting force impulse-response function are estimated on line. The present method relies on feedback and feedforward forces derived using a Lyapunov function comprised of a system Hamiltonian that combines the mechanical and information exergy functions. Energy capture results under oscillation constraints show that, while the present implementation leaves significant room for improvement relative to near-optimal wave-by-wave control with exact parameters, considerable improvement is still observed relative to resistive control with exact parameters.

A simplified approach for computation of nonlinear ship loads and motions using a 3D time-domain panel method

Forces and motions on an advancing ship are studied using an approximate nonlinear 3D panel method, formulated based on transient free surface Green's function. Nonlinearities arising from the large-amplitude incident waves are considered in the computations of Froude–Krylov and hydrostatic restoring forces for which a suitable algorithm is developed that can find the exact wetted surface under the incident wave profile. As regards the perturbation potential consisting of the diffraction and radiation effects, although the numerical solution is based on linearized free-surface constraints and discretization of the mean wetted hull under the mean free-surface, a modified form of the body-kinematic condition is applied. Noting that the incident wave-kinematics are largest at the exact free-surface, the adopted procedure is expected to incorporate some of the nonlinearities in the diffraction part of the perturbation potential, albeit partially. Influence of nonlinearities on motions and loads are presented for a Wigley hull and S175 hull in head waves. For the S175 hull, bending moment results are also included. These latter results are particularly important for Class Societies interested in structural loads, and it is found that incorporation of the nonlinearities even within the adopted approximations can result in significantly different pressures and structural loads.

Body nonlinear time domain calculation of vertical ship responses in extreme seas accounting for 2nd order Froude-Krylov pressure

A body nonlinear time domain method based on strip theory with a weakly nonlinear formulation for the free surface condition is proposed and used to analyze the vertical responses of a cruise ship in random seas. The term ‘body nonlinearity’ implies the dependence of the hydrodynamic forces on the instantaneous wetted surface area of the ship hull. The radiation forces are calculated by means of Cummins formulation and are calculated for the wetted hull under the incident wave profile. A practical engineering approach is followed for the estimation of the body nonlinear radiation and diffraction forces. The hydrostatic forces are calculated for the wetted hull under the incident wave profile. The free surface condition is represented using a weakly nonlinear formulation and the incident irregular waves have nonlinearities up to second order. The wave pressure is calculated from the first- and second-order wave potentials using the Bernoulli equation and is integrated over the exact wetted surface to calculate the Froude-Krylov forces. The numerical results are compared with the experimental results measured in a wave tank. The comparative study is carried out by analyzing the statistics of the waves and through probability of exceedance of the wave peaks.

An analysis of the cross-shore beach morphodynamics of a sandy and a composite gravel beach

In this paper, beach profile surveys acquired over more than a decade at a sandy beach (Narrabeen Beach, New South Wales, Australia) and a composite sand–gravel beach (Milford-on-Sea, Christchurch Bay, UK) are analysed to compare and contrast cross-shore morphodynamics of the two beach types. The different behavioural characteristics of the two beach types at decadal, inter-annual and intra-annual time scales are investigated. Comparisons of beach profiles with Dean's equilibrium profile and Vellinga's erosion profile show that the Dean's profile satisfactorily represents the time mean profiles of both beach types. Statistical and Empirical Orthogonal Function (EOF) analyses confirm the generally accepted model that the inter-tidal zone is the most morphodynamically active region on a sandy beach whereas the swash zone is the most dynamic region on a mixed sand–gravel beach. The results also imply that during storms composite sand–gravel beaches may become unstable due to cutback of the upper beach while sandy beaches are more likely to be unstable as a result of beach lowering due to sediment transport from the inter-tidal zone to the sub-tidal zone during storms. EOF results also show that Milford-on-Sea beach is in a state of steady recession while the Narrabeen Beach shows a cyclic erosion–accretion variability. A multivariate technique (Canonical Correlation Analysis, CCA) shows that on the composite beach a strong correlation exists between incident wave steepness and profile response, which could be attributed to the unsaturated surf zone, whereas on the sandy beach any correlation is much less evident.

A comparative linear and nonlinear ship motion study using 3-D time domain methods

This paper reports on 3D time domain seakeeping computations at different level of modeling of nonlinear effects. Four successively improved levels of computations are considered: (i) a linear computation, (ii) Froude-Krylov nonlinear computation, (iii) body nonlinear computation where the perturbation potential is computed based on the instantaneous hull under the mean free-surface, and finally (iv) the body-exact nonlinear computation, where the perturbation potential is determined based on the wetted hull under the incident wave profile after suitable mapping of the hull into a computational domain. Computations are carried out for a Wigley hull (having less ‘geometric’ nonlinearity due to vertical sides), and a S175 hull at different forward speeds. The results are obtained for both regular and irregular waves.

The method of waveform images for finite waveguides with resistive terminations subject to arbitrary initial conditions

Reflection at normal incidence of a plane wave can be described by imaging the incident wave profile on the opposite side of the boundary. This concept has been introduced in a few texts, but only for nondissipative conditions. In this paper the procedure to describe a purely resistive boundary is generalized, and then the concept is extended to describe the transient response of a one-dimensional, finite length waveguide. The field generated by arbitrary initial conditions is characterized by an infinite number of images, which leads to a representation of the acoustic field as oppositely propagating waves in an unbounded waveguide. Both graphical and mathematical descriptions of these waves are derived, with the former shown to provide significant insights. Mathematical analysis of the image construction leads to identification of several fundamental acoustic phenomena, including acoustic modes and reverberation time. From an instructional viewpoint the ability to explore fundamental acoustic phenomena without recourse to solving differential equations makes the waveform image concept especially useful as an introductory tool.

A Study on responses of motion and mooring forces of floating structures induced by tsunami in shallow sea

The objective of present paper is to develop the practical numerical analysis system for calculating responses of motion and mooring force on floating structures induced by tsunami in shallow sea region.In the present analysis system, incident wave profile of tsunami in shallow sea have been assumed to dispersed wave based on the data base of tsunami height in all over Japan. And more boundary value problem for dispersed wave have been analyzed by the boundary element method in time domain and also the responses of motion and mooring forces for floating structures have been calculated by convolution integral method.The numerical calculation by the present method have been carried out and the results by present method have been compared with the results by CADMASU-SURF based on NS equation and with the experiment results. From these comparisons, the authors have discussed as follows: 1) From above comparisons, the accuracy and the usefulness of present numerical method have been examined. 2) From the comparisons between the numerical results for dispersed wave and solitary wave, the deference for characteristics of motion and mooring force have been discussed

Runup of Tsunamis with Transient Wave Profiles Incident on a Conical Island

Based on the linear long wave theory, analytical solutions are obtained for the propagation of tsunamis with an arbitrary incident wave profile around a conical island. The validity of the theory is verified through comparisons with two laboratory datasets. Effects of incident wave profile on the distribution of runup height and on the maximum runup height along the coastline of an island axe discussed on the basis of this theory.

Forces on a Vertical Wall due to Long Waves, Bores, and Dry-Bed Surges

The forces and overturning moments on a vertical wall due to the reflection of solitary waves, undular bores, turbulent bores, and surges on a dry bed were determined experimentally. The incident wave celerity, wave profile, runup, force, overturning moment, and pressures were measured. The wave profiles and runup time histories were obtained with a laser-induced fluorescence system. The transition from undular to turbulent bores exhibits a large increase in the maximum measured wave slope, runup, force, and moment. For all cases, the maximum measured force and overturning moment were always less than that computed from the maximum measured runup using hydrostatic considerations. When properly normalized, the runup and force on a vertical wall due to the impingement of bores on a mildly sloping beach and a horizontal bed are shown to agree quite well. The results of this study may be used to estimate the forces on a vertical wall due to turbulent bores traveling on beaches with slopes no steeper than 1/50.

Scattering of Acoustic Waves from a Moving Elastic Nonlinearity

A Doppler-like phenomenon for acoustic waves is investigated by studying the scattering of a plane acoustic wave from a moving elastic nonlinearity in a nonlinear acoustic medium. By using the Green's-function technique, the first-order waves scattered in both forward and backward directions are calculated in terms of radiations arising from secondary sources induced in the region of the moving elastic nonlinearity. Three typical profiles of the moving elastic nonlinearity (rectangular, sawtooth, and trapezoidal) are considered. A Doppler-frequency shift similar to that in the electromagnetic-wave case is found in the backward-scattered wave but not in the forward-scattered wave. This frequency shift depends on the phase velocity of the acoustic wave in the unperturbed medium and the velocity of the moving elastic nonlinearity but not on the detail profile of the elastic nonlinearity. The intensity of the frequency-shifted scattered wave depends very strongly on the wavenumber of the incident wave, width and detail profile of the elastic nonlinearity, and less strongly on the velocity of the elastic nonlinearity. A possible experimental structure for investigating the Doppler-like phenomenon is suggested. The application of the Doppler-like phenomenon as a tool for investigating dynamical properties of a moving elastic nonlinearity or an elastic shock wave in liquids or solids is also indicated.

Dynamic Yield Behavior of Explosively Loaded Metals Determined by a Quartz Transducer Technique

Explosively generated plane waves were passed through plates of duraluminum, iron, and steels of various compositions and heat treatments. X-cut quartz disks of large diameter-to-thickness ratios (≥5) were used to obtain continuous stress-time profiles of elastic-plastic wave structures associated with yielding. For times less than wave transit time through the disk, the short-circuit current output is directly proportional to the specimen-to-quartz interface stress up to 21 kbar. The incident wave profile in the specimen is then determined from the interface stress-time profile on the basis of an assumed model. Advantages of the technique are excellent time resolution, high sensitivity, and relative simplicity of use. The profiles for duraluminum,normalized SAE 1018 steel, and normalized Armco iron exhibit a relatively slow rise to the yield stress,subsequent stress relaxation, except in duraluminum, and then a gradual rising transition into the plastic wave. In comparison, SAE 4340 and other tool steel profiles exhibit a faster initial rise, no stress relaxation,and a steeper transition into the plastic wave. The dynamic yield stress in the tool steels increases with Rockwell hardness, and the separation between the elastic and plastic wavefronts decreases. In general, as the specimen thickness is increased, the dynamic yield stress decreases and the initial rise time increases.