Relevant bibliographies by topics / Ocean waves – – Mathematical models

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Ocean waves – – Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Ocean waves – – Mathematical models"

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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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Dissertations / Theses on the topic "Ocean waves – – Mathematical models"

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Button, Peter. "Models for ocean waves." Master's thesis, University of Cape Town, 1988. http://hdl.handle.net/11427/14299.

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Includes bibliography.
Ocean waves represent an important design factor in many coastal engineering applications. Although extreme wave height is usually considered the single most important of these factors there are other important aspects that require consideration. These include the probability distribution of wave heights, the seasonal variation and the persistence, or duration, of calm and storm periods. If one is primarily interested in extreme wave height then it is possible to restrict one's attention to events which are sufficiently separated in time to be effectively independently (and possibly even identically) distributed. However the independence assumption is not tenable for the description of many other aspects of wave height behaviour, such as the persistence of calm periods. For this one has to take account of the serial correlation structure of observed wave heights, the seasonal behaviour of the important statistics, such as mean and standard deviation, and in fact the entire seasonal probability distribution of wave heights. In other words the observations have to be regarded as a time series.
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Chan, Johnson Lap-Kay. "Numerical procedure for potential flow problems with a free surface." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/28637.

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A numerical procedure based upon a boundary integral method for gravity wave making problems is studied in the time domain. The free-surface boundary conditions are combined and expressed in a Lagrangian notation to follow the free-surface particle's motion in time. The corresponding material derivative term is approximated by a finite difference expression, and the velocity terms are extrapolated in time for the completion of the formulations. The fluid-body intersection position at the free surface is predicted by an interpolation function that requires information from both the free surface and the submerged surface conditions. Solutions corresponding to a linear free-surface condition and to a non-linear free-surface condition are obtained at small time increment values. Numerical modelling of surface wave problems is studied in two dimensions and in three dimensions. Comparisons are made to linear analytical solutions as well as to published experimental results. Good agreement between the numerical solutions and measured values is found. For the modelling of a three dimensional wave diffraction problem, results at high wave amplitude are restricted because of the use of quadrilateral elements. The near cylinder region of the free surface is not considered to be well represented because of the coarse element size. Wave forces calculated on the vertical cylinder are found to be affected by the modelled tank length. When the simulated wave length is comparable to the wave tank's dimension, numerical results are found to be less than the experimental measurements. However, when the wave length is shorter than the tank's length, solutions are obtained with very good precision.
Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
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Alves, Jose Henrique Gomes de Mattos Mathematics UNSW. "A Saturation-Dependent Dissipation Source Function for Wind-Wave Modelling Applications." Awarded by:University of New South Wales. Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17786.

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This study reports on a new formulation of the spectral dissipation source term Sds for wind-wave modelling applications. This new form of Sds features a nonlinear dependence on the local wave spectrum, expressed in terms of the azimuthally integrated saturation parameter B(k)=k^4 F(k). The basic form of this saturation-dependent Sds is based on a new framework for the onset of deep-water wave breaking due to the nonlinear modulation of wave groups. The new form of Sds is succesfully validated through numerical experiments that include exact nonlinear computations of fetch-limited wind-wave evolution and hindcasts of two-dimensional wave fields made with an operational wind-wave model. The newly-proposed form of Sds generates integral spectral parameters that agree more closely with observations when compared to other dissipation source terms used in state-of-the-art wind-wave models. It also provides more flexibility in controlling properties of the wave spectrum within the high wavenumber range. Tests using a variety of wind speeds, three commonly-used wind input source functions and two alternative full-development evolution limits further demonstrate the robustness and flexibility of the new saturation-dependent dissipation source term. Finally, improved wave hindcasts obtained with an implementation of the new form of Sds in a version of the WAM model demonstrate its potential usefulness in operational wind-wave forecasting applications.
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Suoja, Nicole Marie. "Directional wavenumber characteristics of short sea waves." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/88473.

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Thesis (Ph. D.)--Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Dept. of Ocean Engineering; and the Woods Hole Oceanographic Institution), 2000.
Includes bibliographical references (leaves 134-141).
by Nicole Marie Suoja.
Ph.D.
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Downer, Joshua, and n/a. "The influence of ocean waves on the distribution of sea ice in an MIZ." University of Otago. Department of Mathematics & Statistics, 2005. http://adt.otago.ac.nz./public/adt-NZDU20070202.120522.

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A marginal ice zone (MIZ) is characterised by distinct ice floes and its direct exposure to the open ocean. Sea ice is typically described as a continuous material but this description can be inappropriate in an MIZ due to the granular nature of the ice cover and the scale of processes acting on the ice floes. In this thesis, the kinematic behaviour of sea ice in an MIZ modelled as a granular material is investigated with an emphasis on the influence of ocean waves. The kinematic behaviour of a set of ice floes subject to ocean wave forcing was recorded in an experiment conducted in the Ross Sea. Kinematic data were recorded from each ice floe using a GPS receiver, tri-axial accelerometer, and compass. The data show (1) the influence of wave forcing and (2) collisions between neighbouring ice floes. It was also discovered that the GPS receivers were able to resolve the effects of ocean wave forcing despite their poor absolute accuracy. The number density and normalised structure factor (NSF) are introduced to describe the spatial structure of a set of ice floes. Four idealised distributions (in 1D and 2D) are analysed to gain insight into the way that different factors determine the shape of the NSF. It is shown that (1) a significant sinusoidal deviation causes a peak in the NSF, (2) ordered structure dominates low spatial frequencies, and (3) disorder dominates high spatial frequencies. A comparison of the contributions from these different factors is used to estimate the significance of a sinusoidal deviation in the positions of the ice floes. A granular model of an MIZ is developed using a novel set of equations of motion to examine the effect of ocean wave forcing. The equations of motion are derived for small ice floes and allows forcing by multiple waves. These equations predict a transient, wave-induced torque, which can be sustained by the application of a second force to the ice floe. Torque induced by the interaction of two forces on an ice floe may be a general feature of sea ice motion. The number density and NSF are used to analyse the distribution of ice floes in the granular model. At low solids-fractions the number density is correlated at the frequency of the wave forcing. As the solids-fraction is increased this correlation is destroyed by collisions between the ice floes and new correlations are created that are related to the packing structure of the ice floes. When the number density is weighted by the velocity of the ice floes, the correlations between floes are related to the convolution of the wave velocity field and the number density. These correlations may be incorporated into the thickness distribution of large-scale models using the maximum entropy method. The granular model was also examined as a percolating network of contacts and it was found that percolation was more likely to occur along the crest of a wave than in the direction of propagation.
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Amenta, Pablo Marco. "On finite difference solutions for the ocean wave spectrum in regions of non-uniform water depth." Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/44698.

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This investigation is concerned with the determination of the sea state in terms of wave spectra. The phenomenum was calculated for two different bathymetries.

The purpose is to develop a finite difference method with an upwind differencing scheme to g solve several formulations of the wave action conservation equation. The computations were done in the wave number space and the frequency direction space. For the case of a beach with constant slope the results were compared with the analytical solution. For the case of an elliptical submerged shoal, they were compared with experimental data.

The results of the computer code showed a fairly good qualitative agreement with the actual values for a smooth distribution of input energy.
Master of Science

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Morris-Thomas, Michael. "An investigation into wave run-up on vertical surface piercing cylinders in monochromatic waves." University of Western Australia. School of Oil and Gas Engineering, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0010.

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[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] Wave run-up is the vertical uprush of water when an incident wave impinges on a free- surface penetrating body. For large volume offshore structures the wave run-up on the weather side of the supporting columns is particularly important for air-gap design and ultimately the avoidance of pressure impulse loads on the underside of the deck structure. This investigation focuses on the limitations of conventional wave diffraction theory, where the free-surface boundary condition is treated by a Stokes expansion, in predicting the harmonic components of the wave run-up, and the presentation of a simplified procedure for the prediction of wave run-up. The wave run-up is studied on fixed vertical cylinders in plane progressive waves. These progressive waves are of a form suitable for description by Stokes' wave theory whereby the typical energy content of a wave train consists of one fundamental harmonic and corresponding phase locked Fourier components. The choice of monochromatic waves is indicative of ocean environments for large volume structures in the diffraction regime where the assumption of potential flow theory is applicable, or more formally A/a < Ο(1) (A and a being the wave amplitude and cylinder radius respectively). One of the unique aspects of this work is the investigation of column geometry effects - in terms of square cylinders with rounded edges - on the wave run-up. The rounded edges of each cylinder are described by the dimensionless parameter rc/a which denotes the ratio of edge corner radius to half-width of a typical column with longitudinal axis perpendicular to the quiescent free-surface. An experimental campaign was undertaken where the wave run-up on a fixed column in plane progressive waves was measured with wire probes located close to the cylinder. Based on an appropriate dimensional analysis, the wave environment was represented by a parametric variation of the scattering parameter ka and wave steepness kA (where k denotes the wave number). The effect of column geometry was investigated by varying the edge corner radius ratio within the domain 0 <=rc/a <= 1, where the upper and lower bounds correspond to a circular and square shaped cylinder respectively. The water depth is assumed infinite so that the wave run-up caused purely by wave-structure interaction is examined without the additional influence of a non-decaying horizontal fluid velocity and finite depth effects on wave dispersion. The zero-, first-, second- and third-harmonics of the wave run-up are examined to determine the importance of each with regard to local wave diffraction and incident wave non-linearities. The modulus and phase of these harmonics are compared to corresponding theoretical predictions from conventional diffraction theory to second-order in wave steepness. As a result, a basis is formed for the applicability of a Stokes expansion to the free-surface boundary condition of the diffraction problem, and its limitations in terms of local wave scattering and incident wave non-linearities. An analytical approach is pursued and solved in the long wavelength regime for the interaction of a plane progressive wave with a circular cylinder in an ideal fluid. The classical Stokesian assumption of infinitesimal wave amplitude is invoked to treat the free-surface boundary condition along with an unconventional requirement that the cylinder width is assumed much smaller than the incident wavelength. This additional assumption is justified because critical wavelengths for wave run-up on a fixed cylinder are typically much larger in magnitude than the cylinder's width. In the solution, two coupled perturbation schemes, incorporating a classical Stokes expansion and cylinder slenderness expansion, are invoked and the boundary value problem solved to third-order. The formulation of the diffraction problem in this manner allows for third-harmonic diffraction effects and higher-order effects operating at the first-harmonic to be found. In general, the complete wave run-up is not well accounted for by a second-order Stokes expansion of the free-surface boundary condition and wave elevation. This is however, dependent upon the coupling of ka and kA. In particular, whilst the modulus and phase of the second-harmonic are moderately predicted, the mean set-up is not well predicted by a second-order Stokes expansion scheme. This is thought to be caused by higher than second-order non-linear effects since experimental evidence has revealed higher-order diffraction effects operating at the first-harmonic in waves of moderate to large steepness when k < < 1. These higher-order effects, operating at the first-harmonic, can be partially accounted for by the proposed long wavelength formulation. For small ka and large kA, subsequent comparisons with measured results do indeed provide a better agreement than the classical linear diffraction solution of Havelock (1940). To account for the complete wave run-up, a unique approach has been adopted where a correction is applied to a first-harmonic analytical solution. The remaining non-linear portion is accounted for by two methods. The first method is based on regression analysis in terms of ka and kA and provides an additive correction to the first-harmonic solution. The second method involves an amplification correction of the first-harmonic. This utilises Bernoulli's equation applied at the mean free-surface position where the constant of proportionality is empirically determined and is inversely proportional to ka. The experimental and numerical results suggest that the wave run-up increases as rc/a--› 0, however this is most significant for short waves and long waves of large steepness. Of the harmonic components, experimental evidence suggests that the effect of a variation in rc/a on the wave run-up is particularly significant for the first-harmonic only. Furthermore, the corner radius effect on the first-harmonic wave run-up is well predicted by numerical calculations using the boundary element method. Given this, the proposed simplified wave run-up model includes an additional geometry correction which accounts for rc/a to first-order in local wave diffraction. From a practical view point, it is the simplified model that is most useful for platform designers to predict the wave run-up on a surface piercing column. It is computationally inexpensive and the comparison of this model with measured results has proved more promising than previously proposed schemes.
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Rotzoll, Kolja. "Hydraulic Parameter Estimation Using Aquifer Tests, Specific Capacity, Ocean Tides, and Wave Setup for Hawai'i Aquifers." Thesis, Water Resources Research Center, University of Hawaii at Manoa, 2007. http://hdl.handle.net/10125/22265.

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The islands of Hawaii face increasing ground-water demands due to population growth in the last decades. Analytical and numerical models are essential tools for managing sustainable ground-water resources. The models require estimates of hydraulic properties, such as hydraulic conductivity and storage parameters. Four methods were evaluated to estimate hydraulic properties for basalts on the island of Maui. First, unconventional step-drawdown tests were evaluated. The results compare favorably with those from classical aquifer tests with a correlation of 0.81. Hydraulic conductivity is log-normally distributed and ranges from 1 to 2,500 m/d with a geometric mean of 276 m/d and a median of 370 m/d. The second approach developed a simplified parameter-estimation scheme through an empirical relationship between specific capacity and hydraulic parameters that utilized Hawaii's state well database. For Maui's basalts, the analysis yields a geometric-mean and median hydraulic conductivity of 423 and 493 m/d, respectively. Results from aquifer tests and specific-capacity relationships were used to generate island-wide hydraulic-conductivity maps using kriging. The maps are expected to be of great benefit in absence of site-specific field assessments. In the third approach, ocean-tide responses in the central Maui aquifer were used to estimate an effective hydraulic diffusivity of 2.3 x 10^7 m^2/d. The position of the study area necessitated refining the existing analytical solution that considers asynchronous and asymmetric tidal influence from two sides in an aquifer. Finally, measured ground-water responses to wave setup were used to estimate hydraulic parameters. Setup responses were significant as far as 5 km inland and dominated barometric-pressure effects during times of energetic swell events. The effective diffusivity estimated from setup was 2.3 x 10^7 m^2/d, matching that based on tides. Additionally, simple numerical ground-water flow models were developed to assess the accuracy of results from analytical solutions for step-drawdown tests, dual-tides and wave setup, and to evaluate sediment-damping effects on tidal propagation. The estimated mean hydraulic conductivities of the four methods range between 300 and 500 m/d for basalts in Maui. The results of different methods are consistent among each other and match previous estimates for basalts.
USGS Pacific Island Water Science Center
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Geiger, Sam R. (Sam Rayburn) 1971. "Hydrodynamic modeling of towed buoyant submarine antenna's [sic] in multidirectional seas." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/29045.

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Thesis (S.M.)--Joint Program in Oceanographic Engineering (Massachusetts Institute of Technology, Dept. of Ocean Engineering, and the and Woods Hole Oceanographic Institution), 2000.
Includes bibliographical references (p. 100-101).
A finite difference computer model is developed to simulate the exposure statistics of a radio frequency buoyant antenna as it is towed in a three-dimensional random seaway. The model allows the user to prescribe antenna properties (length, diameter, density, etc.), sea conditions (significant wave height, development of sea), tow angle, and tow speed. The model then simulates the antenna-sea interaction for the desired duration to collect statistics relating to antenna performance. The model provides design engineers with a tool to predict antenna performance trends, and to conduct design tradeoff studies. The floating antenna envisioned is for use by a submarine operating at modest speed and depth.
by Sam R. Geiger.
S.M.
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Wortham, Cimarron James Lemuel IV. "A multi-dimensional spectral description of ocean variability with applications." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/79296.

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Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), February 2013.
"February 2013." Cataloged from PDF version of thesis.
Includes bibliographical references (p. 175-184).
Efforts to monitor the ocean for signs of climate change are hampered by ever-present noise, in the form of stochastic ocean variability, and detailed knowledge of the character of this noise is necessary for estimating the significance of apparent trends. Typically, uncertainty estimates are made by a variety of ad hoc methods, often based on numerical model results or the variability of the data set being analyzed. We provide a systematic approach based on the four-dimensional frequency-wavenumber spectrum of low-frequency ocean variability. This thesis presents an empirical model of the spectrum of ocean variability for periods between about 20 days and 15 years and wavelengths of about 200-10,000 km, and describes applications to ocean circulation trend detection, observing system design, and satellite data processing. The horizontal wavenumber-frequency part of the model spectrum is based on satellite altimetry, current meter data, moored temperature records, and shipboard ADCP data. The spectrum is dominated by motions along a "nondispersive line". The observations considered are consistent with a universal [omega] -² power law at the high end of the frequency range, but inconsistent with a universal wavenumber power law. The model spectrum is globally varying and accounts for changes in dominant phase speed, period, and wavelength with location. The vertical structure of the model spectrum is based on numerical model results, current meter data, and theoretical considerations. We find that the vertical structure of kinetic energy is surface intensified relative to the simplest theoretical predictions. We present a theory for the interaction of linear Rossby waves with rough topography; rough topography can explain both the observed phase speeds and vertical structure of variability. The improved description of low-frequency ocean variability presented here will serve as a useful tool for future oceanographic studies.
by Cimarron James Lemuel Wortham, IV.
Ph.D.
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Books on the topic "Ocean waves – – Mathematical models"

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Dommermuth, Douglas G. Time series analysis of ocean waves. Cambridge, Mass: Massachusetts Institute of Technology, Sea Grant College Program, 1986.

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Won, Y. S. Spectral Boussinesq modelling of random waves. [Delft]: Delft University of Technology, Dept. of Civil Engineering, Fluid Mechanics Group, 1992.

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Leeuwen, P. J. van. Low frequency wave generation due to breaking wind waves. [Delft]: Faculty of Civil Engineering, Delft University of Technology, 1992.

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Operational analysis and prediction of ocean wind waves. New York: Springer-Verlag, 1989.

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(Firm), Knovel, ed. Waves and wave forces on coastal and ocean structures. Hackensack, N.J: World Scientific, 2006.

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N, Pelinovskiĭ E., and Slunyaev Alexey, eds. Rogue waves in the ocean: Observations, theories and modelling. New York: Springer, 2009.

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Kharif, Christian. Rogue waves in the ocean: Observations, theories and modelling. New York: Springer, 2009.

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Efimov, V. V. Chislennoe modelirovanie vetrovogo volnenii͡a︡. Kiev: Nauk. dumka, 1991.

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Wilkin, John L. Scattering of coastal-trapped waves by irregularities in coastline and topography. Woods Hole, Mass: Woods Hole Oceanographic Institution, 1988.

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Wilkin, John L. Scattering of coastal-trapped waves by irregularities in coastline and topography. Woods Hole, Mass: Woods Hole Oceanographic Institution, 1988.

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Book chapters on the topic "Ocean waves – – Mathematical models"

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Mertens, Christian, Janna Köhler, Maren Walter, Jin-Song von Storch, and Monika Rhein. "Observations and Models of Low-Mode Internal Waves in the Ocean." In Mathematics of Planet Earth, 127–43. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05704-6_4.

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Olbers, Dirk, Carsten Eden, Erich Becker, Friederike Pollmann, and Johann Jungclaus. "The IDEMIX Model: Parameterization of Internal Gravity Waves for Circulation Models of Ocean and Atmosphere." In Mathematics of Planet Earth, 87–125. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05704-6_3.

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Schober, Constance M., and Annalisa Calini. "Rogue Waves in Higher Order Nonlinear Schrödinger Models." In Extreme Ocean Waves, 1–21. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21575-4_1.

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Calini, Annalisa, and Constance M. Schober. "Rogue Waves in Higher Order Nonlinear Schrödinger Models." In Extreme Ocean Waves, 31–51. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8314-3_2.

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Murray, James D. "Biological Waves: Single Species Models." In Mathematical Biology, 274–310. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-08539-4_11.

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Murray, James D. "Biological Waves: Single Species Models." In Mathematical Biology, 274–310. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-08542-4_11.

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Murray, James D. "Biological Waves: Multi-species Reaction Diffusion Models." In Mathematical Biology, 311–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-08539-4_12.

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Murray, James D. "Biological Waves: Multi-Species Reaction Diffusion Models." In Mathematical Biology, 311–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-08542-4_12.

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Sentis, Rémi. "Coupling Electron Waves and Laser Waves." In Mathematical Models and Methods for Plasma Physics, Volume 1, 159–98. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03804-9_5.

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Matsumoto, Y., M. Kameda, F. Takemura, H. Ohashi, and A. Ivandaev. "Wave dynamics of bubbly liquids mathematical models and numerical simulation." In Shock Waves, 535–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-77648-9_84.

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Conference papers on the topic "Ocean waves – – Mathematical models"

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Murakami, H., and O. Rios. "A Mathematical Model for a Gyroscopic Ocean-Wave Energy Converter." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62834.

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Global attempts to increase generation of clean and reproducible energy have contributed to considerable progress in ocean-wave power-generation technologies. The efficiency of ocean-wave energy converters has improved by almost an order of magnitude in the last decade. In this report, we consider a floating-type gyroscopic ocean-wave power-generator that has proven to generate 50 kW in a prototype test conducted by a Japanese company in 2012. A gyroscopic power generator consists of a buoy, a gimbal, and spinning rotors mounted on a gimbal. The gimbal is installed on the deck of the buoy and rotates when the buoy oscillates or rocks by ocean waves. The gimbal axis is connected to an electric generator. The objectives of our research are to understand quantitatively the mechanisms of gyroscopic ocean-wave power-generators and to improve the component design of the generator to maximize power output. To this end, we develop a mathematical model and a scale model of a gyroscopic ocean-wave power-generator. This integrated approach is to numerically simulate power generation and to clarify the effect of relevant design parameters.
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Murakami, Hidenori, Oscar Rios, and Ardavan Amini. "A Mathematical Model With Preliminary Experiments of a Gyroscopic Ocean Wave Energy Converter." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51163.

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Global attempts to increase generation of clean and reproducible natural energy have greatly contributed to the progress of solar, wind, biomass, and geothermal energy generation. To meet the goal set by the Renewable Portfolio Standards (RPS) in the United States, it is advisable for several of the coastal states to tap into the least explored resource: ocean-wave energy. There are many advantages to ocean-wave energy generation. First, the energy per unit area is 20 to 30 times larger compared with solar and five to ten times larger when compared to wind energy. Second, waves are more easily predicted than wind. Currently, there are several challenges with capturing ocean energy: With respect to the environment, noise pollution and effects on marine life need to be taken into consideration; with respect to design, ocean-wave power generators need to withstand large waves due to hurricanes and be designed to lessen visual pollution. There are various methods and devices used to capture ocean wave energy. Point absorbers, such as PowerBuoy, can harness vertical or heaving motion into electricity while attenuators like Pelamis use the induced movement of its joints from the incoming waves. Unfortunately, many have few parameters that can be varied to optimize power generation and or suffer from the various challenges mentioned above. The gyroscopic ocean wave energy converter harnesses the rocking or pitching motion induced by the ocean waves and converts it into rotary motion that is then fed to a generator. Furthermore, it is a fully enclosed floating device that has several parameters that can be varied to optimize power output. Previous work has demonstrated the viability of such a device, but the theoretical modeling of these converters is still in its infancy compared to that of other ocean wave energy converters. The objective of the research presented is to fully understand the mechanisms of power generation in the gyroscopic ocean wave energy converter. Using the moving frame method, a mathematical model of the device is developed. The nonlinear equations of motion are derived through the use of this novel method and then solved numerically. The results are then used to optimize the system and identify key parameters and their effect on the output power generated. Additionally, the resulting equations serve as a tool for identifying an appropriate control strategy for the system. Finally, a scale model of a gyroscopic ocean wave energy converter is developed to validate the equations of motion that have been derived.
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Nelli, Filippo, David M. Skene, Luke G. Bennetts, Micheal H. Meylan, Jason P. Monty, and Alessandro Toffoli. "Experimental and Numerical Models of Wave Reflection and Transmission by an Ice Floe." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61248.

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The marginal ice zone (MIZ) is the outer part of the sea-ice covered ocean, where ice can be found in the form of large floating chucks better known as floes. Since it is the area where the most part of the interaction between ice cover and ocean waves takes place, it requires careful modelling. However existing mathematical models, based on the traditional thin-plate theory, underestimate waves attenuation for the most energetic waves, since the energy dissipation occurring during the process is not taken into account. New laboratory experimental and direct numerical models are presented here. In the experimental model a thin plastic plate is tested under the action of incident waves with varying amplitudes and periods. The same experimental set-up was reproduced using a numerical model, which was developed by coupling a High Order Spectral Numerical Wave Tank with the Navier-Stokes solver IHFOAM. Data from the experiments and numerical models confirm that non-linear effects lead to a decrease of wave transmission.
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Kalogirou, A., and O. Bokhove. "Mathematical and Numerical Modelling of Wave Impact on Wave-Energy Buoys." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54937.

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We report on the mathematical and numerical modelling of amplified rogue waves driving a wave-energy device in a contraction. This wave-energy device consists of a floating buoy attached to an AC-induction motor and constrained to move upward only in a contraction, for which we have realised a working scale-model. A coupled Hamiltonian system is derived for the dynamics of water waves and moving wave-energy buoys. This nonlinear model consists of the classical water wave equations for the free surface deviation and velocity potential, coupled to a set of equations describing the dynamics of a wave-energy buoy. As a stepping stone, the model is solved numerically for the case of linear shallow water waves causing the motion of a simple buoy structure with V-shaped cross-sections, using a variational (dis)continuous Galerkin finite element method.
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Ramadasan, Sudheesh, Longbin Tao, and Arun Kr Dev. "Vortex-Induced-Vibration of Jack-Ups With Cylindrical Legs in Regular Waves." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95764.

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Abstract A simple mathematical model is developed based on the single-degree-of-freedom analogy and principle of conservation of energy evaluating various modes of Vortex-Induced-Vibration (VIV) of a jack-up with cylindrical legs in regular waves. Similar to uniform current, mass ratio, damping ratio and mode factor are found to be the important parameters controlling the cross-flow VIV and radius of gyration also for the yaw VIV. Criteria for the initiation of the mentioned VIV modes are developed for the cases of a single 2D cylinder experiencing planar oscillatory flow, four rigidly coupled 2D cylinders in rectangular configuration experiencing planar oscillatory flow and jack-up experiencing regular waves. The newly developed VIV model is validated by a set of experiments conducted in a wind, wave and current flume. The importance of mass damping parameter is further demonstrated in suppressing VIV in regular waves. The mathematical method will equip engineers to consider the effect of VIV due to regular waves in jack-up designs.
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Yang, Seung Ho. "Study on the Parametric Rolling of Medium-Sized Containership Based on Nonlinear Time Domain Analysis." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18067.

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Abstract The numerical analysis of parametric rolling of medium-sized containership has been carried out. Target containership was modeled by using two different numerical models, which are nonlinear numerical model and simplified dynamic mathematical model respectively. The simulations were performed in full-loaded operating condition for regular and irregular waves. For regular waves, the analysis was conducted with a wide range of wave periods including the vicinity of the wave period expected to cause parametric rolling of the target containership. On the other hand, regarding irregular waves, the wave period range that is highly likely to occur according to significant wave height was selected and used as input values of wave spectrum for nonlinear time domain analysis. The analysis results are summarized as wave height versus wave period diagrams with the occurrences of parametric rolling motions for each speed. And also, time series based on time domain analysis are represented and compared between nonlinear numerical model and simplified dynamic mathematical model. In addition, the sensitivity of key parameters such as vessel speed, wave period, and roll damping to parametric rolling was investigated and estimated under operating condition. Finally, when the parametric rolling occurred, the characteristics of heave, pitch, and roll motions were analyzed. This study could be used as the basic data for determining the operational conditions for safe operation as well as initial design of the medium-sized containership.
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Gao, Junliang, Chunyan Ji, and Yingyi Liu. "Numerical Study of Transient Harbor Oscillations Induced by N-Waves." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54237.

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The response amplitudes of different resonant modes in an elongated harbor with constant depth induced by N-waves with different amplitudes and different types are calculated using the Normal Mode Decomposition (NMD) method. Wave conditions inside the harbor are simulated with a fully nonlinear Boussinesq model FUNWAVE-TVD. It is found that, for the small amplitude of the incident N-wave, wave energy inside the harbor is dominated by the lowest few modes, while only a small proportion of the wave energy is distributed over the higher modes. However, with the increase of the incident wave amplitude, most of the wave energy inside the harbor tends to concentrate on the higher resonant modes, hence the relative wave energy distributed over the lowest few modes decreases. On the other hand, the wave energy distribution inside the harbor is also significantly affected by the type of the N-wave. The wave energy inside the harbor excited by the MS-type incident N-wave is more concentrated than that excited by the TS-type N-wave. The MS- and TS-type N-waves correspond to the N-wave expressions proposed by Madsen and Schäffer (Madsen, Schäffer, 2010. Analytical solutions for tsunami runup on a plane beach single waves, N-waves and transient waves. Journal of Fluid Mechanics 645, 27–57) and Tadepalli and Synolakis (Tadepalli, Synolakis, 1994. The run-up of N-waves on sloping beaches. Proceedings of the Royal Society London A: Mathematical, Physical & Engineering Sciences 445, 99–112), respectively.
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Quadvlieg, Frans, Roberto Tonelli, Elia Palermo, and Per Teigen. "Mathematical Model for Efficient Prediction of Lifeboat Sailaway Performance in Calm Water and Waves." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-42232.

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Free fall lifeboats have been developed for emergency evacuation from offshore installations, when conventional means of transportation cannot be applied. As a consequence, the ability of the lifeboats to perform safe drop- and sail away under all circumstances has to be demonstrated. This paper focuses on efficient and robust numerical simulation of these operations. To predict the lifeboat behavior under a large variety of stochastic conditions, such as irregular waves, in combination with wind and current, calls for many individual simulations of the sailaway performance. The present paper presents a brand new mathematical model that is able to predict the behavior of a free fall lifeboat during drop-phase, the submerged phase, the surfacing phase and the “sailing in waves” phase (combined, not gluing time traces from different predictions together). The proposed mathematical model is completely non-linear in nature and considers instantaneous submergence and attitude of the lifeboat. All forces and moments in 6 degrees of freedom are calculated instantaneously. Consequently, accelerations, velocities and displacements, are calculated based on this. The paper describes the build-up of the mathematical model. This is based on a summation of forces due to impact forces, cross flow drag forces, generated lift, centrifugal forces, buoyancy forces, propulsion (propeller and nozzle), steering forces due to steering action and resistance. Obviously, also the instantaneous added masses play an important role. This results in a mathematical model for rigid body motions in 6 degrees of freedom, which can be used for predicting the motion response during drop- and sail away. This means a validity range in very extreme weather and in calm water. The paper will show basic validation and several applications.
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Iijima, Kazuhiro, Akira Tatsumi, and Masahiko Fujikubo. "Elasto-Plastic Beam Afloat on Water Subjected to Waves." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-78646.

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This paper addresses development of a mathematical model which describes the behavior of an elasto-plastic beam afloat on water surface. The mathematical model is valid for predicting the collapse of a Very Large Floating Structure (VLFS) subjected to extreme wave-induced vertical bending moment. It is a follow-up of the previous work in which the collapse behavior of a VLFS is pursued by adopting a segmented beam approach. In this research, the whole VLFS is modelled with elasto-plastic beam elements. The hydrodynamic behavior is modeled by using Rankine source panel method based on time-domain potential theory. It is shown that the elasto-plastic beam approach gives almost the same result as the segmented beam approach for predicting the one-element collapse behavior. The elastoplastic beam approach is extensively used to predict the progressive collapse spread over multiple sections, which cannot be followed by the segmented beam approach.
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Qu, Yan, Zhijun Song, Bin Teng, and Yunxiang You. "Dynamic Response of SPAR in Internal Solitary Waves." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-49413.

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Internal solitary wave is considered as a potential hazard environmental condition to the floating structures in South China Sea. This paper presents results of the dynamic response analysis of a SPAR in internal solitary waves (ISW). Mathematical model of the ISW is selected to simulate the current process induced by the ISW. The result shows that the Korteweg–de Vries (KdV) gives rational result compared with the Modified Korteweg–de Vries (MKdV) equation. Dynamic motion of SPAR were estimated by using the current profile derived from KDV theory, load determined by Morrison equation and the nonlinear model of the mooring system.
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Reports on the topic "Ocean waves – – Mathematical models"

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Galperin, Boris. Modeling the Effects of Anisotropic Turbulence and Dispersive Waves on Oceanic Circulation and their Incorporation in Navy Ocean Models. Fort Belvoir, VA: Defense Technical Information Center, September 2010. http://dx.doi.org/10.21236/ada542675.

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