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1
Kim, Mun Sung, Kwang Hyo Jung, and Sung Boo Park. "WAVE INDUCED COUPLED MOTIONS AND STRUCTURAL LOADS BETWEEN TWO OFFSHORE FLOATING STRUCTURES IN WAVES." Brodogradnja 69, no. 3 (2018): 149–73. http://dx.doi.org/10.21278/brod69309.
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As oil or gas field moves deeper offshore area, offshore offloading operations such as Tandem or Side-by-Side arrangement between two floating structures take place in many locations throughout the world and also have many hydrodynamic problems. Therefore, the researches on the motion response and hydrodynamic force including first and second order between two floating structures are needed to have the more safe offloading operability in waves. In this paper, prediction of wave induced motion responses and structural loads at mid-ship section with hydrodynamic interaction effect between two offshore floating structures in various heading waves are studied by using a linearized three-dimensional potential theory. Numerical calculations using three-dimensional pulsating source distribution techniques have been carried out for hydrodynamic pressure distribution, wave exciting force, twelve coupled linear motion responses, relative motions and wave loads of the barge and the ship in oblique waves. The computational results give a good correlation with the experimental results and also with other numerical results. As a result, the present computational tool can be used effectively to predict the wave induced motions and structural loads of multiple offshore floating structures in waves.
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Fouques, Sébastien, Harald E. Krogstad, and Dag Myrhaug. "A Second Order Lagrangian Model for Irregular Ocean Waves." Journal of Offshore Mechanics and Arctic Engineering 128, no. 3 (2005): 177–83. http://dx.doi.org/10.1115/1.2199563.
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Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.
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Xiang, Gong, and C. Guedes Soares. "Incorporating irregular nonlinear waves in simulation of dropped cylindrical objects." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 234, no. 1 (2019): 272–83. http://dx.doi.org/10.1177/1475090218825170.
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This study investigates the use of second-order irregular waves for estimating loads on dropped objects. The theory for the irregular nonlinear wave model is integrated into a motion prediction model to simulate the falling process of a dropped cylinder under irregular waves. Through frequency analysis, the simulated irregular waves are transformed into wave spectrum by fast Fourier transform and compared with the target wave spectrum. A good agreement between simulated wave spectrum and target wave spectrum indicates the validity of the irregular nonlinear wave model. The effects of cylinder mass density, wave amplitude and initial wave phase on the trajectory and terminal conditions of dropped cylindrical object are systematically investigated, and the simulated results are compared with those induced by regular waves.
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Beck, Robert F., and Arne E. Loken. "Three-Dimensional Effects in Ship Relative-Motion Problems." Journal of Ship Research 33, no. 04 (1989): 261–68. http://dx.doi.org/10.5957/jsr.1989.33.4.261.
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The total relative motion between a ship and the sea surface, including the effects of the ship motions, the incident waves, the diffracted waves, and the radiated waves, is discussed. The radiated and diffracted wave components are calculated using the theory of Salvesen, Tuck, and Faltinsen (1970) with the zero-speed potentials determined by fully three-dimensional calculations. Comparisons with experiments and other theoretical calculations for a simple mathematical hull form are given. The proposed theory shows significant improvement over slender-body theory for the diffraction component and is equal to or better than strip theory for the radiation component.
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Nikurashin, Maxim, and Raffaele Ferrari. "Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Theory." Journal of Physical Oceanography 40, no. 5 (2010): 1055–74. http://dx.doi.org/10.1175/2009jpo4199.1.
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Abstract Observations and inverse models suggest that small-scale turbulent mixing is enhanced in the Southern Ocean in regions above rough topography. The enhancement extends O(1) km above the topography, suggesting that mixing is supported by the breaking of gravity waves radiated from the ocean bottom. In this study, it is shown that the observed mixing rates can be sustained by internal waves generated by geostrophic motions flowing over bottom topography. Weakly nonlinear theory is used to describe the internal wave generation and the feedback of the waves on the zonally averaged flow. Vigorous inertial oscillations are driven at the ocean bottom by waves generated at steep topography. The wave radiation and dissipation at equilibrium is therefore the result of both geostrophic flow and inertial oscillations differing substantially from the classical lee-wave problem. The theoretical predictions are tested versus two-dimensional high-resolution numerical simulations with parameters representative of Drake Passage. This work suggests that mixing in Drake Passage can be supported by geostrophic motions impinging on rough topography rather than by barotropic tidal motions, as is commonly assumed.
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ALAM, MOHAMMAD-REZA, YUMING LIU, and DICK K. P. YUE. "Resonant-wave signature of an oscillating and translating disturbance in a two-layer density stratified fluid." Journal of Fluid Mechanics 675 (April 6, 2011): 477–94. http://dx.doi.org/10.1017/s0022112011000309.
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We investigate the nonlinear wave signature of a translating and oscillating disturbance under the influence of ambient waves in a two-layer fluid. The main interests are the generation and features of the far-field waves due to nonlinear wave resonances. We show, using perturbation theory, that free waves on the surface and/or interface can be produced by triad-resonant interactions, a mechanism not obtained in a homogeneous fluid. These occur among the radiated waves due to the disturbance motion (disturbance waves); and between the disturbance waves and free ocean waves (ambient waves). Such resonance-generated waves can appear upstream or downstream, and may propagate away from or towards the disturbance. In realistic situations where ambient waves and disturbance oscillations contain multiple frequencies, numerous resonant and near-resonant interactions at second and higher orders may occur, making the theoretical analysis of the problem intractable. For this purpose, we develop a direct simulation capability using a high-order spectral method, which provides independent validation of the theoretical predictions. Our investigations show that, under specific but realistic conditions, resonance interactions may lead to significant far-field short waves that are more amenable to remote sensing. If the characteristics of the disturbance are known, we illustrate how nonlinear wave resonances provide a mechanism for more precise estimation of ocean stratification properties using surface wave measurements. Finally we show that when a moving disturbance oscillates at multiple frequencies, ensuing multiple resonances may lead to energy spreading across a broader spectrum, resulting in the loss of information about the body motion.
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Evans, D. V., and C. M. Linton. "Submerged Floating Breakwaters." Journal of Offshore Mechanics and Arctic Engineering 113, no. 3 (1991): 205–10. http://dx.doi.org/10.1115/1.2919921.
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In this paper we show how a submerged body can, if properly tuned to the incoming waves, reflect an appreciable amount of the incident wave energy by creating waves through its own motion which effectively cancel the incident waves passing over it. A general theory for this phenomenon is described which is applied to the cases of a hinged vertical plate and a submerged tethered horizontal circular cylinder.
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Thorpe, S. A. "The distortion of short internal waves produced by a long wave, with application to ocean boundary mixing." Journal of Fluid Mechanics 208 (November 1989): 395–415. http://dx.doi.org/10.1017/s0022112089002880.
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The propagation of a train of short, small-amplitude, internal waves through a long, finite-amplitude, two-dimensional, internal wave is studied. An exact solution of the equations of motion for a Boussinesq fluid of constant density gradient is used to describe the long wave, and its distortion of the density gradient as well as its velocity field are accounted for in determining the propagation characteristics of the short waves. To illustrate the magnitude of the effects on the short waves, particular numerical solutions are found for short waves generated by an idealized flow induced by a long wave adjacent to sloping, sinusoidal topography in the ocean, and the results are compared with a laboratory experiment. The theory predicts that the long wave produces considerably distortion of the short waves, changing their amplitudes, wavenumbers and propagation directions by large factors, and in a way which is generally consistent with, but not fully tested by, the observations. It is suggested that short internal waves generated by the interaction of relatively long waves with a rough sloping topography may contribute to the mixing observed near continental slopes.
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McAllister, M. L., and T. S. van den Bremer. "Lagrangian Measurement of Steep Directionally Spread Ocean Waves: Second-Order Motion of a Wave-Following Measurement Buoy." Journal of Physical Oceanography 49, no. 12 (2019): 3087–108. http://dx.doi.org/10.1175/jpo-d-19-0170.1.
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AbstractThe notion that wave-following buoys provide less accurate measurements of extreme waves than their Eulerian counterparts is a perception commonly held by oceanographers and engineers (Forristall 2000, J. Phys. Oceanogr., 30, 1931–1943, https://doi.org/10.1175/1520-0485(2000)030<1931:WCDOAS>2.0.CO;2). By performing a direct comparison between the two types of measurement under laboratory conditions, we examine one of the hypotheses underlying this perception and establish whether wave measurement buoys in extreme ocean waves correctly follow steep crests and behave in a purely Lagrangian manner. We present a direct comparison between Eulerian gauge and Lagrangian buoy measurements of steep directionally spread and crossing wave groups on deep water. Our experimental measurements are compared with exact (Herbers and Janssen 2016, J. Phys. Oceanogr., 46, 1009–1021, https://doi.org/10.1175/JPO-D-15-0129.1) and new approximate expressions for Lagrangian second-order theory derived herein. We derive simple closed-form expressions for the second-order contribution to crest height representative of extreme ocean waves—namely, for a single narrowly spread wave group, two narrowly spread crossing wave groups, and a single strongly spread wave group. In the limit of large spreading or head-on crossing, Eulerian and Lagrangian measurements become equivalent. For the range of conditions that we test, we find that our buoy behaves in a Lagrangian manner, and our experimental observations compare extremely well to predictions made using second-order theory. In general, Eulerian and Lagrangian measurements of crest height are not significantly different for all degrees of directional spreading and crossing. However, second-order bound-wave energy is redistributed from superharmonics in Eulerian measurements to subharmonics in Lagrangian measurement, which affects the “apparent” steepness inferred from time histories and poses a potential issue for wave buoys that measure acceleration.
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Smit, P. B., T. T. Janssen, and T. H. C. Herbers. "Nonlinear Wave Kinematics near the Ocean Surface." Journal of Physical Oceanography 47, no. 7 (2017): 1657–73. http://dx.doi.org/10.1175/jpo-d-16-0281.1.
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AbstractEstimation of second-order, near-surface wave kinematics is important for interpretation of ocean surface remote sensing and surface-following instruments, determining loading on offshore structures, and understanding of upper-ocean transport processes. Unfortunately, conventional wave theories based on Stokes-type expansions do not consider fluid motions at levels above the unperturbed fluid level. The usual practice of extrapolating the fluid kinematics from the unperturbed free surface to higher points in the fluid is generally reasonable for narrowband waves, but for broadband ocean waves this results in dramatic (and nonphysical) overestimation of surface velocities. Consequently, practical approximations for random waves are at best empirical and are often only loosely constrained by physical principles. In the present work, the authors formulate the governing equations for water waves in an incompressible and inviscid fluid, using a boundary-fitted coordinate system (i.e., sigma or s coordinates) to derive expressions for near-surface kinematics in nonlinear random waves from first principles. Comparison to a numerical model valid for highly nonlinear waves shows that the new results 1) are consistent with second-order Stokes theory, 2) are similar to extrapolation methods in narrowband waves, and 3) greatly improve estimates of surface kinematics in random seas.
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Song, Yang, Yan Lin, Ming Xia Zhang, and Pin Le Qin. "The Simulation of Ship Oscillatory Motions in Irregular Waves." Applied Mechanics and Materials 66-68 (July 2011): 1296–300. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.1296.
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Based on the theory of nonlinear random dynamic and ship oscillatory motions, by analyzing the spectrum of the random ocean wave and the force of the ship, the roll and pitch motion equations were erected respectively, then the irregular waves were created according to the superposition theory. Meanwhile, the coupling motion between rolling and heaving was studied, then the time-domain responses were the driving data of the motions simulation. Using VisualBasic, the interaction interface was established. Using MATLAB, the motions were solved. Using OpenGL the 3-D model of ship was described. We just need input the ship and environment parameters then the results will be displayed with the 2-D figures and the 3-D model quickly, then the visualization of ship motions simulation is achieved. The program developed can simulate 3-D ships and can be used for designers to analyze the properties of ship intuitively.
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Zhang, Bao-Ji, Gao Yu, and Wen-Xuan She. "Offshore Wind Turbine Coupled Motion in Regular Waves." Marine Technology Society Journal 54, no. 2 (2020): 5–16. http://dx.doi.org/10.4031/mtsj.54.2.2.
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AbstractThis study aims to accurately predict the hydrodynamic performance and motion responses of offshore wind turbines on the basis of computational fluid dynamics (CFD) theory. Continuous and Navier-Stokes (N-S) equations are employed as control equations, and the k-ε model is used as a turbulence model. The finite difference method is utilized to discretize the equation. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm is applied to solve the control equation, and the volume-of-fluid (VOF) method is used to capture the free surface. The numerical wave tank of irregular wave is also established. The hydrodynamic performances and motion responses of the offshore wind turbines under regular waves are studied. First, we assume a floating foundation without the influence of a rotational fan and examine its motion responses and wave force in three typical sea conditions, namely, Levels 5, 6, and 7. Thereafter, we use a series of force and torque acting on the rotating center of the offshore to substitute for the influence of the rotational fan on the floating foundation. Then, we study the hydrodynamic performance influenced by blade rotation of the floating foundation in various sea conditions and three wind speeds, namely, 5, 8, and 11 m/s. Research results can provide usable theoretical principle and technical support for the investigation of the hydrodynamic performance and motion responses of similar offshore wind turbines.
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Sun, Shi Yan, Hai Long Chen, and Gang Xu. "Water Entry of A Wedge Into Waves in Three Degrees Offreedom." Polish Maritime Research 26, no. 1 (2019): 117–24. http://dx.doi.org/10.2478/pomr-2019-0013.
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Abstract The hydrodynamic problem of a two-dimensional wedge entering into a nonlinear wave in three degrees of freedom is investigated based on the incompressible velocity potential theory. The problem is solved through the boundary element method in the time domain. To avoid numerical difficulties due to an extremely small contact area at the initial stage, a stretched coordinate system is used based on the ratio of the Cartesian system in the physical space to the distance travelled by the wedge in the vertical direction. The mutual dependence of body motion and wave loading is decoupled by using the auxiliary function method. Detailed results about body accelerations, velocities and displacements at different Froude numbers or different waves are provided, and the mutual effect between body motion and wave loading is analysed in depth.
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Zhang, Bao-Ji, Jie Liu, Ning Xu, Lei Niu, and Wen-Xuan She. "Numerical Simulation of Ship Motions in Regular and Irregular Waves." Marine Technology Society Journal 53, no. 1 (2019): 97–106. http://dx.doi.org/10.4031/mtsj.53.1.10.
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AbstractA numerical simulation method is presented in this study to predict ship resistance and motion responses in regular and irregular waves. The unsteady RANS (Reynolds Average Navier-Stokes) method is selected as the governing equation, and a volume of fluid (VoF) model is used to capture the free surface, combining the k-ε equations. A finite volume method (FVM) is utilized to discretize both the RANS equations and VoF transport equation. The pressure implicit split operator (PISO) method is set as the velocity-pressure coupling equation. The overset mesh technique is utilized to simulate ship motions in waves. A DTMB5415 ship is selected as a case study to predict its pitch and heave responses in regular and irregular waves at different wave length and wave steepness. The ship is free to move in the pitch and heave directions. The CFD (Computational Fluid Dynamics) results are found to be in good agreement with the strip theory and experimental data. It can be found that the CFD method presented in this study can provide a theoretical basis and technical support for green design and manufacture of ships.
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Kim, J. W., and R. C. Ertekin. "Hydroelasticity of an infinitely long plate in oblique waves: Linear Green-Naghdi theory." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 216, no. 2 (2002): 179–97. http://dx.doi.org/10.1243/147509002762224388.
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The Level I Green-Naghdi (GN) theory is developed, within the assumptions of linearity, to analyse the hydroelastic response of an infinitely long elastic plate of finite width. The plate is freely floating on the free surface of finite depth and in regular oblique waves. An equation of motion is obtained that is similar to the shallow-water wave equation of Stoker, but which possesses an improved dispersion relation and includes the added-mass force due to the vertical motion of the fluid column. Comparisons with the available experimental data for the special case of beam seas show good agreement with the present theory. An explicit solution is also obtained when the plate is very wide. A local analysis near the critical wave number is made for the solution, and it is shown that the deflection of the plate, not necessarily at its edges, can be made arbitrarily large by increasing the width of the plate.
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Lin, Shan, Jiawang Chen, Naikuang Liang, and Ying Chen. "A Study on Wave-Induced Artificial Upwelling." Marine Technology Society Journal 50, no. 1 (2016): 48–55. http://dx.doi.org/10.4031/mtsj.50.1.8.
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AbstractArtificial upwelling, a general technique to enhance the marine primary productivity and fishery resources by means of pumping the nutrient-rich deep ocean water (DOW) to the euphotic layer, has attracted great attention in recent years. One of the most practical methods of artificial upwelling is utilizing ocean waves. In this article, the wave-induced method, which can induce artificial upwelling immediately without external power, is discussed. This method is based on the Bernoulli equation of the small amplitude wave and utilizes a floating structure. The upwelling water head of the nonlinear characteristics in the wave motion is calculated, which is deduced by linear wave theory. This method predicts and estimates the upwelling flow rate, which is determined by the water head difference induced by waves. For example, when the sea depth is 100 m with an ideal regular progressive wave of 5 m in height and 0.1 Hz in frequency under an ideal condition, it could produce a 2,200 m3/h flow rate upwelling. However, in the real sea field, the efficiency of floating structure upwelling declined due to the increase of actual resistance.
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Fang, Ming-Chung, Ming-Ling Lee, and Chwang-Kuo Lee. "Time Simulation of Water Shipping for a Ship Advancing in Large Longitudinal Waves." Journal of Ship Research 37, no. 02 (1993): 126–37. http://dx.doi.org/10.5957/jsr.1993.37.2.126.
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The technique of time-domain numerical simulation for the occurrence of water shipping on board in head waves is presented. The nonlinear effects of the large-amplitude motion are treated. These nonlinear factors include the effect of large wave amplitude, large ship motion, the change of hull configuration below the free surface and the nonlinear resultant wave. Therefore, the variation of the potentials and the hydrodynamic coefficients for a ship at each time step must be carefully treated. While handling the determination of the instantaneous wave surface around the ship hull, the complete incident, diffracted, and radiated wave system is used rather than the incident wave only. The complexity of the ship speed effect on the related terms is also treated at each time step, especially for the radiation problems. An experimental setup is also designed to measure the motion response and the relative motion, and comparisons are made. The results show excellent agreement and the validity of the theory is confirmed. The successful development of the present technique can be extended to analyze the dynamic stability, capsize phenomena, and ship motion in irregular waves
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Raghukumar, Kaustubha, Grace Chang, Frank Spada, Craig Jones, Tim Janssen, and Andrew Gans. "Performance Characteristics of “Spotter,” a Newly Developed Real-Time Wave Measurement Buoy." Journal of Atmospheric and Oceanic Technology 36, no. 6 (2019): 1127–41. http://dx.doi.org/10.1175/jtech-d-18-0151.1.
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AbstractThe Spotter is a low-cost, real-time, solar-powered wave measurement buoy that was recently developed by Spoondrift Technologies, Inc. (Spoondrift). To evaluate the data quality of the Spotter device, we performed a series of validation experiments that included comparisons between Spotter-derived motions and prescribed wave motions (monochromatic and random waves) on a custom-built, motion-controlled validation stand and simultaneous in-water measurements using a conventional wave measurement buoy, the Datawell DWR-G4 (Datawell). Spotter evaluations included time-domain validation (i.e., wave by wave) and comparisons of wave spectra, directional moments, and bulk statistical parameters such as significant wave height, peak period, mean wave direction, and directional spread. Spotter wave measurements show excellent fidelity and lend a high degree of confidence in data quality. Overall, Spotter-derived bulk statistical parameters were within 10% of respective Datawell-derived quantities. The Spotter’s low cost and compact form factor enabled unique field deployments of multiple wave measurement buoys for direct measurements of wave characteristics such as ocean wave decorrelation length scales, wave speed, and directional spread. Wave decorrelation lengths were found to be inversely proportional to the width of the spectrum, and wave speeds compared well against linear wave theory.
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de Kat, Jan O., and Johan E. W. Wichers. "Behavior of a Moored Ship in Unsteady Current, Wind, and Waves." Marine Technology and SNAME News 28, no. 05 (1991): 251–64. http://dx.doi.org/10.5957/mt1.1991.28.5.251.
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The influence of wind, waves and current on the dynamic behavior of a single-point moored ship is investigated. Numerical simulations were used to compute the low-frequency motions of a tanker in the horizontal plane and the bow hawser force. Parameters varied comprised loading condition, hawser length and environment. A detailed overview is given of the theory for calculating the various force contributions in the numerical model. The onset of unstable motion behavior is described for both steady and unsteady wind, wave and current conditions. Unstable behavior tends to be more predominant for the lightly loaded condition. In the fully loaded condition the vessel behavior is generally very stable, except when the current direction is unsteady.
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Raman-Nair, W., J. Millan, J. Power, and A. Somoes-Re. "Numerical Model of Towing Dynamics of a Long Flexible Life Raft in Irregular Waves." Marine Technology and SNAME News 46, no. 04 (2009): 213–18. http://dx.doi.org/10.5957/mtsn.2009.46.4.213.
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The equations of motion for the coupled dynamics of a long flexible life raft and fast rescue craft in an irregular ocean wave are formulated in two dimensions using the methods of Kane and Levinson (Dynamics: Theory and Applications, McGraw Hill Inc., 1985). The flexible raft is modeled as spring connected lumped masses, and it is assumed that the motion normal to the wave surface is small and can be neglected; that is, the bodies move along the propagating wave profile. The wave forces are applied using Morison's equation for bodies in accelerated flow. Wind loads are similarly modeled 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 in severe sea states.
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Homayoun, Esmaeil, Hassan Ghassemi, and Hamidreza Ghafari. "Power Performance of the Combined Monopile Wind Turbine and Floating Buoy with Heave-type Wave Energy Converter." Polish Maritime Research 26, no. 3 (2019): 107–14. http://dx.doi.org/10.2478/pomr-2019-0051.
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Abstract This study deals with a new concept of near-shore combined renewable energy system which integrates a monopile wind turbine and a floating buoy with heave-type wave energy converter( WEC). Wave energy is absorbed by power-take-off (PTO) systems. Four different shapes of buoy model are selected for this study. Power performance in regular waves is calculated by using boundary element method in ANSYS-AQWA software in both time and frequency domains. This software is based on three-dimensional radiation/diffraction theory and Morison’s equation using mixture of panels and Morison elements for determining hydrodynamic loads. For validation of the approach the numerical results of the main dynamic responses of WEC in regular wave are compared with the available experimental data. The effects of the heaving buoy geometry on the main dynamic responses such as added mass, damping coefficient, heave motion, PTO damping force and mean power of various model shapes of WEC in regular waves with different periods, are compared and discussed. Comparison of the results showed that using WECs with a curvature inward in the bottom would absorb more energy from sea waves.
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Nikurashin, Maxim, and Raffaele Ferrari. "Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Application to the Southern Ocean." Journal of Physical Oceanography 40, no. 9 (2010): 2025–42. http://dx.doi.org/10.1175/2010jpo4315.1.
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Abstract Recent estimates from observations and inverse models indicate that turbulent mixing associated with internal wave breaking is enhanced above rough topography in the Southern Ocean. In most regions of the ocean, abyssal mixing has been primarily associated with radiation and breaking of internal tides. In this study, it is shown that abyssal mixing in the Southern Ocean can be sustained by internal waves generated by geostrophic motions that dominate abyssal flows in this region. Theory and fully nonlinear numerical simulations are used to estimate the internal wave radiation and dissipation from lowered acoustic Doppler current profiler (LADCP), CTD, and topography data from two regions in the Southern Ocean: Drake Passage and the southeast Pacific. The results show that radiation and dissipation of internal waves generated by geostrophic motions reproduce the magnitude and distribution of dissipation previously inferred from finescale measurements in the region, suggesting that it is one of the primary drivers of abyssal mixing in the Southern Ocean.
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Soares, C. Guedes, N. Fonseca, and R. Pascoal. "Experimental and Numerical Study of the Motions of a Turret Moored FPSO in Waves." Journal of Offshore Mechanics and Arctic Engineering 127, no. 3 (2004): 197–204. http://dx.doi.org/10.1115/1.1951774.
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This paper presents the results of an experimental program carried out with a model of a FPSO (Floating Production, Storage and Offloading) unit moored and subjected to incoming waves. In regular waves, a wide range of wavelengths were tested and the effect of the wave amplitude was also investigated. In irregular waves the model was subjected to different sea states, including very severe significant wave heights. The measured responses include the six degrees of freedom absolute motions, relative motions, and the mooring forces. The experimental data of surge, heave, and pitch is compared with calculated results from a Green’s function panel method and a strip theory program. In general, the agreement between experimental and numerical data is very good.
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Xia, Jinzhu, and Zhaohui Wang. "Time-Domain Hydroelasticity Theory of Ships Responding to Waves." Journal of Ship Research 41, no. 04 (1997): 286–300. http://dx.doi.org/10.5957/jsr.1997.41.4.286.
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A time-domain linear theory of fluid-structure interaction between floating structures and the incident waves is presented. The structure is assumed to be elastic and represented by general separation of variables, whereas the fluid is described as an initial boundary value problem of potential free surface flow. The general interface boundary condition is used in the mathematical formulation of the fluid motion around the flexible structure. The general time-domain theory is simplified to a slender-body theory for the analysis of wave-induced global responses of monohull ships. The structure is represented by a nonuniform beam, while the generalized hydrodynamic coefficients can be obtained from two-dimensional potential flow theory. The linear slender body theory is generalized to treat the nonlinear loading effects of rigid motion and structural response of ships traveling in rough seas. The nonlinear hydrostatic restoring force and hydrodynamic momentum action are considered. A numerical solution is presented for the slender body theory. Numerical examples are given for two ship cases with different geometry features, a warship hull and the S175 containership with two different bow flare forms. The predicted results include linear and nonlinear rigid motions and structural responses of ships advancing in regular and irregular waves. The results clearly demonstrate the importance and the magnitude of nonlinear effects in ship motions and internal forces. Numerical calculations are compared with experimental results of rigid and elastic material ship model tests. Good agreement is obtained.
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Roberts, J. B., and N. M. C. Dacunha. "Roll Motion of a Ship in Random Beam Waves: Comparison Between Theory and Experiment." Journal of Ship Research 29, no. 02 (1985): 112–26. http://dx.doi.org/10.5957/jsr.1985.29.2.112.
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The results of an experimental study of a ship rolling in random beam waves at zero speed are presented. The experiments were conducted in a large wave tank using a 1:20 scale model of the fisheries protection vessel Sulisker. By digitally processing the roll response measurements, obtained over long periods of time, estimates of the probability distribution of the roll peak amplitudes were obtained and compared with some corresponding theoretical predictions. The theory was found to give good agreement with the experimental findings for four different wave elevation spectra. In particular, the experimentally observed deviation from the Rayleigh distribution at high peak amplitudes was correctly predicted by the theory. This deviation is largely due to the pronounced nonlinear character of the roll damping.
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Jonathan, P., and P. H. Taylor. "On Irregular, Nonlinear Waves in a Spread Sea." Journal of Offshore Mechanics and Arctic Engineering 119, no. 1 (1997): 37–41. http://dx.doi.org/10.1115/1.2829043.
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Optimal design and reassessment of offshore structures requires a good understanding of the ocean environment. The motion of the sea surface can be viewed as a three-dimensional, nonlinear stochastic process in time. In order to characterize the wave environment adequately, we need to model its random, nonlinear, and spread nature. In this paper, we address: • the expected shape of a wave near a crest or trough, • the expected shape of the ocean surface at one point, given a crest at a different point, • an efficient method to incorporate nonlinear effects within linear wave simulations, • the magnitude of wave nonlinearity as a function of wave amplitude. Detailed comparison of theory and full-scale offshore measurements at the Shell Expro Tern platform show good agreement.
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Schellin, T. E., and T. Koch. "Calculated Dynamic Response of an Articulated Tower in Waves—Comparison With Model Tests." Journal of Offshore Mechanics and Arctic Engineering 109, no. 1 (1987): 43–51. http://dx.doi.org/10.1115/1.3256989.
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Calculated dynamic response of an articulated tower in waves is compared with model tests. The theory used is based on Morison’s equation and linear wave theory and requires specified hydrodynamic force coefficients. Calculations are done with three different sets of coefficients. Firstly, coefficients are assumed not to vary with wave period. Secondly, they are selected from experimental data of oscillating flow past stationary cylinders. Thirdly, they are based on calculations using diffraction theory. Added mass and inertia coefficients have a predominant effect on calculated response, drag coefficients have almost no effect. Calculated tower top motion and horizontal force at the universal joint correlate well for all three sets of coefficients, indicating that hydrodynamic coefficients for normal flow are reasonably well selected and need not be specified with undue precision. In contrast, hydrodynamic coefficients for axial flow need to be chosen carefully. Calculated vertical force at the joint, using initially specified axial flow coefficients, correlates poorly with measurements. Correlation is greatly improved using reduced coefficients for axial flow. Calculated response is reasonably linear with wave height. Spectral analysis techniques are used to determine statistical measures for three irregular seastates. Agreement with corresponding model test results is satisfactory.
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Osborne. "Breather Turbulence: Exact Spectral and Stochastic Solutions of the Nonlinear Schrödinger Equation." Fluids 4, no. 2 (2019): 72. http://dx.doi.org/10.3390/fluids4020072.
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I address the problem of breather turbulence in ocean waves from the point of view of the exact spectral solutions of the nonlinear Schrödinger (NLS) equation using two tools of mathematical physics: (1) the inverse scattering transform (IST) for periodic/quasiperiodic boundary conditions (also referred to as finite gap theory (FGT) in the Russian literature) and (2) quasiperiodic Fourier series, both of which enhance the physical and mathematical understanding of complicated nonlinear phenomena in water waves. The basic approach I refer to is nonlinear Fourier analysis (NLFA). The formulation describes wave motion with spectral components consisting of sine waves, Stokes waves and breather packets that nonlinearly interact pair-wise with one another. This contrasts to the simpler picture of standard Fourier analysis in which one linearly superposes sine waves. Breather trains are coherent wave packets that “breath” up and down during their lifetime “cycle” as they propagate, a phenomenon related to Fermi-Pasta-Ulam (FPU) recurrence. The central wave of a breather, when the packet is at its maximum height of the FPU cycle, is often treated as a kind of rogue wave. Breather turbulence occurs when the number of breathers in a measured time series is large, typically several hundred per hour. Because of the prevalence of rogue waves in breather turbulence, I call this exceptional type of sea state a breather sea or rogue sea. Here I provide theoretical tools for a physical and dynamical understanding of the recent results of Osborne et al. (Ocean Dynamics, 2019, 69, pp. 187–219) in which dense breather turbulence was found in experimental surface wave data in Currituck Sound, North Carolina. Quasiperiodic Fourier series are important in the study of ocean waves because they provide a simpler theoretical interpretation and faster numerical implementation of the NLFA, with respect to the IST, particularly with regard to determination of the breather spectrum and their associated phases that are here treated in the so-called nonlinear random phase approximation. The actual material developed here focuses on results necessary for the analysis and interpretation of shipboard/offshore platform radar scans and for airborne lidar and synthetic aperture radar (SAR) measurements.
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Kristiansen, D., and O. M. Faltinsen. "Non-linear wave-induced motions of cylindrical-shaped floaters of fish farms." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 223, no. 3 (2009): 361–75. http://dx.doi.org/10.1243/14750902jeme147.
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This paper addresses the two-dimensional hydrodynamical problem of a floating circular cylinder in waves by means of model tests and numerical simulations. The problem is relevant for floaters of fish farms. Dedicated model tests and computational fluid dynamics (CFD)-simulations, using a presently developed numerical wave tank are presented. Large amplitude sway motion of the cylinder at a wave frequency equal to half the natural sway frequency was observed, both experimentally and numerically. This is argued to be associated with non-linear hydrodynamic effects and instabilities. Further, linear potential flow theory is shown to overpredict the sway motion at resonance of about 500 per cent compared with experiments and simulations. This discrepancy is explained to be mainly attributable to viscous damping caused by flow separation. Higher-order harmonic components of the hydrodynamic forces are significant and should be considered in fatigue life analyses of fish farms.
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Chen, Chen, Zhao, and Wang. "Wave Height and Wave Period Derived from a Shipboard Coherent S-Band Wave Radar in the South China Sea." Remote Sensing 11, no. 23 (2019): 2812. http://dx.doi.org/10.3390/rs11232812.
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To expand the scope of ocean wave observations, a shipboard coherent S-band wave radar system was developed recently. The radar directly measures the wave orbital velocity from the Doppler shift of the received radar signal. The sources of this Doppler shift are analyzed. After removing the Doppler shifts caused by the ocean current and platform, the radial velocities of water particles of the surface gravity waves are retrieved. Subsequently, the wavenumber spectrum can be obtained based on linear wave theory. Later, the significant wave height and wave periods (including mean wave period and peak wave period) can be calculated from the wavenumber spectrum. This radar provides a calibration-free way to measure wave parameters and is a novel underway coherent microwave wave radar. From 9 September to 11 September, 2018, an experiment involving radar-derived and buoy-measured wave measurements was conducted in the South China Sea. The Doppler spectra obtained when the ship was in the state of navigation or mooring indicated that the quality of the radar echo was fairly good. The significant wave heights and wave periods measured using the radar are compared with those obtained from the wave buoy. The correlation coefficients of wave heights and mean wave periods between these two instruments both exceed 0.9 while the root mean square differences are respectively less than 0.15 m and 0.25 s, regardless of the state of motion of the ship. These results indicate that this radar has the capability to accurately measure ocean wave heights and wave periods.
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Zhang, Zhiyang, Ningyu Li, Liang Zhang, Weixing Liu, and Qingwei Ma. "Hydrodynamic Performance Analysis and Optimization of Cylindrical Wave Energy Converters." Marine Technology Society Journal 52, no. 4 (2018): 106–19. http://dx.doi.org/10.4031/mtsj.52.4.11.
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AbstractTo examine the hydrodynamic performance of cylindrical wave energy converters (WECs), the expressions of velocity potentials and excitation forces were formulated by using the characteristic function expansion method, based on linear regular wave theory. The hydrodynamic coefficients in the frequency domain were obtained for different geometries in a certain water depth by using the boundary matching method. The concept of total energy per unit mass of irregular waves was introduced to optimize and maximize the ability of wave energy conversion. The effects of weight distribution on coupled surge-pitch motion were also considered in order to optimize the safety performance of the device. The results show that there will be sharp resonance at a certain frequency and the draft-to-radius ratios of WECs have a great effect on the hydrodynamic performance when its mass is fixed. The unit mass of energy in heave is highly dependent on the ratio and mass of the WEC. The weight distribution has no effect on the hydrodynamic performance of the device but has a great effect on the pitch motion, and the center of gravity has a decisive effect on the safety performance of the WEC.
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Korsmeyer, F. T., and H. B. Bingham. "The Forward Speed Diffraction Problem." Journal of Ship Research 42, no. 02 (1998): 99–112. http://dx.doi.org/10.5957/jsr.1998.42.2.99.
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This paper examines the theory and computational methods behind predicting the linear unsteady motion of a ship with steady forward speed in waves. The focus is on the wave exciting force impulse-response function as computed via the transient free-surface Green function. The linear equation of motion for a ship in waves was first written in a rational form, using the concept of the impulse-response function, by Cummins (1962). Some years later King et al (1988) added the corresponding wave exciting force in its appropriate convolution form. We extend this work by clarifying the definition of the impulsive incident wave in following seas, and show it to be easily computable. Continuing truncated calculations towards infinite time becomes especially important in following waves, and the method suggested by Bingham et al (1994) is employed here. A novel filtering scheme is also introduced to prevent short wave contamination of the solution. These developments allow calculations in following waves to be presented for the first time using this approach. The integral equation formulation of the linear seakeeping problem is reviewed in some detail, and the relevant equations derived. Transient Haskind relations for bodies with forward speed are also derived although, like their frequency-domain counterparts, these are only approximate. Computed, first-order exciting forces and response-amplitude operators for real ship geometries, in head and following seas, are presented that demonstrate the usefulness of the transient approach for the diffraction problem.
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Langhorne, Patricia J., Vernon A. Squire, Colin Fox, and Timothy G. Haskell. "Break-up of sea ice by ocean waves." Annals of Glaciology 27 (1998): 438–42. http://dx.doi.org/10.3189/s0260305500017869.
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The manner in which sea ice breaks up determines its floe-size distribution. This, together with any redistribution due to ocean currents or winds, alters the fluxes between the atmosphere and the underlying ocean. Many materials fail at stresses well below their flexural strength when subject to repeated bending, such processes being termed fatigue. in some materials a stress exists below which the material will maintain its integrity even if subjected to an infinite number of load cycles. This stress is termed the endurance limit. We report a scries of field experiments to investigate the fatigue behaviour of first-year sea ice that subjected in situ cantilever beams to repeated bending with zero mean stress. These tests suggest that an endurance limit exists for sea ice, and that it is approximately 60% of the flexural strength. Using theory and data from wave experiments performed in similar conditions to the fatigue experiments, estimates are made of the conditions under which wave-induced break-up occurs. These indicate that fatigue may be a neglected ingredient of sea-ice failure due to wave-induced motion.
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Schellin, Thomas E., and Ould el Moctar. "Numerical Prediction of Impact-Related Wave Loads on Ships." Journal of Offshore Mechanics and Arctic Engineering 129, no. 1 (2006): 39–47. http://dx.doi.org/10.1115/1.2429695.
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We present a numerical procedure to predict impact-related wave-induced (slamming) loads on ships. The procedure was applied to predict slamming loads on two ships that feature a flared bow with a pronounced bulb, hull shapes typical of modern offshore supply vessels. The procedure used a chain of seakeeping codes. First, a linear Green function panel code computed ship responses in unit amplitude regular waves. Ship speed, wave frequency, and wave heading were systematically varied to cover all possible combinations likely to cause slamming. Regular design waves were selected on the basis of maximum magnitudes of relative normal velocity between ship critical areas and wave, averaged over the critical areas. Second, a nonlinear strip theory seakeeping code determined ship motions under design wave conditions, thereby accounting for the nonlinear pressure distribution up to the wave contour and the frequency dependence of the radiation forces (memory effect). Third, these nonlinearly computed ship motions constituted part of the input for a Reynolds-averaged Navier–Stokes equations code that was used to obtain slamming loads. Favorable comparison with available model test data validated the procedure and demonstrated its capability to predict slamming loads suitable for design of ship structures.
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Plotnikov, P. I., and J. F. Toland. "Modelling nonlinear hydroelastic waves." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1947 (2011): 2942–56. http://dx.doi.org/10.1098/rsta.2011.0104.
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This paper uses the special Cosserat theory of hyperelastic shells satisfying Kirchoff’s hypothesis and irrotational flow theory to model the interaction between a heavy thin elastic sheet and an infinite ocean beneath it. From a general discussion of three-dimensional motions, involving an Eulerian description of the flow and a Lagrangian description of the elastic sheet, a special case of two-dimensional travelling waves with two wave speed parameters, one for the sheet and another for the fluid, is developed only in terms of Eulerian coordinates.
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Ley, Jens, and Ould el Moctar. "A Comparative Study of Computational Methods for Wave-Induced Motions and Loads." Journal of Marine Science and Engineering 9, no. 1 (2021): 83. http://dx.doi.org/10.3390/jmse9010083.
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Ship hull structural damages are often caused by extreme wave-induced loads. Reliable load predictions are required to minimize the risk of structural failures. One conceivable approach relies on direct computations of extreme events with appropriate numerical methods. In this perspective, we present a systematic study comparing results obtained with different computational methods for wave-induced loads and motions of different ship types in regular and random irregular long-crested extremes waves. Significant wave heights between 10.5 and 12.5 m were analyzed. The numerical methods differ in complexity and are based on strip theory, boundary element methods (BEM) and unsteady Reynolds-Averaged Navier–Stokes (URANS) equations. In advance to the comparative study, the codes applied have been enhanced by different researchers to account for relevant nonlinearities related to wave excitations and corresponding ship responses in extreme waves. The sea states investigated were identified based on the Coefficient of Contribution (CoC) method. Computed time histories, response amplitude operators and short-term statistics of ship responses and wave elevation were systematically compared against experimental data. While the results of the numerical methods, based on potential theory, in small and moderate waves agreed favorably with the experiments, they deviated considerably from the measurements in higher waves. The URANS-based predictions compared fairly well to experimental measurements with the drawback of significantly higher computation times.
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Hua, Jianbo. "A Probabilistic Study of the Simultaneous Effect of Ship Motions on the Cargo Shifting Onboard." Marine Technology and SNAME News 33, no. 01 (1996): 25–34. http://dx.doi.org/10.5957/mt1.1996.33.1.25.
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Cargo movement aboard ship can occur even in waves that produce only moderate rolling motion. It is caused when the simultaneous effect of vertical acceleration, horizontal acceleration and roll motion on the cargo onboard—defined as the equivalent roll angle—becomes sufficiently large for the problem to develop. In this paper, an analytical expression is derived for the probabilistic calculation of the equivalent roll angle, which has a nonlinear characteristic. Also, a so-called indirect time-domain simulation method is described for calculating the problem. Both methods are based on motion transfer functions calculated according to strip theory. The calculations presented here show both methods to be in good agreement. A probabilistic calculation of the equivalent roll angle of a roll-on/roll-off (RO/RO) ship is carried out using the two methods and focusing on parameters such as significant wave height, mean wave period, ship speed, and relative course angle. It is proved from the point of view of probability that the nonlinearity of equivalent roll angle results in a magnifying effect on its extreme value. The calculation shows also that in severe wave conditions large peak values of equivalent roll greater than 35 deg can be experienced by the studied RO/RO ship.
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Faltinsen, Odd M., and Rong Zhao. "Slow-Drift Motions of a Moored Two-Dimensional Body in Irregular Waves." Journal of Ship Research 33, no. 02 (1989): 93–106. http://dx.doi.org/10.5957/jsr.1989.33.2.93.
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Weak points in the traditional way of analyzing slow-drift motion are discussed. A theory consistent to second order in wave amplitude and first order in slow-drift velocity for the slow-drift motion of a structure is presented. The interaction between the waves and the local quasi-steady flow due to the slow-drift velocity is incorporated. A new numerical procedure to solve the first-and second-order problem is presented. Generalized Haskind relations for the first-order excitation force and the force due to the second-order potential are derived.
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Tulin, Marshall P., Yitao Yao, and Pei Wang. "The Generation and Propagation of Ship Internal Waves in a Generally Stratified Ocean at High Densimetric Froude Numbers, Including Nonlinear Effects." Journal of Ship Research 44, no. 03 (2000): 197–227. http://dx.doi.org/10.5957/jsr.2000.44.3.197.
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A nonlinear theory for internal wave generation and propagation is derived here for slender ships traveling at high densimetric Froude number (Fh &gt;&gt; 1) in water of small density variation. It is based on an asymptotic equation for the evolution of the internal wave vorticity generated under the ship by a known inviscid ship flow and then self-propagating in the wake. In its numerical implementation, arbitrary pycnoclines and slender ship hulls may be used, and boundary conditions on the ship hull are satisfied; the free surface is treated here as rigid, although this may be relaxed. The theory has been implemented by a suitable numerical method and numerous simulations have been carried out. The results have been compared with earlier OEL experiments. In the near field, emphasis is given to a triple-lobe pattern in the pycnocline, an upwelling along the centerline of motion with a trough on either side, forming close behind the ship. Two distinct types of triple lobes are identified:dominant central lobe and very weak troughs, and;weak central lobe and dominant troughs. The former (a) is shown to result in linear propagation into the far field. The latter (b) results in far-field patterns preceded by a deep trough whose propagation is nonlinear. The comparisons of both simulated trends and actual amplitudes with measurements are good, surprisingly so considering the small scale of the experiment and the asymptotic nature of the theory. The effect of the turbulent wake on the internal waves in the experiments is restricted to a very narrow region behind the ship; the bulk of the wave pattern including the leading waves seem unaffected. Simulations show that under certain conditions of stratification, triple-lobe patterns with abnormally large troughs are generated and lead to strong nonlinear effects; these deep troughs propagate sidewards to large distances aft (over 40 ship lengths) with slow decay, and result in much larger surface currents and strain rates than in the normal case. Correspondingly, fast waves of depression, which decay slowly, were discovered through the simulation of two-dimensional initial value problems, where the initial area of depression was significantly less than required of a true soliton; these "quasi-solitons" are briefly studied here.
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Le Caillec, J. M., R. Garello, and B. Chapron. "Two dimensional estimates from ocean SAR images." Nonlinear Processes in Geophysics 3, no. 3 (1996): 196–215. http://dx.doi.org/10.5194/npg-3-196-1996.
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Abstract. Synthetic Aperture Radar (SAR) images of the ocean yield a lot of information on the sea-state surface providing that the mapping process between the surface and the image is clearly defined. However it is well known that SAR images exhibit non-gaussian statistics and that the motion of the scatterers on the surface, while the image is being formed, may yield to nonlinearities. The detection and quantification of these nonlinearities are made possible by using Higher Order Spectra (HOS) methods and more specifically, bispectrum estimation. The development of the latter method allowed us to find phase relations between different parts of the image and to recognise their level of coupling, i.e. if and how waves of different wavelengths interacted nonlinearly. This information is quite important as the usual models assume strong nonlinearities when the waves are propagating in the azimuthal direction (i.e. along the satellite track) and almost no nonlinearities when propagating in the range direction. In this paper, the mapping of the ocean surface to the SAR image is reinterpreted and a specific model (i.e. a Second Order Volterra Model) is introduced. The nonlinearities are thus explained as either produced by a nonlinear system or due to waves propagating into selected directions (azimuth or range) and interacting during image formation. It is shown that quadratic nonlinearities occur for waves propagating near the range direction while for those travelling in the azimuthal direction the nonlinearities, when present, are mostly due to wave interactions but are almost completely removed by the filtering effect coming from the surface motion itself (azimuth cut-off). An inherent quadratic interaction filtering (azimuth high pass filter) is also present. But some other effects, apparently nonlinear, are not detected with the methods described here, meaning that either the usual relation developed for the Ocean-to-SAR transform is somewhat incomplete, although the mechanisms leading to its formulation seem to be correct, or that these nonlinearities cannot be detected in the classical bispectrum theory.
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MacKinnon, J. A., M. H. Alford, Oliver Sun, Rob Pinkel, Zhongxiang Zhao, and Jody Klymak. "Parametric Subharmonic Instability of the Internal Tide at 29°N." Journal of Physical Oceanography 43, no. 1 (2013): 17–28. http://dx.doi.org/10.1175/jpo-d-11-0108.1.
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Abstract Observational evidence is presented for transfer of energy from the internal tide to near-inertial motions near 29°N in the Pacific Ocean. The transfer is accomplished via parametric subharmonic instability (PSI), which involves interaction between a primary wave (the internal tide in this case) and two smaller-scale waves of nearly half the frequency. The internal tide at this location is a complex superposition of a low-mode waves propagating north from Hawaii and higher-mode waves generated at local seamounts, making application of PSI theory challenging. Nevertheless, a statistically significant phase locking is documented between the internal tide and upward- and downward-propagating near-inertial waves. The phase between those three waves is consistent with that expected from PSI theory. Calculated energy transfer rates from the tide to near-inertial motions are modest, consistent with local dissipation rate estimates. The conclusion is that while PSI does befall the tide near a critical latitude of 29°N, it does not do so catastrophically.
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Centeno, R., K. S. Varyani, and C. Guedes Soares. "Experimental Study on the Influence of Hull Spacing on Hard-Chine Catamaran Motions." Journal of Ship Research 45, no. 03 (2001): 216–27. http://dx.doi.org/10.5957/jsr.2001.45.3.216.
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An experimental program was performed with hard-chine catamaran models in regular waves. The distance between the demi-hulls of the models was changed to assess its effects on the wave-induced motions. The results allowed the study of some aspects related to catamaran motions, like the interference between the hulls and resonance frequencies. The experimental results are compared with calculations performed with a recently developed code based on a two-dimensional potential flow theory in which viscous forces are included through a cross-flow drag approach. The effect of the hull distance in the heave and pitch motion responses and the importance of the viscous forces in such hull configurations are shown.
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Wu, Zhiwen, Canrong Xie, Guoxiong Mei, and Hongyuan Dong. "Dynamic analysis of parametrically excited marine riser under simultaneous stochastic waves and vortex." Advances in Structural Engineering 22, no. 1 (2018): 268–83. http://dx.doi.org/10.1177/1369433218783968.
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This study investigates the dynamic analysis of parametrically excited marine riser under simultaneous stochastic waves and vortex. A general analysis considers the parametric excitation resulting from platform motion, ocean wave loading directly on the rise, and vortex-shedding excitation due to flow bypassing the risers. Stochastic wave force and vortex excitation acting on the riser in the time domain is formulated by the stochastic phase spectrum method and derived by the linear-wave theory using a Pierson–Moskowitz wave spectrum to simulate real sea conditions. A derived parametrically excited top tensioned riser model subjected to simultaneous stochastic waves and vortex excitations is proposed. The efficacy of the present method is assessed by solutions obtained from other existing methods and experimental data of two test models. The present method is evaluated by solutions computed from existing methods and experimental data of two test models, and a general good agreement of the analyses between the proposed approach and other methods is observed. The availability of resonance, parametric stability, energy distribution and transfer, and the sensitivity of key parameters estimated by single-frequency and multi-frequency excitation are compared and discussed. Comparing with the results obtained from the harmonic excitation method, the present method can be used to make more reasonable and accurate calculations of the dynamic response of risers operating in real sea conditions.
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Clarke, Allan J. "Analytical Theory for the Quasi-Steady and Low-Frequency Equatorial Ocean Response to Wind Forcing: The “Tilt” and “Warm Water Volume” Modes." Journal of Physical Oceanography 40, no. 1 (2010): 121–37. http://dx.doi.org/10.1175/2009jpo4263.1.
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Abstract Analytical theory is used to examine the linear response of a meridionally unbounded stratified ocean to large-scale, low-frequency wind forcing. The following results, applied mainly to the equatorial Pacific, were obtained. (i) Provided that the wind stress curl vanishes at large distance from the equator, a general Sverdrup solution is valid in the quasi-steady (frequency ω → 0) limit. The meridionally averaged zonal flow toward the western boundary layer is zero so that there is no net mass flow into the boundary layer and the large-scale boundary condition is therefore satisfied. This solution predicts a zero pycnocline response in the eastern equatorial Pacific. It therefore predicts that, for the eastern equatorial Pacific, a slow weakening of the equatorial trade winds will not lead to long-term El Niño conditions there. (ii) Consistent with observations and other previous work, for finite but small frequencies there are two modes of equatorial motion. One is a “tilt” mode in which the equatorial sea level and thermocline are tilted by the in-phase zonal wind stress and the other is an equatorial warm water volume (WWV) mode in which the discharge of equatorial warm water (negative WWV anomaly) lags the wind stress forcing by a quarter of a period. (iii) The amplitude of the WWV mode approaches zero like ω1/2. Therefore, as ω → 0, the equatorial solution reduces to the tilt mode. (iv) The WWV mode is not due to a dominant meridional divergence driven by the wind, as suggested by some previous work. Meridional and zonal divergence approximately cancel. Reflection of energy at both ocean boundaries together with the strong dependence of long Rossby wave speed on latitude is crucial to the existence of the disequilibrium WWV mode. Because higher-latitude Rossby waves travel so much more slowly, the Rossby waves reflecting from the western ocean boundary are not in phase. This gives rise to a reflected equatorial Kelvin wave and a WWV that is not in phase with the wind stress forcing. (v) Observations from past work have shown that much low-frequency wave energy, particularly westward propagating Rossby wave energy poleward of about 5°N and 5°S, is damped out before it reaches the western ocean boundary. In this way dissipation likely has a strong influence on the equatorial Kelvin wave reflection and hence the disequilibrium WWV.
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Hearn, G. E., K. C. Tong, and S. M. Lau. "Sensitivity of Wave Drift Damping Coefficient Predictions to the Hydrodynamic Analysis Models Used in the Added Resistance Gradient Method." Journal of Offshore Mechanics and Arctic Engineering 110, no. 4 (1988): 337–47. http://dx.doi.org/10.1115/1.3257071.
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This paper is concerned with the formulation and simplifications of the general fluid structure interaction analysis for an advancing oscillating vessel in waves to provide alternative 3D hydrodynamic models to determine first and second-order wave-induced fluid loadings, and, hence, the prediction of low-frequency wave damping coefficients. Heuristic arguments which lead to the Added Resistance Gradient (ARG) method of calculating low-frequency damping coefficients together with two 3D-based calculation procedures are presented. Predictions of added resistance and motion responses are compared with other published data. The intermediate hydrodynamic coefficient predictions based on 2D and 3D hydrodynamic models are compared. Low-frequency damping coefficient predictions based on the two proposed 3D calculation procedures are compared with experimental measurements and earlier published generalized strip theory values. Assessment of the applicability of the procedures, the result of their application, and further possible generalizations of the methods are discussed.
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Herbers, T. H. C., and T. T. Janssen. "Lagrangian Surface Wave Motion and Stokes Drift Fluctuations." Journal of Physical Oceanography 46, no. 4 (2016): 1009–21. http://dx.doi.org/10.1175/jpo-d-15-0129.1.
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AbstractNonlinear effects in Lagrangian sea surface motions are important to understanding variability in wave-induced mass transport, wave-driven diffusion processes, and the interpretation of measurements obtained with moored or free-drifting buoys. This study evaluates the Lagrangian vertical and horizontal motions of a particle at the surface in a natural, random sea state using second-order, finite-depth wave theory. In deep water, the predicted low-frequency (infragravity) surface height fluctuations are much larger than Eulerian bound wave motions and of the opposite sign. Comparison to surface elevation bispectra observed with a moored buoy in steady, high-wind conditions shows good agreement and confirms that—in contrast to the Eulerian sea surface motion with predominant phase coupling between the spectral peak and double-frequency harmonic components—nonlinearity in Lagrangian wave observations is dominated by phase-coupled infragravity motions. Sea surface skewness estimates obtained from moored buoys in deep and shallow sites, over a wide range of wind–sea and swell conditions, are in good agreement with second-order theory predictions. Theory and field data analysis of surface drift motions in deep water reveal energetic [O(10) cm s−1] infragravity velocity fluctuations that are several orders of magnitude larger and 180° out of phase with Eulerian infragravity motions. These large fluctuations in Stokes drift may be important in upper-ocean diffusion processes.
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Aiki, Hidenori, and Richard J. Greatbatch. "Thickness-Weighted Mean Theory for the Effect of Surface Gravity Waves on Mean Flows in the Upper Ocean." Journal of Physical Oceanography 42, no. 5 (2012): 725–47. http://dx.doi.org/10.1175/jpo-d-11-095.1.
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Abstract The residual effect of surface gravity waves on mean flows in the upper ocean is investigated using thickness-weighted mean (TWM) theory applied in a vertically Lagrangian and horizontally Eulerian coordinate system. Depth-dependent equations for the conservation of volume, momentum, and energy are derived. These equations allow for (i) finite amplitude fluid motions, (ii) the horizontal divergence of currents, and (iii) a concise treatment of both kinematic and viscous boundary conditions at the sea surface. Under the assumptions of steady and monochromatic waves and a uniform turbulent viscosity, the TWM momentum equations are used to illustrate the pressure- and viscosity-induced momentum fluxes through the surface, which are implicit in previous studies of the wave-induced modification of the classical Ekman spiral problem. The TWM approach clarifies, in particular, the surface momentum flux associated with the so-called virtual wave stress of Longuet-Higgins. Overall, the TWM framework can be regarded as an alternative to the three-dimensional Lagrangian mean framework of Pierson. Moreover, the TWM framework can be used to include the residual effect of surface waves in large-scale circulation models. In specific models that carry the TWM velocity appropriate for advecting tracers as their velocity variable, the turbulent viscosity term should be modified so that the viscosity acts only on the Eulerian mean velocity.
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Nikurashin, Maxim, Raffaele Ferrari, Nicolas Grisouard, and Kurt Polzin. "The Impact of Finite-Amplitude Bottom Topography on Internal Wave Generation in the Southern Ocean." Journal of Physical Oceanography 44, no. 11 (2014): 2938–50. http://dx.doi.org/10.1175/jpo-d-13-0201.1.
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Abstract Direct observations in the Southern Ocean report enhanced internal wave activity and turbulence in a kilometer-thick layer above rough bottom topography collocated with the deep-reaching fronts of the Antarctic Circumpolar Current. Linear theory, corrected for finite-amplitude topography based on idealized, two-dimensional numerical simulations, has been recently used to estimate the global distribution of internal wave generation by oceanic currents and eddies. The global estimate shows that the topographic wave generation is a significant sink of energy for geostrophic flows and a source of energy for turbulent mixing in the deep ocean. However, comparison with recent observations from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean shows that the linear theory predictions and idealized two-dimensional simulations grossly overestimate the observed levels of turbulent energy dissipation. This study presents two- and three-dimensional, realistic topography simulations of internal lee-wave generation from a steady flow interacting with topography with parameters typical of Drake Passage. The results demonstrate that internal wave generation at three-dimensional, finite bottom topography is reduced compared to the two-dimensional case. The reduction is primarily associated with finite-amplitude bottom topography effects that suppress vertical motions and thus reduce the amplitude of the internal waves radiated from topography. The implication of these results for the global lee-wave generation is discussed.
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Žagar, N., J. Tribbia, J. L. Anderson, and K. Raeder. "Uncertainties of Estimates of Inertia–Gravity Energy in the Atmosphere. Part II: Large-Scale Equatorial Waves." Monthly Weather Review 137, no. 11 (2009): 3858–73. http://dx.doi.org/10.1175/2009mwr2816.1.
Full textAbstract:
Abstract This paper analyzes the spectra and spatiotemporal features of the large-scale inertia-gravity (IG) circulations in four analysis systems in the tropics. Of special interest is the Kelvin wave (KW), which represents between 7% and 25% of the total IG wave (zonal wavenumber k ≠ 0) energy. The mixed Rossby–gravity (MRG) mode comprises between 4% and 15% of the IG wave energy. At the longest scales, the KW spectra are fitted by a law while the MRG energy spectrum appears flat. At shorter scales both modes follow a −3 law. Energy spectra of the total IG wave motion at long zonal scales (zonal wavenumber smaller than 7) have slopes close to −1. The average circulation associated with KW is characterized by reverse flows in the upper and lower troposphere consistent with the ideas behind simple tropical models. The inverse projection is used to quantify the role of Kelvin and MRG waves in current analysis systems in the upper troposphere over the Indian Ocean. At these levels, easterlies between 10°S and 30°N are represented by the KW to a significant degree while the cross-equatorial flow toward the descending branch of the Hadley cell at 10°S is associated with the MRG waves. The transient structure of equatorial waves is presented in the space of normal modes defined by the zonal wavenumbers, meridional Hough functions, and the vertical eigenfunctions. The difference in the depth of the model domain in DART–CAM and NCEP–NCAR on one hand and ECMWF and NCEP on the other appears to be one reason for different wave propagation properties. In the latter case the vertical energy propagation is diagnosed by filtering the propagating KW modes back to physical space. The results agree with the linear theory of vertically propagating equatorial waves.
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Soares, C. Guedes, R. Pascoal, E. M. Antão, A. J. Voogt, and B. Buchner. "An Approach to Calculate the Probability of Wave Impact on an FPSO Bow." Journal of Offshore Mechanics and Arctic Engineering 129, no. 2 (2006): 73–80. http://dx.doi.org/10.1115/1.2426983.
Full textAbstract:
This work aims at characterizing the probability of wave impact and determining the position of impact on an FPSO (floating production storage and offloading platform) bow geometry. In order to determine the instants when impact occurs, an experimental program was performed on a specific bow shape. The bow was instrumented with pressure transducers and the test program, also making use of video recordings, was designed such that it was possible to determine the correlation between undisturbed wave shape and the impact pressure time traces. It has been found that the wave impact at the bow is highly correlated with the local wave steepness, which for very high waves has at least second-order effects. A comparison between the probability distributions of local wave steepness of the experimental undisturbed wave time trace and numerical simulations of second-order wave theory is provided and it confirmed that the latter is very adequate for calculations. The experimental results were further used to determine how the probability of impact varies with free surface vertical velocity. It was found that the significant wave height of the sea state itself does not have significant influence on the result and a regression model was derived for the bow type in the experiments. The proposed model for determining the probability of having an impact is based on combining distributions, adjusted a priori to the numerically generated second-order free surface vertical velocity, and the experimental probability of impact of a known certain seastate and free surface velocity. The analytical description makes it fast and easy to expand to other cases of interest and some example calculations are shown to demonstrate the relative ease of the procedure proposed. The position of the impact is determined by the nonlinear wave crests and the ship motions. The ship motions can be determined based on a linear response to the nonlinear waves considered.