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1
Drzewiecki, Marcin. "The Propagation of the Waves in the CTO S.A. Towing Tank." Polish Maritime Research 25, s1 (May 1, 2018): 22–28. http://dx.doi.org/10.2478/pomr-2018-0018.
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Abstract The paper presents the results of research focused on the wave propagation in the CTO S.A. deepwater towing tank. In the scope of paper, the wavemaker transfer function was determined for regular waves, based on the Biésel Transfer Function and further for irregular waves, based on Hasselman model of nonlinear energy transfer. The phenomena: wave damping, wave breakdown and wave reflection, were measured, analyzed and mathematically modeled. Developed mathematical models allow to calculate the impact of mentioned phenomena on the wave propagation and furthermore to calculate the wave characteristics along the whole measurement area in the CTO S.A. deepwater towing tank, based on wavemaker flap motion control.
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Królicka, Agnieszka. "State equations in the mathematical model of dynamic behaviour of multihull floating unit." Polish Maritime Research 17, no. 1 (January 1, 2010): 33–38. http://dx.doi.org/10.2478/v10012-010-0003-6.
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State equations in the mathematical model of dynamic behaviour of multihull floating unit This paper concerns dynamic behaviour of multihull floating unit of catamaran type exposed to excitations due to irregular sea waves. Dynamic analysis of multihull floating unit necessitates, in its initial stage, to determine physical model of the unit and next to assume an identified mathematical model. Correctly elaborated physical models should contain information on the basis of which a mathematical model could be built. Mathematical models describe mutual relations between crucial quantities which characterize a given system in time domain. The dynamic analysis of multihull unit was performed under assumption that the unit's model has been linear and exposed to action of irregular sea waves. Mathematical model of such dynamic system is represented by state equations. The formulated equations take into account encounter of head wave which generates symmetrical motions of the unit, i.e. surge, heave and pitch. For solving the equations the following three wave spectra were taken into consideration: - ISSC (International Ship Structures Congress) spectrum - Pierson-Moskowitz spectrum - Paszkiewicz spectrum.
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Small, J., L. Shackleford, and G. Pavey. "Ocean feature models − their use and effectiveness in ocean acoustic forecasting." Annales Geophysicae 15, no. 1 (January 31, 1997): 101–12. http://dx.doi.org/10.1007/s00585-997-0101-7.
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Abstract. The aim of this paper is to test the effectiveness of feature models in ocean acoustic forecasting. Feature models are simple mathematical representations of the horizontal and vertical structures of ocean features (such as fronts and eddies), and have been used primarily for assimilating new observations into forecasts and for compressing data. In this paper we describe the results of experiments in which the models have been tested in acoustic terms in eddy and frontal environments in the Iceland Faeroes region. Propagation-loss values were obtained with a 2D parabolic-equation (PE) model, for the observed fields, and compared to PE results from the corresponding feature models and horizontally uniform (range-independent) fields. The feature models were found to represent the smoothed observed propagation-loss field to within an rms error of 5 dB for the eddy and 7 dB for the front, compared to 10–15-dB rms errors obtained with the range-independent field. Some of the errors in the feature-model propagation loss were found to be due to high-amplitude 'oceanographic noise' in the field. The main conclusion is that the feature models represent the main acoustic properties of the ocean but do not show the significant effects of small-scale internal waves and fine-structure. It is recommended that feature models be used in conjunction with stochastic models of the internal waves, to represent the complete environmental variability.
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Qiao, Fangli, Yeli Yuan, Jia Deng, Dejun Dai, and Zhenya Song. "Wave–turbulence interaction-induced vertical mixing and its effects in ocean and climate models." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2065 (April 13, 2016): 20150201. http://dx.doi.org/10.1098/rsta.2015.0201.
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Heated from above, the oceans are stably stratified. Therefore, the performance of general ocean circulation models and climate studies through coupled atmosphere–ocean models depends critically on vertical mixing of energy and momentum in the water column. Many of the traditional general circulation models are based on total kinetic energy (TKE), in which the roles of waves are averaged out. Although theoretical calculations suggest that waves could greatly enhance coexisting turbulence, no field measurements on turbulence have ever validated this mechanism directly. To address this problem, a specially designed field experiment has been conducted. The experimental results indicate that the wave–turbulence interaction-induced enhancement of the background turbulence is indeed the predominant mechanism for turbulence generation and enhancement. Based on this understanding, we propose a new parametrization for vertical mixing as an additive part to the traditional TKE approach. This new result reconfirmed the past theoretical model that had been tested and validated in numerical model experiments and field observations. It firmly establishes the critical role of wave–turbulence interaction effects in both general ocean circulation models and atmosphere–ocean coupled models, which could greatly improve the understanding of the sea surface temperature and water column properties distributions, and hence model-based climate forecasting capability.
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Liaw, C. Y. "Numerical Modeling and Subharmonic Bifurcations of a Compliant Cylinder Exposed to Waves." Journal of Offshore Mechanics and Arctic Engineering 111, no. 1 (February 1, 1989): 29–36. http://dx.doi.org/10.1115/1.3257135.
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The occurrence of subharmonic responses in compliant structures including nonlinear coupling between the wave force and the structural motion is studied using simplified models of a cylinder submerged in waves. In particular, the existence and sensitivity of subharmonics in the responses are evaluated by varying the mathematical model for wave force, the structure/wave frequency ratio, the drag coefficient and the wave height. It is concluded that subharmonic bifurcation of order 1/2 can be a common phenomenon in compliant structural systems, especially if the system has a low ratio of drag force to inertia force.
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Wang, Gang, Hong-Quan Yu, and Jin-Hai Zheng. "EXPERIMENTAL STUDY OF GUIDED WAVES OVER THE OCEAN RIDGE." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 54. http://dx.doi.org/10.9753/icce.v36.waves.54.
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Long waves can be trapped by oceanic ridges due to refraction effect, and such guided waves travel along the ridge and transfer their energy to rather long distance. The guided wave is constrained over the top of the ridge and propagates slower than the free long wave, which leads to the largest amplitude waves arriving later and duration of tsunami activity longer. The existence of trapping effect of ocean ridges has not only been demonstrated mathematically (Buchwald 1969; Zheng et al. 2016), but also been verified by the interpretation of tide-gauge data and numerical models on global tsunami events (Koshimura et al. 2001; Titov et al. 2005).
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Francescutto, Alberto, Gabriele Bulian, and Claudio Lugni. "The Sixth International Stability Workshop was held in October 2002." Marine Technology and SNAME News 41, no. 02 (April 1, 2004): 74–81. http://dx.doi.org/10.5957/mt1.2004.41.2.74.
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This paper addresses, starting from an extensive series of tests in longitudinal regular waves (already done) and irregular waves (in progress), the problems connected with the threshold formulation for parametric rolling and its amplitude modeling above threshold. Both head and following waves have been considered, also in view of the greater attention to head sea conditions called for during International Maritime Organisation Subcommittee on Stability and Load Lines, and on Fishing Vessels Safety (IMO/ SLF) discussion on the revision of the Intact Stability Code. Particular attention is given in the regular wave case to the nonlinear damping, nonlinear restoring, and nonlinear parametric excitation terms. The mathematical models so developed are "compared" with experimental results by means of an ad hoc parameter estimation technique. It is, on the other hand, well known that several different thresholds can be proposed in the case of irregular waves and that the nonlinear modeling of roll motion variance above threshold is at present not properly addressed. Here, too, a series of experiments will be conducted in the presence of narrow band irregular waves having the bandwidth as parameter. A mathematical description of the nonlinear parametric rolling can be obtained with the use of approximate analytical techniques.
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Dahle, Emil Aall, and Dag Myrhaug. "Risk Analysis Applied to Capsize of Fishing Vessels." Marine Technology and SNAME News 32, no. 04 (October 1, 1995): 245–47. http://dx.doi.org/10.5957/mt1.1995.32.4.245.
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Although contributing only moderately to the total ship loss rate, capsize provides the dominating human loss rate contribution for the smaller vessel. This is of special concern for fishing vessels because their human loss rate is considered as unacceptable in many countries in the world. In the paper, it is suggested that a risk analysis method be applied to manage the risk of capsize. The analysis is derived in steps. First, dangerous wave events are selected; steep near-breaking waves above certain heights, synchronous waves, and high waves with the same speed as the ship are selected. Next, the frequency of occurrence is calculated based upon published wave statistics and recent research. Then, the vessel's response to the selected wave events has to be found by model tests or by using simple analytical models. Finally, the probability of occurrence of wave/vessel encounters per year that will cause capsize is calculated. Various rational ways of reducing the probability to an acceptable level are presented and discussed, and are illustrated by practical examples for two U.S. fishing areas, one on the West Coast and one on the East Coast. The application of already available information and knowledge is advocated with less emphasis on development of complicated mathematical models.
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Pushkarev, A. N., and V. E. Zakharov. "SELF-SIMILAR AND LASER-LIKE REGIMES IN NUMERICAL MODELING OF HASSELMANN KINETIC EQUATION FOR OCEAN WAVES." XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (April 30, 2019): 103–6. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).31.
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The absence of mathematically justified criteria in the models of prediction of wind waves of the ocean, used by the world’s largest centers NOAA (USA) and ECMWF (UK), based on numerical modeling of the Hasselmann kinetic equation, led to erroneous hierarchy and erroneous nonlinear interaction approximation, wind forcing and waves dissipation terms due to wave-breaking. Existing models of wind waves operate in the paradigm of the adjustable «black box», each time requiring reconfiguration. On the basis of numerical simulation, we were able to construct a model, taking into account the wind forcing of the power type in combination with the «implicit» dissipation.
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Veeresha, Pundikala, Haci Mehmet Baskonus, and Wei Gao. "Strong Interacting Internal Waves in Rotating Ocean: Novel Fractional Approach." Axioms 10, no. 2 (June 16, 2021): 123. http://dx.doi.org/10.3390/axioms10020123.
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The main objective of the present study is to analyze the nature and capture the corresponding consequences of the solution obtained for the Gardner–Ostrovsky equation with the help of the q-homotopy analysis transform technique (q-HATT). In the rotating ocean, the considered equations exemplify strong interacting internal waves. The fractional operator employed in the present study is used in order to illustrate its importance in generalizing the models associated with kernel singular. The fixed-point theorem and the Banach space are considered to present the existence and uniqueness within the frame of the Caputo–Fabrizio (CF) fractional operator. Furthermore, for different fractional orders, the nature has been captured in plots. The realized consequences confirm that the considered procedure is reliable and highly methodical for investigating the consequences related to the nonlinear models of both integer and fractional order.
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di Martino, B., F. Flori, C. Giacomoni, and P. Orenga. "Mathematical and Numerical Analysis of a Tsunami Problem." Mathematical Models and Methods in Applied Sciences 13, no. 10 (October 2003): 1489–514. http://dx.doi.org/10.1142/s0218202503003008.
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In this paper, we present a tsunami model based on the displacement of the lithosphere and the mathematical and numerical analysis of this model. More precisely, we give an existence and uniqueness result for a problem which models the flow and formation of waves at the time of a submarine earthquake in the vicinity of the coast. We propose a model which describes the behavior of the fluid using a bi-dimensional shallow-water model by means of a depth-mean velocity formulation. The ocean is coupled to the Earth's crust whose movement is assumed to be controlled on a large scale by plate equations. Finally, we give some numerical results showing the formation of a tsunami.
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Sclavounos, Paul D. "Karhunen–Loeve representation of stochastic ocean waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2145 (May 9, 2012): 2574–94. http://dx.doi.org/10.1098/rspa.2012.0063.
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A new stochastic representation of a seastate is developed based on the Karhunen–Loeve spectral decomposition of stochastic signals and the use of Slepian prolate spheroidal wave functions with a tunable bandwidth parameter. The new representation allows the description of stochastic ocean waves in terms of a few independent sources of uncertainty when the traditional representation of a seastate in terms of Fourier series requires an order of magnitude more independent components. The new representation leads to parsimonious stochastic models of the ambient wave kinematics and of the nonlinear loads and responses of ships and offshore platforms. The use of the new representation is discussed for the derivation of critical wave episodes, the derivation of up-crossing rates of nonlinear loads and responses and the joint stochastic representation of correlated wave and wind profiles for use in the design of fixed or floating offshore wind turbines. The forecasting is also discussed of wave elevation records and vessel responses for use in energy yield enhancement of compliant floating wind turbines.
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Pierson, Willard J., and Azed Jean-Pierre. "Monte Carlo Simulations of Nonlinear Ocean Wave Records with Implications for Models of Breaking Waves." Journal of Ship Research 43, no. 02 (June 1, 1999): 121–34. http://dx.doi.org/10.5957/jsr.1999.43.2.121.
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A Monte Carlo method for simulating nonlinear ocean wave records as a function of time is described. It is based on a family of probability density functions developed by Karl Pearson and requires additional knowledge of the dimensionless moments of a postulated nonlinear wave record, which are the skewness and kurtosis. A frequency spectrum is used to simulate a linear record. It is then transformed to a nonlinear record for the chosen values of the skewness and kurtosis. The result is not a perturbation expansion of the nonlinear equations that describe unbroken waves. It yields a simulated wave record that reproduces the chosen values for the skewness and, if needed, the kurtosis of a wave record so that the statistical properties are modeled. A brief history of the development of the linear model, presently in use, is given along with a survey of wave data that show the variability of the nonlinear properties of wave records. The need for a nonlinear model of waves for naval architecture, remote sensing and other design problems is shown. This method cannot provide any information on whether a particular wave will break. Some of the recent results on breaking waves and "green water" are reviewed. The possibility that this method can be extended based on the concept of a "local absorbing patch" is described.
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Lin, Ray-Qing, Weijia Kuang, and Arthur M. Reed. "Numerical Modeling of Nonlinear Interactions Between Ships and Surface Gravity Waves, Part 1: Ship Waves in Calm Water." Journal of Ship Research 49, no. 01 (March 1, 2005): 1–11. http://dx.doi.org/10.5957/jsr.2005.49.1.1.
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This paper presents a pseudo-spectral model for nonlinear ship-surface wave interactions. The algorithm used in the model is a combination of spectral and boundary element methods: the boundary element method is used to translate physical quantities between the nonuniform ship surface and the regular grid of the spectral representation; the spectral method is used throughout the remainder of the fluid domain. All possible wave-wave interactions are included in the model (up to N-wave interactions for the truncation order N of the spectral expansions). This paper focuses on the mathematical theory and numerical method of the model and presents some numerical results for steady Kelvin waves in calm water. The nonlinear bow waves at high Froude numbers from the pseudo-spectral model are much closer to the experimental results than those from linear ship wave models. Our results demonstrate that the pseudo-spectral model is significantly faster than previous ship wave models: with the same resolution, the CPU time of the pseudo-spectral model is orders of magnitude less than those of previous models. Convergence speed of this model is ANLogN instead of BN2, where N is the number of unknown (note that the N for the traditional boundary element method may be significantly larger than the N for the pseudo-spectral method for the same quality solution). A and B are CPU time requirements in each time step for our model and others, respectively.
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Squire, Vernon A. "A fresh look at how ocean waves and sea ice interact." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2129 (August 20, 2018): 20170342. http://dx.doi.org/10.1098/rsta.2017.0342.
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Because of their capacity to alter floe size distribution and concentration and consequently to influence atmosphere-ocean fluxes, there is a compelling justification and demand to include waves in ice/ocean models and earth system models. Similarly, global wave forecasting models like WAVEWATCH III ® need better parametrizations to capture the effects of a sea ice cover such as the marginal ice zone on incoming wave energy. Most parametrizations of wave propagation in sea ice assume without question that the frequency-dependent attenuation which is observed to occur with distance x travelled is exponential, i.e. A = A 0 e − αx . This is the solution of the simple first-order linear ordinary differential equation d A /d x = − αA , which follows from an Airy wave mode ansatz . Yet, in point of fact, it now appears that exponential decay may not be observed consistently and a more general equation of the type d A /d x = − αA n is proposed to allow for a broader range of attenuation behaviours should this be necessary to fit data. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.
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Kundu, Anjan, Abhik Mukherjee, and Tapan Naskar. "Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2164 (April 8, 2014): 20130576. http://dx.doi.org/10.1098/rspa.2013.0576.
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Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.
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van den Bremer, T. S., and Ø. Breivik. "Stokes drift." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2111 (December 11, 2017): 20170104. http://dx.doi.org/10.1098/rsta.2017.0104.
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During its periodic motion, a particle floating at the free surface of a water wave experiences a net drift velocity in the direction of wave propagation, known as the Stokes drift (Stokes 1847 Trans. Camb. Philos. Soc. 8 , 441–455). More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel and the average Eulerian flow velocity of the fluid. This paper reviews progress in fundamental and applied research on the induced mean flow associated with surface gravity waves since the first description of the Stokes drift, now 170 years ago. After briefly reviewing the fundamental physical processes, most of which have been established for decades, the review addresses progress in laboratory and field observations of the Stokes drift. Despite more than a century of experimental studies, laboratory studies of the mean circulation set up by waves in a laboratory flume remain somewhat contentious. In the field, rapid advances are expected due to increasingly small and cheap sensors and transmitters, making widespread use of small surface-following drifters possible. We also discuss remote sensing of the Stokes drift from high-frequency radar. Finally, the paper discusses the three main areas of application of the Stokes drift: in the coastal zone, in Eulerian models of the upper ocean layer and in the modelling of tracer transport, such as oil and plastic pollution. Future climate models will probably involve full coupling of ocean and atmosphere systems, in which the wave model provides consistent forcing on the ocean surface boundary layer. Together with the advent of new space-borne instruments that can measure surface Stokes drift, such models hold the promise of quantifying the impact of wave effects on the global atmosphere–ocean system and hopefully contribute to improved climate projections. This article is part of the theme issue ‘Nonlinear water waves’.
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Avila, Deivis, Graciliano Nicolás Marichal, Ramón Quiza, and Felipe San Luis. "Prediction of Wave Energy Transformation Capability in Isolated Islands by Using the Monte Carlo Method." Journal of Marine Science and Engineering 9, no. 9 (September 7, 2021): 980. http://dx.doi.org/10.3390/jmse9090980.
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In this work, a mathematical computer simulation model is used to predict the possible energy generated from different Waves Energy Converters (WECs) in the Canary Islands. The Monte Carlo Method is the computer simulation model proposed to predict the generated energy. The Waves Energy Converter systems analyzed in the study were, the Aqua Buoy, Wave Dragon and Pelamis converters. The models were implemented and validated, with the dataset of Gran Canaria deep water buoy. This buoy belongs to a network of buoys belonging to Spain’s State Ports and they cover a dataset period of 22 years. The research has concluded that it is possible to affirm that the achieved model is a strong tool to compute the possible energy of any WECs, when the power matrix is known. The model based on the Monte Carlo simulation can be used in isolated islands of the Atlantic Ocean and can be extrapolated to other regions with the same characteristics.
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Wang, Benlong, and Hua Liu. "Space–time behaviour of magnetic anomalies induced by tsunami waves in open ocean." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2157 (September 8, 2013): 20130038. http://dx.doi.org/10.1098/rspa.2013.0038.
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The magnetic anomaly induced by an inhomogeneous velocity field under tsunami waves in open ocean is investigated. With asymptotical analysis, an explicit series solution of the kinematic dynamo problem is established for weak dispersive water waves. The magnetic field induced by typical tsunami models, including single wave and -wave, can be directly obtained using the proposed series solution. The characteristics of the magnetic field induced by two realistic tsunami events are investigated. By analysis, the magnetic magnitude induced by a 1 m high tsunami is estimated as of the order of 10 nT at the sea surface, which depends on the wave parameters as well as the Earth's magnetic field. The space and time behaviour of the magnetic field shows fair similarity with the field data at Easter Island during the 2010 Chile tsunami.
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LINTON, C. M. "Towards a three-dimensional model of wave–ice interaction in the marginal ice zone." Journal of Fluid Mechanics 662 (October 15, 2010): 1–4. http://dx.doi.org/10.1017/s0022112010004258.
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Over the past forty or so years, considerable advances have been made in our understanding of the effects of ocean waves on sea ice, and vice versa, with observations, experiments and theory all playing their part. Recent years have seen the development of ever more sophisticated mathematical models designed to represent the physics more accurately and incorporate new features. What is lacking is an approach to three-dimensional scattering for ice floes that is both accurate and efficient enough to be used as a component in a theory designed to model the passage of directional wave spectra through the marginal ice zone. Bennetts & Williams (J. Fluid Mech., 2010, this issue, vol. 662, pp. 5–35) have brought together a number of solution techniques honed on simpler problems to provide just such a component.
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Duran, Serbay, Asıf Yokuş, Hülya Durur, and Doğan Kaya. "Refraction simulation of internal solitary waves for the fractional Benjamin–Ono equation in fluid dynamics." Modern Physics Letters B 35, no. 26 (August 13, 2021): 2150363. http://dx.doi.org/10.1142/s0217984921503632.
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In this study, the modified [Formula: see text]-expansion method and modified sub-equation method have been successfully applied to the fractional Benjamin–Ono equation that models the internal solitary wave event in the ocean or atmosphere. With both analytical methods, dark soliton, singular soliton, mixed dark-singular soliton, trigonometric, rational, hyperbolic, complex hyperbolic, complex type traveling wave solutions have been produced. In these applications, we consider the conformable operator to which the chain rule is applied. Special values were given to the constants in the solution while drawing graphs representing the stationary wave. By making changes of these constants at certain intervals, the refraction dynamics and physical interpretations of the obtained internal solitary waves were included. These physical comments were supported by simulation with 3D, 2D and contour graphics. These two analytical methods used to obtain analytical solutions of the fractional Benjamin–Ono equation have been analyzed in detail by comparing their respective states. By using symbolic calculation, these methods have been shown to be the powerful and reliable mathematical tools for the solution of fractional nonlinear partial differential equations.
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Xu, Chuan-Xiu, Sheng-Chun Piao, Shi-E. Yang, Hai-Gang Zhang, and Li Li. "This Submission is for Special Issue on Underwater Acoustics: Perfectly Matched Layer Technique for Parabolic Equation Models in Ocean Acoustics." Journal of Computational Acoustics 25, no. 01 (March 2017): 1650021. http://dx.doi.org/10.1142/s0218396x16500211.
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In ocean waveguides, the ocean bottom is usually approximated as a half-space. Thus, there exist no reflection waves at the half-space bottom and condition of radiation at infinity should be satisfied. In numerical solutions like parabolic equation methods, the depth domain has to be truncated, which can generate reflection waves from the truncated ocean bottom. To reduce the effect of reflection waves and to simulate an unbounded ocean bottom accurately, an artificial absorbing layer (ABL) was used. As was demonstrated, an ABL meets well the demand of accuracy in sound field calculation. However, both the sea-bottom layer and the artificial absorbing layer are needed to be set quite thick by using an ABL technique. Fortunately, a PML with several wavelengths can keep similar calculation accuracy with an ABL with dozens of wavelengths. In this paper, perfectly matched layer (PML) techniques for three parabolic equation (PE) models RAM, RAMS and a three-dimensional PE model in underwater acoustics are presented. A key technique of PML “complex coordinate stretching” is used to truncate unbounded domains and to simulate infinity radiation conditions instead of the ABL in those models. The numerical results illustrate that the PML technique is of higher efficiency than the ABL technique at truncating the infinity domain with minimal spurious reflections in PE models.
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Gibson, R. S., and C. Swan. "The evolution of large ocean waves: the role of local and rapid spectral changes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2077 (July 25, 2006): 21–48. http://dx.doi.org/10.1098/rspa.2006.1729.
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This paper concerns the formation of large-focused or near-focused waves in both unidirectional and directional sea-states. When the crests of wave components of varying frequency superimpose at one point in space and time, a large, transient, focused wave can occur. These events are believed to be representative of the largest waves arising in a random sea and, as such, are of importance to the design of marine structures. The details of how such waves form also offer an explanation for the formation of the so-called freak or rogue waves in deep water. The physical mechanisms that govern the evolution of focused waves have been investigated by applying both the fully nonlinear wave model of Bateman et al . (Bateman et al . 2001 J. Comput. Phys . 174 , 277–305) and the Zakharov's evolution equation (Zakharov 1968 J. Appl. Mech. Tech. Phys . 9 , 190–194). Aspects of these two wave models are complementary, and their combined use allows the full nonlinearity to be considered and, at the same time, provides insights into the dominant physical processes. In unidirectional seas, it has been shown that the local evolution of the wave spectrum leads to larger maximum crest elevations. In contrast, in directional seas, the maximum crest elevation is well predicted by a second-order theory based on the underlying spectrum, but the shape of the largest wave is not. The differences between the evolution of large waves in unidirectional and directional sea-states have been investigated by analysing the results of Bateman et al . (2001) using a number of spectral analysis techniques. It has been shown that during the formation of a focused wave event, there are significant and rapid changes to the underlying wave spectrum. These changes alter both the amplitude of the wave components and their dispersive properties. Importantly, in unidirectional sea-states, the bandwidth of the spectrum typically increases; whereas, in directional sea-states it decreases. The changes to the wave spectra have been investigated using Zakharov's equation (1968). This has shown that the third-order resonant effects dominate changes to both the amplitude of the wave components and the dispersive properties of the wave group. While this is the case in both unidirectional and directional sea-states, the consequences are very different. By examining these consequences, directional sea-states in which large wave events that are higher and steeper than second-order theory would predict have been identified. This has implications for the types of sea-states in which rogue waves are most likely to occur.
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Ambrose, David M., Jerry L. Bona, and David P. Nicholls. "On ill-posedness of truncated series models for water waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2166 (June 8, 2014): 20130849. http://dx.doi.org/10.1098/rspa.2013.0849.
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The evolution of surface gravity waves on a large body of water, such as an ocean, is reasonably well approximated by the Euler system for ideal, free-surface flow under the influence of gravity. The well-posedness theory for initial-value problems for these equations, which has a long and distinguished history, reveals that solutions exist, are unique, and depend continuously upon initial data in various function–space contexts. This theory is subtle, and the design of stable, accurate, numerical schemes is likewise challenging. Depending upon the wave regime in question, there are many different approximate models that can be formally derived from the Euler equations. As the Euler system is known to be well-posed, it seems appropriate that associated approximate models should also have this property. This study is directed to this issue. Evidence is presented calling into question the well-posedness of a well-known class of model equations which are widely used in simulations. A simplified version of these models is shown explicitly to be ill-posed and numerical simulations of quadratic- and cubic-order water-wave models, initiated with initial data predicted by the explicit analysis of the simplified model, lends credence to the general contention that these models are ill-posed.
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Meng, Zhongliang, Yanjun Liu, Jian Qin, and Yun Chen. "Mathematical Modeling and Experimental Verification of a New Wave Energy Converter." Energies 14, no. 1 (December 31, 2020): 177. http://dx.doi.org/10.3390/en14010177.
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As traditional energy sources are increasingly depleting, ocean energy has become an emergent potential clean energy source. Wave energy, as an important part of ocean-derived energy, has been studied and utilized by coastal countries worldwide, which have developed various wave energy converters. In this paper, a new wave energy converter is designed, and water movement in fluid channels is analyzed. The results are, then, used to generate a mathematical model that simulates water movement. Based on this approach, the water movement state is analyzed, and a formula for calculating the natural frequency of water movement in the power generator is derived. The formula shows that the characteristic length of the water movement in the proposed generator and the backboard tilt angle at the exit point of the fluid channel are two design-related variables that can be used to alter the natural frequency; a regular wave experiment is conducted based on the fluid model, which is designed based on the natural frequency formula, to verify the changes in model torque and speed as well as whether the model can operate under normal wave conditions. This study lays a theoretical foundation for the design of further experiments and engineering prototypes to verify the validity of mathematical models by way of experimental analysis.
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Eidsmoen, H. "Optimum Control of a Floating Wave-Energy Converter With Restricted Amplitude." Journal of Offshore Mechanics and Arctic Engineering 118, no. 2 (May 1, 1996): 96–102. http://dx.doi.org/10.1115/1.2828829.
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In this paper, the use of optimal control techniques for improving the energy absorption by a wave-energy converter (WEC) is investigated. A mathematical model is developed for a floating body, which is exposed to an irregular incident wave, and is moving relative to a fixed reference. This model includes a control force from the power take-off and control machinery, and a friction force which restricts the oscillation amplitude. This force models end-stop devices, which are necessary to protect the machinery. An optimal control strategy is determined, based on variations of a Lagrange functional. This gives a set of adjoint equations in addition to the state equations, as a necessary condition for optimum. An algorithm is given for solving the problem numerically by iteration, based on a gradient method. It is shown that the optimal motion in a sinusoidal wave is not sinusoidal when the excursion is constrained. Instead, the motion should be stopped in certain intervals. In irregular waves the constrained solution is close to the unconstrained solution when the excursion is small. Moreover, the timings of the extrema and of the zero crossings agree fairly well. When the excursion is constrained, the mean output power is reduced compared to the unconstrained case, but the ratio between the output energy and the total energy passing through the machinery is increased. This means that the conversion efficiency of the machinery is less critical.
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Kashiwagi, Masashi. "Hydrodynamic Study on Added Resistance Using Unsteady Wave Analysis." Journal of Ship Research 57, no. 04 (December 1, 2013): 220–40. http://dx.doi.org/10.5957/jsr.2013.57.4.220.
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It is known that the added resistance in waves can be computed from ship-generated unsteady waves through the unsteady wave analysis method. To investigate the effects of nonlinear ship-generated unsteady waves and bluntness of the ship geometry on the added resistance, measurements of unsteady waves, wave-induced ship motions, and added resistance were carried out using two different (blunt and slender) modified Wigley models. The ship-generated unsteady waves are also produced by the linear superposition using the waves measured for the diffraction and radiation problems and the complex amplitudes of ship motions measured for the motion-free problem in waves. Then a comparison is made among the values of the added resistance by the direct measurement using a dynamometer and by the wave analysis method using the Fourier transform of measured and superposed waves. It is found that near the peak of the added resistance where ship motions become large, the degree of nonlinearity in the unsteady wave becomes prominent, especially at the forefront part of the wave. Thus, the added resistance evaluated with measured waves at larger amplitudes of incident wave becomes much smaller than the values by the direct measurement and by the wave analysis with superposed waves or measured waves at smaller amplitude of incident wave. Discussion is also made on the characteristics of the added resistance in the range of short incident waves.
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Torhaug, Rune, Steven R. Winterstein, and Arne Braathen. "Nonlinear Ship Loads: Stochastic Models for Extreme Response." Journal of Ship Research 42, no. 01 (March 1, 1998): 46–55. http://dx.doi.org/10.5957/jsr.1998.42.1.46.
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In this study we focus on stochastic analysis methods for selective simulations, and we consider the extreme midspan moment of a fast-moving ship subjected to random Gaussian waves. We concentrate on analysis within a stationary sea state and our purpose is to accurately estimate hourly maximum ship response (compared with the correct result per hour) within a sea state with as little computational resources as possible. We consider how the use of a limited number of short simulations with "critical wave episodes" (short wave segments which are likely candidates to produce extreme response in the simulated hour-long history) reduces the cost of nonlinear time-domain ship response analysis.
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Oyejobi, Damilola O., Mohammed Jameel, Nor Hafizah Ramli Sulong, and Niaz B. Khan. "Investigation of tendon dynamics effects on tension leg platform response in random seas." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 233, no. 4 (November 16, 2018): 1082–102. http://dx.doi.org/10.1177/1475090218811718.
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This study investigated tendon dynamics effects of tension leg platform models with tendons modelled by finite element spring and beam elements for uncoupled and coupled tension leg platform in random waves and current environment. The purpose of the study is to proffering numerical solution of single mathematical equation of motion for fully integrated-coupled tension leg platform floater with tendons model. Structural modelling of complete tension leg platform is achieved with the help of ABAQUS/Standard finite element tools which is incorporated with ABAQUS/Aqua module for the application of hydrodynamic loadings on the partially submerged tension leg platform hull and fully submerged platform tendons. For the uncoupled tension leg platform model, weight, inertia, hydrodynamic force and damping forces are ignored on the tendons modelled with springs, while the stiffness of the tendons is considered as a static restoring force. The coupled tension leg platform model had all the forces applied on the tendons modelled with beam elements. Conclusively, modelling and analysis of the tension leg platform as uncoupled and coupled models have expanded our understanding to know that surge motion response is fairly predicted by the two models, however, heave and pitch motions, and variations in tendon tension differ significantly; hence, coupled tension leg platform model is recommended. The influence of a removed tendon due to accident or maintenance on the tension leg platform motions is also reported.
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GRIGORIEVA, NATALIE S. "THE EFFECT OF OCEAN CURRENT ON SOUND PROPAGATION." Journal of Computational Acoustics 02, no. 04 (December 1994): 441–51. http://dx.doi.org/10.1142/s0218396x94000257.
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The effect of medium motion on sound propagation in the ocean is investigated. In a moving fluid, the sound propagation is described by a system of seven linear partial differential equations for seven unknown elements of a sound wave. These are the sound pressure, the particle oscillation velocity in a sound wave as well as the changes of medium density, its entropy, and concentration of the salt caused by passage of a sound wave. In the case of stratified moving medium, the point source field is represented in the form of a sum of quasinormal waves. If the ocean perturbed by a current is weakly inhomogeneous along the horizontal direction, the modification of the well-known method of horizontal rays/vertical modes is used. The "effective" sound speed for the model of stratified ocean is introduced. It allows the qualitative estimation of the medium motion effect on sound propagation taking into account the deformation of the initial sound speed profile. A sequence of direct numerical simulations of sound propagation problems has been carried out for the Gulf Stream models. It is shown that a large-scale current may alter the nature of guided wave sound propagation. For example, a current may lead to noticeable strengthening of a near surface waveguide. It results in smoothed field pattern and significant illumination of the shadow zones. Taking account of the medium inhomogeneity along the horizontal direction leads to the shift of the shadow zones and the illuminated domains relative to the source. If a sound path crosses the Gulf Stream ring, the medium motion effect on sound propagation may be ignored.
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Ren, Yanwei, Huanhe Dong, Xinzhu Meng, and Hongwei Yang. "Research on Time-Space Fractional Model for Gravity Waves in Baroclinic Atmosphere." Mathematical Problems in Engineering 2018 (October 24, 2018): 1–14. http://dx.doi.org/10.1155/2018/1345346.
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The research of gravity solitary waves movement is of great significance to the study of ocean and atmosphere. Baroclinic atmosphere is a complex atmosphere, and it is closer to the real atmosphere. Thus, the study of gravity waves in complex atmosphere motion is becoming increasingly essential. Deriving fractional partial differential equation models to describe various waves in the atmosphere and ocean can open up a new window for us to understand the fluid movement more deeply. Generally, the time fractional equations are obtained to reflect the nonlinear waves and few space-time fractional equations are involved. In this paper, using multiscale analysis and perturbation method, from the basic dynamic multivariable equations under the baroclinic atmosphere, the integer order mKdV equation is derived to describe the gravity solitary waves which occur in the baroclinic atmosphere. Next, employing the semi-inverse and variational method, we get a new model under the Riemann-Liouville derivative definition, i.e., space-time fractional mKdV (STFmKdV) equation. Furthermore, the symmetry analysis and the nonlinear self-adjointness of STFmKdV equation are carried out and the conservation laws are analyzed. Finally, adopting the exp(-Φ(ξ)) method, we obtain five different solutions of STFmKdV equation by considering the different cases of the parameters (η,σ). Particularly, we study the formation and evolution of gravity solitary waves by considering the fractional derivatives of nonlinear terms.
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Miyata, Hideaki, Makoto Kanai, Noriaki Yoshiyasu, and Yohichi Furuno. "Diffraction Waves About an Advancing Wedge Model in Deep Water." Journal of Ship Research 34, no. 02 (June 1, 1990): 105–22. http://dx.doi.org/10.5957/jsr.1990.34.2.105.
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The diffraction of regular waves by advancing wedge models is studied both experimentally and numerically. The nonlinear features of diffracted waves are visualized by wave pattern pictures and the formation is analyzed by the grid-projection method. The experimental observation indicates that the diffracted waves have a number of nonlinear characteristics similar to shock waves due to the interaction of incident waves with the advancing obstacle in the flow-field caused by the advancing motion. Bow waves of both oblique type and normal detached type are observed at remarkably lower Froude numbers than in the case of a ship in steady advance motion. Their occurrence systematically depends on the Froude number and the wedge angle. The numerical simulation of this phenomenon by a finite-difference method shows approximate agreement with the experimental results.
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Ahmed, Sadia, and Huseyin Arslan. "Analysis of Underwater Acoustic Communication Channels." Marine Technology Society Journal 47, no. 3 (May 1, 2013): 99–117. http://dx.doi.org/10.4031/mtsj.47.3.7.
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AbstractThe underwater acoustic communication (UAC) channel presents many difficulties such as high frequency, space, and time selectivity, frequency-dependent noise, and significant range and band limitation on transmission. Traditional UAC channel models that model such channels primarily include environmental models based on experimental data; models that are developed using mathematical equations such as wave equations, modal methods, and parabolic equations; and using statistical distributions. These methods/models are often limited in their coverage and accurate representations of every possible UAC channel environment. It is also physically impractical and cost ineffective to try to measure/estimate each channel to determine its model. In this paper, the authors will present the analysis of UAC channels according to the UAC channel environments classified and presented in a prior work by the authors, in which cognitive intelligence is used in the selection of the appropriate channel representations according to each sensed environment. To the best knowledge of the authors, this type of analysis and representation of UAC channels with respect to each UAC environment has not been addressed in the literature to date and therefore presents a significant contribution.
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Zilman, Gregory. "Forces Exerted on a Hovercraft by a Moving Pressure Distribution: Robustness of Mathematical Models." Journal of Ship Research 50, no. 01 (March 1, 2006): 38–48. http://dx.doi.org/10.5957/jsr.2006.50.1.38.
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The wave resistance, side force, and yawing moment acting on a hovercraft moving on the free surface of a heavy fluid is studied. The hovercraft is represented by a distributed excess pressure. Various types of pressure and bounding contours are considered. The sensitivity of the results to numerous uncertainties in the problem's physical parameters is investigated. It is found that constant pressure over a rectangular region moving with an angle of drift results in peculiar side force values. Several robust mathematical models of a moving hovercraft are proposed and analyzed.
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Weymouth, Gabriel D., and Dick K. P. Yue. "Physics-Based Learning Models for Ship Hydrodynamics." Journal of Ship Research 57, no. 01 (March 1, 2013): 1–12. http://dx.doi.org/10.5957/jsr.2013.57.1.1.
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We present the concepts of physics-based learning models (PBLM) and their relevance and application to the field of ship hydrodynamics. The utility of physics-based learning is motivated by contrasting generic learning models for regression predictions, which do not presume any knowledge of the system other than the training data provided with methods such as semi-empirical models, which incorporate physical insights along with data-fitting. PBLM provides a framework wherein intermediate models, which capture (some) physical aspects of the problem, are incorporated into modern generic learning tools to substantially improve the predictions of the latter, minimizing the reliance on costly experimental measurements or high-resolution high-fidelity numerical solutions. To illustrate the versatility and efficacy of PBLM, we present three wave-ship interaction problemsat speed waterline profiles;ship motions in head seas; andthree-dimensional breaking bow waves. PBLM is shown to be robust and produce error rates at or below the uncertainty in the generated data at a small fraction of the expense of high-resolution numerical predictions.
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Åberg, Sofia. "Wave intensities and slopes in Lagrangian seas." Advances in Applied Probability 39, no. 4 (December 2007): 1020–35. http://dx.doi.org/10.1239/aap/1198177237.
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In many applications, such as remote sensing or wave slamming on ships and offshore structures, it is important to have a good model for wave slope. Today, most models are based on the assumption that the sea surface is well described by a Gaussian random field. However, since the Gaussian model does not capture several important features of real ocean waves, e.g. the asymmetry of crests and troughs, it may lead to unconservative safety estimates. An alternative is to use a stochastic Lagrangian wave model. Few studies have been carried out on the Lagrangian model; in particular, very little is known about its probabilistic properties. Therefore, in this paper we derive expressions for the level-crossing intensity of the Lagrangian sea surface, which has the interpretation of wave intensity, as well as the distribution of the wave slope at an arbitrary crossing. These results are then compared to the corresponding intensity and distribution of slope for the Gaussian model.
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Fürth, Mirjam, Mingyi Tan, Zhi-Min Chen, and Makoto Arai. "A Dissipative Green’s Function Approach to Modeling Gravity Waves behind Submerged Bodies." Journal of Ship Research 65, no. 01 (March 17, 2021): 72–85. http://dx.doi.org/10.5957/josr.08170054.
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Potential flow-based methods are common in early design stages because of their associated speed and relative simplicity. By separating the resistance components of a ship into viscous and wave resistance, an inviscid method such as potential flow can be used for wave resistance determination. However, gravity waves are affected by viscosity and decay with time and distance. It has, therefore, long been assumed that the inclusion of a damping parameter in potential flow would better model the wave resistance. This article presents a Kelvin-Neumann dissipative potential flow model. A Rayleigh damping term is inserted into the Navier-Stokes equations to capture the decay of waves. A new 3D Green’s function based on the Havelock-Lunde formulation is derived by the use of a Fourier transform. An upper limit for the Rayleigh damping term is found by comparison with experiments and a possible improvement on conventional potential flow models for the wave making resistance prediction of a submerged ellipsoid is proposed.
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Jones, Alan F., and A. Hulme. "The Hydrodynamics of Water on Deck." Journal of Ship Research 31, no. 02 (June 1, 1987): 125–35. http://dx.doi.org/10.5957/jsr.1987.31.2.125.
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We consider the wave motion produced in a rolling water-filled tank, which models the hydrodynamics of water trapped on a ship's deck. The waves produced are seen to depend on the values of four dimensionless parameters. Discussion is given of the most physically relevant of the many possible parameter regimes. Solutions are found by a combination of asymptotic and numerical methods. It is shown that significant turning moments can be exerted on the vessel by the transient waves that are produced in the general case. Even larger effects are possible if the forcing frequency happens to lie close to a resonance frequency of the system.
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Jefferys, E. R. "Nonlinear Marine Structures With Random Excitation." Journal of Offshore Mechanics and Arctic Engineering 110, no. 3 (August 1, 1988): 246–53. http://dx.doi.org/10.1115/1.3257058.
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Various important types of offshore structure contain significant nonlinearities or time-varying coefficients in their equations of motion. Well-known examples include tension leg platforms, free-hanging risers, single-buoy moorings, ships moored against fenders and vessels constrained by stiffening moorings. When subject to sinusoidal wave excitation, time domain mathematical models of these structures can display large subharmonic or chaotic motions. This paper shows that such behavior is often an artifact of the regularity of the excitation and is usually unlikely to present a significant problem in a random sea. Narrow-band vessel response can, however, generate near-harmonic motions to create conditions in which these instabilities may become important.
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Lei, Y., S. X. Zhao, X. Y. Zheng, and W. Li. "Effects of Fish Nets on the Nonlinear Dynamic Performance of a Floating Offshore Wind Turbine Integrated with a Steel Fish Farming Cage." International Journal of Structural Stability and Dynamics 20, no. 03 (March 2020): 2050042. http://dx.doi.org/10.1142/s021945542050042x.
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This paper aims to study the effects of fish nets on the nonlinear dynamic performance of a floating offshore wind turbine integrated with a steel fish farming cage (FOWT-SFFC). Fully coupled aero-hydro-servo-elastic numerical models of FOWT-SFFC, with and without nets, are constructed to probe the nonlinear time-domain stochastic response. The first-order potential flow model with quadratic drag forces is employed to calculate the hydrodynamic loading on the foundation. The effects of nets on the damping ratios of 6 degree-of-freedom motions and on their displacement response amplitude operators (RAOs) are respectively investigated in numerical decay tests and monochromatic regular waves. The results show that the nets help to increase the damping level for the whole system and reduce motion RAOs when wave periods are around the natural periods of motions, while nets play insignificant role in motions when wave periods are far away from motion natural periods. The dynamic performances of FOWT-SFFC with and without nets under random ocean waves, the combined random wind and random waves as well as current are comprehensively compared and discussed. The simulation results indicate that in wind-sea dominated conditions, the nets tend to slightly increase the dynamic responses of FOWT-SFFC, especially the components corresponding to natural periods. Nonetheless, under sea states that comprise both wind-sea waves and swell, nets help to reduce the dynamic responses of FOWT-SFFC by introducing additional damping.
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Waniewski, T. A., C. E. Brennen, and F. Raichlen. "Bow Wave Dynamics." Journal of Ship Research 46, no. 01 (March 1, 2002): 1–15. http://dx.doi.org/10.5957/jsr.2002.46.1.1.
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Experimental studies of air entrainment by breaking waves are essential for advancing the understanding of these flows and creating valid models. The present study used experimental simulations of a ship bow wave to examine its dynamics and air entrainment processes. The simulated waves were created by a deflecting plate mounted at an angle in a supercritical free-surface flow in a flume. Measurements of the bow wave geometry at two scales and also for a bow wave created by a wedge in a towing tank are presented. Contact line and bow wave profile measurements from the different experiments are compared and demonstrate the similarity of the flume simulations to the towing tank experiments. The bow wave profile data from the towing tank experiments were used to investigate the scaling of the wave with the flow and the dependence on geometric parameters. In addition, surface disturbances observed on the plunging wave are documented herein because of the role they play in air entrainment. The air entrainment itself is explored in Waniewski et al (2001).
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REEDER, D. BENJAMIN, LINUS Y. S. CHIU, and CHI-FANG CHEN. "EXPERIMENTAL EVIDENCE OF HORIZONTAL REFRACTION BY NONLINEAR INTERNAL WAVES OF ELEVATION IN SHALLOW WATER IN THE SOUTH CHINA SEA: 3D VERSUS Nx2D ACOUSTIC PROPAGATION MODELING." Journal of Computational Acoustics 18, no. 03 (September 2010): 267–78. http://dx.doi.org/10.1142/s0218396x10004176.
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A joint Taiwanese-U.S. field experiment was conducted in the South China Sea (SCS), entitled the South China Sea Oceanic Processes Experiment (Taiwan)/Non-Linear Internal Waves Initiative (US) (SCOPE/NLIWI), the ocean acoustics portion of which occurred during April 12–22, 2007. The acoustics objective was to quantify the temporal and spatial variability in acoustic propagation characteristics on the continental shelf in the presence of locally-generated and trans-basin nonlinear internal waves (NLIW). Broadband (400 Hz center frequency) m-sequence signals transmitted nearly continuously by a source moored near the seabed were received by vertical line arrays at 3 and 6 km range. The acoustic transect was oriented approximately parallel to the wave fronts of the shoaling trans-basin NLIW's which had crossed the deep basin from their origin in the Luzon Strait. The acoustic propagation variability due to strong vertical and horizontal refraction induced by the very large NLIW's creates an extremely complex acoustic field as a function of time and space. Experimental data and numerical acoustic propagation modeling results are presented to (1) examine and estimate the contribution of internal wave induced horizontal refraction to the received acoustic field; and (2) to quantify the range of propagation angles relative to the internal wave fronts within which strong horizontal refraction occurs and 3D propagation models are required to accurately predict the range- and depth-dependent acoustic propagation.
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Liu, Wei-Qin, Luo-Nan Xiong, Guo-Wei Zhang, Meng Yang, Wei-Guo Wu, and Xue-Min Song. "Research on Hydroelastic Response of an FMRC Hexagon Enclosed Platform." Symmetry 13, no. 7 (June 22, 2021): 1110. http://dx.doi.org/10.3390/sym13071110.
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The numerical hydroelastic method is used to study the structural response of a hexagon enclosed platform (HEP) of flexible module rigid connector (FMRC) structure that can provide life accommodation, ship berthing and marine supply for ships sailing in the deep ocean. Six trapezoidal floating structures constitute the HEP structure so that it is a symmetrical very large floating structure (VLFS). The HEP has the characteristics of large area and small depth, so its hydroelastic response is significant. Therefore, this paper studies the structural responses of a hexagon enclosed platform of FMRC structure in waves by means of a 3D potential-flow hydroelastic method based on modal superposition. Numerical models, including the hydrodynamic model, wet surface model and finite element method (FEM) model, are established, a rigid connection is simulated by many-point-contraction (MPC) and the number of wave cases is determined. The load and structural response of HEP are obtained and analyzed in all wave cases, and frequency-domain hydroelastic calculation and time-domain hydroelastic calculation are carried out. After obtaining a number of response amplitude operators (RAOs) for stress and time-domain stress histories, the mechanism of the HEP structure is compared and analyzed. This study is used to guide engineering design for enclosed-type ocean platforms.
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NAGEM, RAYMOND J., and DING LEE. "COUPLED 3D WAVE EQUATIONS WITH IRREGULAR FLUID-ELASTIC INTERFACE: THEORETICAL DEVELOPMENT." Journal of Computational Acoustics 10, no. 04 (December 2002): 421–44. http://dx.doi.org/10.1142/s0218396x02001656.
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A coupled three-dimensional fluid-elastic wave propagation mathematical model has been developed to handle environmental interactions in the ocean between a fluid medium and an elastic bottom. The existing model combines three-dimensional fluid and elastic wave propagation models with the incorporation of a set of horizontal fluid-elastic interface conditions. This paper extends the above model to consider an irregular fluid-elastic interface. The theoretical development of the irregular fluid-elastic interface equations is presented. Comparison of the fluid-elastic irregular interface to the horizontal case is one of the major objectives of this paper. Another major objective of this paper is the construction of a complete set of three-dimensional fluid-elastic wave equations, including the irregular interface, in a form suitable for stable numerical solution.
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Wei Yang, Hong, Min Guo, and Hailun He. "Conservation Laws of Space-Time Fractional mZK Equation for Rossby Solitary Waves with Complete Coriolis Force." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 1 (February 23, 2019): 17–32. http://dx.doi.org/10.1515/ijnsns-2018-0026.
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AbstractThe study of Rossby solitary waves are of great significance in physical oceanography, atmospheric physics, water conservancy project, military and communications engineering, etc. All the time, in the study of Rossby solitary waves, people have been focusing on integer order models. Recently, fractional calculus has become a new research hotspot, and it has opened a new door to research atmospheric and ocean. Thus, the fractional order model has the potential value in the study of Rossby solitary waves. In the present paper, according to the quasi-geostrophic potential vorticity equation with the complete Coriolis force, we get a new integer order mZK equation. Using the semi-inverse method and the fractional variational principle, the space-time fractional mZK(STFmZK) equation is obtained. To better understand the property of Rossby solitary waves, we study Lie symmetry analysis, nonlinear self-adjointness, similarity reduction by applying the STFmZK equation. In the end, the conservation and Caputo fractional derivative are discussed, respectively.
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Zhang, Jian, Yanjun Liu, Jingwen Liu, Tongtong He, and Yudong Xie. "Dynamic Characteristics of Magnetic Coupling in Horizontal Axis Wave Energy Device." Polish Maritime Research 24, s3 (November 27, 2017): 165–70. http://dx.doi.org/10.1515/pomr-2017-0119.
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Abstract To solve the dynamic response problems of magnetic coupling in the horizontal axis wave energy device, this has researched the dynamic characteristicsof magnetic coupling. The fitting formula about torque and angle of the magnetic coupling is obtained through experiments. The mathematical models of the magnetic coupling torque transmission are established. The steady state error of the magnetic coupling and the transfer function of the output angle are obtained. The analytical solution of the step response of the output angle in time domain is derived. The influence of the torsional rigidity, the damping coefficient and the driven rotor’s rotational inertia on dynamic characteristics of the magnetic coupling isanalyzed. According to the analysis results, the design rules of magnetic coupling are proposed.
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Goyal, Rushil, Kriti Singh, and Arkal Vittal Hegde. "Quarter Circular Breakwater: Prediction of Transmission Using Multiple Regression and Artificial Neural Network." Marine Technology Society Journal 48, no. 1 (January 1, 2014): 92–98. http://dx.doi.org/10.4031/mtsj.48.1.7.
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AbstractThe physical model study of coastal structures is a nonlinear process influenced by innumerable parameters. As a result of a lack of definite systems, intricacies, and high costs involved in the physical models, we need a simple mathematical tool to predict wave transmission through quarter circular breakwater (QBW). QBW is a state-of-the-art breakwater essentially based on the exploitation of the concepts of semicircular breakwater. This paper discusses the use of soft computing tools such as MATLAB-based multiple regression (MR) and artificial neural network (ANN) to predict the wave transmission coefficient of QBW. To assess the accuracy of the proposed model and its ability to forecast, correlation coefficient and mean squared error are availed. On comparing the results obtained from MR and ANN, it is concluded that ANN gives more accurate results and can be used as a powerful tool for the modeling of hydrodynamic breakwater transmission through QBW. It serves as a viable alternative to the conventional physical model to simulate the hydrodynamic transmission performance of QBW.
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Łubiński, Jacek, and Henryk Olszewski. "Hybrid Finite Element Method Development for Offshore Structures’ Calculation with the Implementation of Industry Standards." Polish Maritime Research 26, no. 4 (December 1, 2019): 90–100. http://dx.doi.org/10.2478/pomr-2019-0070.
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Abstract In the design process of offshore steel structures, it is typical to employ commercial calculation codes in which simulation and evaluation of results are performed on the basis of the available standards (e.g. API, DNV, Lloyds). The modeling and solution rely on finite element methods and cover the simulation of the structure’s properties along with the influence of the marine environment – sea currents, wave and wind loading, as well as the influence of vibrations, buoyancy and accompanying mass of water. Both commercial and open source mathematical modeling software which is available nowadays allows for cost effective and flexible implementation of advanced models for offshore industrial structures with high level of credibility and safety. The models can be built to suit task-specific requirements and evaluated on the basis of the selected criterial system best suited to the needs of the customer. Examples of methodology for environmental and structural model development are presented, along with simulation results covering a wide scope of data, ranging from stress and deformation to resonant characteristics and issues of technological feasibility.
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Mitchell, Neil C. "Aspects of marine geoscience: a review and thoughts on potential for observing active processes and progress through collaboration between the ocean sciences." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1980 (December 13, 2012): 5567–612. http://dx.doi.org/10.1098/rsta.2012.0395.
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Much progress has been made in the UK in characterizing the internal structures of major physiographic features in the oceans and in developing understanding of the geological processes that have created or shaped them. UK researchers have authored articles of high impact in all areas described here. In contrast to terrestrial geoscience, however, there have been few instrumented observations made of active processes by UK scientists. This is an area that could be developed over the next decades in the UK. Research on active processes has the potential ability to engage the wider public: Some active processes present significant geo-hazards to populations and offshore infrastructure that require monitoring and there could be commercial applications of technological developments needed for science. Some of the suggestions could involve studies in shallow coastal waters where ship costs are much reduced, addressing tighter funding constraints over the near term. The possibilities of measuring aspects of volcanic eruptions, flowing lava, turbidity currents and mass movements (landslides) are discussed. A further area of potential development is in greater collaboration between the ocean sciences. For example, it is well known in terrestrial geomorphology that biological agents are important in modulating erosion and the transport of sediments, ultimately affecting the shape of the Earth's surface in various ways. The analogous effect of biology on large-scale geomorphology in the oceans is also known but remains poorly quantified. Physical oceanographic models are becoming increasingly accurate and could be used to study further the patterns of erosion, particle transport and deposition in the oceans. Marine geological and geophysical data could in turn be useful for further verification of such models. Adapting them to conditions of past oceans could address the shorter-period movements, such as due to internal waves and tides, which have been barely addressed in palaeoceanography.
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Perrault, Douglas Edward. "Probability of Sea Condition for Ship Strength, Stability, and Motion Studies." Journal of Ship Research 65, no. 01 (March 17, 2021): 1–14. http://dx.doi.org/10.5957/josr.05190024.
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Modeling and simulation continues to be an important tool for determining the response of sea-going vessels to wind and waves. To provide appropriate forcing functions to the models, it is important to have environmental data of sufficient fidelity to facilitate an assessment of platform response, which is as accurate as possible within the practical constraints of time and resources. Fortunately, there are a variety of sources of good wave data, including the U.S. National Oceanic and Atmospheric Administration. This study examines the wave data in the context of simulation codes for assessing characteristics of ocean craft response. It also looks at some practical considerations to limit the scope of simulations. The work is strongly influenced by modeling and simulation of naval surface ships, looking for extreme behaviors, but many of the issues discussed are broadly applicable to other applications. Copyright 2021 Her Majesty the Queen in Right of Canada, Department of National Defence