Tesi: "Ocean waves – – Mathematical models"

1

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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2

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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3

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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4

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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5

Downer, Joshua, e 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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6

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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7

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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8

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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9

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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10

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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11

Coutis, Peter F. School of Mathematics UNSW. "Currents, coasts and cays : a study of tidal upwelling and island wakes". Awarded by:University of New South Wales. School of Mathematics, 2000. http://handle.unsw.edu.au/1959.4/18207.

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In this thesis, the phenomenon of flow-topography interaction is considered in the context of two dynamically distinct case studies. In the first study, tidally-driven upwelling is investigated usingfield data collected in Hydrographers Passage (20????S), a narrow, navigable channel in the dense outer reef matrix of the southern Great Barrier Reef, Australia. In the second study, island wake formations at Cato Island (155????32????E, 23????15????S) in the deep, Western Coral Sea are examined using a combination of field data and numerical experiments. The result of the Hydrographers Passage study are of considerable scientific interest since they apply to numerous smaller non-navigable reef-edge passages dotted throughout the southern Great Barrier Reef. Strong, semi-diurnal flood tides flowing through a gap in a distal patch reef system at the shelf break generate strong upwelling, providing a pulsed, semi-diurnal input of nutrients to the reefs offshore of the passage. If stable in the long term, this mechanism could have profound evolutionary implications for large reefal areas in the southern Great Barrier Reef. In the second study, two sets of field observations at Cato Island coincided with conditions of strong (~0.7m s-1), vertically sheared incident currents and weaker (~0.3m s-1), more variable incident flows. The combination of dynamically distinct flow regimes and a tall, steep-sided island penetrating oligotrophic surface waters provides a unique opportunity to investigate the impact of island wakes on hydrographic structure and biological enhancement. Field data indicate that flow disturbances downstream of Cato Island are likely to generate biological enhancement during conditions of eddy shedding and non-shedding wakes. A primitive equation numerical model configured on the basis of field observations faithfully reproduces the key features of both data sets; mechanisms responsible for producing these key features are proposed. Previous numerical studies of island wakes have concentrated primarily on eddy shedding flows. In this thesis, the sub-critical (non-shedding) flow scenario is also considered. It is demonstrated that particle retention in island wakes has a ????hair trigger???? characteristic controlled by incident flow speed. This observation leads to a new proposal to explain the long-standing recruitment problem of biological oceanography.

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12

Abdolmaleki, Kourosh. "Modelling of wave impact on offshore structures". University of Western Australia. School of Mechanical Engineering, 2007. http://theses.library.uwa.edu.au/adt-WU2008.0055.

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[Truncated abstract] The hydrodynamics of wave impact on offshore structures is not well understood. Wave impacts often involve large deformations of water free-surface. Therefore, a wave impact problem is usually combined with a free-surface problem. The complexity is expanded when the body exposed to a wave impact is allowed to move. The nonlinear interactions between a moving body and fluid is a complicated process that has been a dilemma in the engineering design of offshore and coastal structures for a long time. This thesis used experimental and numerical means to develop further understanding of the wave impact problems as well as to create a numerical tool suitable for simulation of such problems. The study included the consideration of moving boundaries in order to include the coupled interactions of the body and fluid. The thesis is organized into two experimental and numerical parts. There is a lack of benchmarking experimental data for studying fluid-structure interactions with moving boundaries. In the experimental part of this research, novel experiments were, therefore, designed and performed that were useful for validation of the numerical developments. By considering a dynamical system with only one degree of freedom, the complexity of the experiments performed was minimal. The setup included a plate that was attached to the bottom of a flume via a hinge and tethered by two springs from the top one at each side. The experiments modelled fluid-structure interactions in three subsets. The first subset studied a highly nonlinear decay test, which resembled a harsh wave impact (or slam) incident. The second subset included waves overtopping on the vertically restrained plate. In the third subset, the plate was free to oscillate and was excited by the same waves. The wave overtopping the plate resembled the physics of the green water on fixed and moving structures. An analytical solution based on linear potential theory was provided for comparison with experimental results. ... In simulation of the nonlinear decay test, the SPH results captured the frequency variation in plate oscillations, which indicated that the radiation forces (added mass and damping forces) were calculated satisfactorily. In simulation of the nonlinear waves, the waves progressed in the flume similar to the physical experiments and the total energy of the system was conserved with an error of 0.025% of the total initial energy. The wave-plate interactions were successfully modelled by SPH. The simulations included wave run-up and shipping of water for fixed and oscillating plate cases. The effects of the plate oscillations on the flow regime are also discussed in detail. The combination of experimental and numerical investigation provided further understanding of wave impact problems. The novel design of the experiments extended the study to moving boundaries in small scale. The use of SPH eliminated the difficulties of dealing with free-surface problems so that the focus of study could be placed on the impact forces on fixed and moving bodies.

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13

Zang, Xiaoyun 1971. "Spectral description of low frequency oceanic variability". Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/59094.

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Thesis (Ph.D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences and the Woods Hole Oceanographic Institution), 2000.
Includes bibliographical references (p. 179-187).
A simple dynamic model is used with various observations to provide an approximate spectral description of low frequency oceanic variability. Such a spectrum has wide application in oceanography, including the optimal design of observational strategy for the deployment of floats, the study of Lagrangian statistics and the estimate of uncertainty for heat content and mass flux. Analytic formulas for the frequency and wavenumber spectra of any physical variable, and for the cross spectra between any two different variables for each vertical mode of the simple dynamic model are derived. No heat transport exists in the model. No momentum flux exists either if the energy distribution is isotropic. It is found that all model spectra are related to each other through the frequency and wavenumber spectrum of the stream-function for each mode, ... , where ... represent horizontal wavenumbers, w stands for frequency, n is vertical mode number, and ... are latitude and longitude, respectively. Given ... , any model spectrum can be estimated. In this study, an inverse problem is faced: ... is unknown; however, some observational spectra are available. I want to estimate ... if it exists. Estimated spectra of the low frequency variability are derived from various measurements: (i) The vertical structure of and kinetic energy and potential energy is inferred from current meter and temperature mooring measurements, respectively. (ii) Satellite altimetry measurements produce the geographic distributions of surface kinetic energy magnitude and the frequency and wavenumber spectra of sea surface height. (iii) XBT measurements yield the temperature wavenumber spectra and their depth dependence. (v) Current meter and temperature mooring measurements provide the frequency spectra of horizontal velocities and temperature. It is found that a simple form for ... does exist and an analytical formula for a geographically varying ... is constructed. Only the energy magnitude depends on location. The wavenumber spectral shape, frequency spectral shape and vertical mode structure are universal. This study shows that motion within the large-scale low-frequency spectral band is primarily governed by quasigeostrophic dynamics and all observations can be simplified as a certain function of ... The low frequency variability is a broad-band process and Rossby waves are particular parts of it. Although they are an incomplete description of oceanic variability in the North Pacific, real oceanic motions with energy levels varying from about 10-40% of the total in each frequency band are indistinguishable from the simplest theoretical Rossby wave description. At higher latitudes, as the linear waves slow, they disappear altogether. Non-equatorial latitudes display some energy with frequencies too high for consistency with linear theory; this energy produces a positive bias if a lumped average westward phase speed is computed for all the motions present.
by Xiaoyun Zang.
Ph.D.

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14

Horko, Michael. "CFD optimisation of an oscillating water column wave energy converter". University of Western Australia. School of Mechanical Engineering, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0089.

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Although oscillating water column type wave energy devices are nearing the stage of commercial exploitation, there is still much to be learnt about many facets of their hydrodynamic performance. This research uses the commercially available FLUENT computational fluid dynamics flow solver to model a complete OWC system in a two dimensional numerical wave tank. A key feature of the numerical modelling is the focus on the influence of the front wall geometry and in particular the effect of the front wall aperture shape on the hydrodynamic conversion efficiency. In order to validate the numerical modelling, a 1:12.5 scale experimental model has been tested in a wave tank under regular wave conditions. The effects of the front lip shape on the hydrodynamic efficiency are investigated both numerically and experimentally and the results compared. The results obtained show that with careful consideration of key modelling parameters as well as ensuring sufficient data resolution, there is good agreement between the two methods. The results of the testing have also illustrated that simple changes to the front wall aperture shape can provide marked improvements in the efficiency of energy capture for OWC type devices.

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15

Bleach, Gordon Phillip. "Acceleration waves in constrained thermoelastic materials". Doctoral thesis, University of Cape Town, 1989. http://hdl.handle.net/11427/15850.

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Bibliography: pages 242-249.
We study the propagation and growth of acceleration waves in isotropic thermoelastic media subject to a broad class of thermomechanical constraints. The work is based on an existing thermodynamic theory of constrained thermoelastic materials presented by Reddy (1984) for both definite and non- conductors, but we differ by adopting a new definition of a constrained non-conductor and by investigating the consequences of isotropy. The set of constraints considered is not arbitrary but is large enough to include most constraints commonly found in practice. We also extend Reddy's (1984) work by including consideration of sets of constraints for which a set of vectors associated with the constraints is linearly dependent. These vectors play a significant role in the propagation conditions and in the growth equations described below. Propagation conditions (of Fresnel-Hadamard type) are derived for both homothermal and homentropic waves, and solutions for longitudinal and transverse principal waves are discussed. The derivations involve the determination of jumps in the time derivative of constraint multipliers which are required in the solution of the corresponding growth equations, and it is found that these multipliers cannot be separately determined if the set of constraint vectors mentioned above is linearly dependent. This difficulty forces us to restrict the constraint set for which the growth equations for homothermal and homentropic waves can be derived. The growth of plane, cylindrical and spherical waves is considered and solutions are discussed, concentrating on the influence of the constraints on the results.

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16

Marchant, Timothy Robert. "On short-crested water waves". Title page, contents and introduction only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phm3151.pdf.

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17

Kiss, Andrew Elek. "Dynamics of laboratory models of the wind-driven ocean circulation". View thesis entry in Australian Digital Theses Program, 2000. http://thesis.anu.edu.au/public/adt-ANU20011018.115707/index.html.

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18

Zink, Florian. "Gravity waves and turbulence in the lower atmosphere /". Title page, contents and abstract only, 2000. http://web4.library.adelaide.edu.au/theses/09PH/09phz778.pdf.

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19

Noad, Imogen Frances. "Absorbing power from ocean waves : a mathematical approach to modelling wave energy converters". Thesis, University of Bristol, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.752773.

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20

Bermejo-Bermejo, Rodolfo. "A finite element model of ocean circulation". Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/26166.

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Preliminary results of a two-layer quasi-geostrophic box model of a wind-driven ocean are presented. The new aspects of this work in relation with conventional eddy models are a finite element formulation of the quasi-geostrophic equations and the use of no-slip boundary condition on the horizontal solid boundaries. In contrast to eddy resolving models that utilize free-slip boundary conditions our results suggest that the obtention of ocean eddies with the no-slip constraints requires a more restricted range of parameters, in particular much lower horizontal eddy viscosity eddy coefficients AH and higher Froude numbers F₁ and F₂. We show explicitly that a given range of parameters, which is eddy generating when the free-slip boundary condition is used, leads to a quasi-laminar flow in both, upper and lower, layers. An analytical model to interpret the numerical results is put forth. It is an extension of an earlier model of Ierley and Young (1983) in that the relative vorticity terms are of primary importance for the dynamics. Thus, it is shown that the boundary layer dynamics is active in the interior of the second layer, and it can be concluded from our method that for given F₁ and F₂ such that the lower layer geostrophic contours are closed, to the existence of the western boundary layer will prevent the homogenization of the potential vorticity so long as AH is large enough to stabilize the northwestern undulations of the flow.
Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate

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21

Mercer, Geoffry Norman. "On standing waves and models of shear dispersion /". Title page, contents and summary only, 1992. http://web4.library.adelaide.edu.au/theses/09PH/09phm5541.pdf.

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22

朱書堂 e Shutang Zhu. "Interaction between waves and porous seawalls". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31239869.

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23

Frankel, Jay Irwin. "A theoretical investigation of thermal waves". Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/76212.

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A unified and systematic study of one-dimensional heat conduction based on thermal relaxation is presented. Thermal relaxation is introduced through the constitutive equation (modified Fourier's law) which relates this heat flux and temperature. The resulting temperature and flux field equations become hyperbolic rather than the usual classical parabolic equations encountered in heat conduction. In this formulation, heat propagates at a finite speed and removes one of the anomalies associated to parabolic heat conduction, i.e., heat propagating at an infinite speed. In situations involving very short times, high heat fluxes, and cryogenic temperatures, a more exact constitutive relation must be introduced to preserve a finite speed to a thermal disturbance. The general one-dimensional temperature and flux formulations for the three standard orthogonal coordinate systems are presented. The general solution, in the temperature domain, is developed by the finite integral transform technique. The basic physics and mathematics are demonstrated by reviewing Taitel's problem. Then attention is turned to the effects of radially dependent systems, such as the case of a cylinder and sphere. Various thermal disturbances are studied showing the unusual physics associated with dissipative wave equations. The flux formulation is shown to be a viable alternative domain to develop the flux distribution. Once the flux distribution has been established, the temperature distribution may be obtained through the conservation of energy. Linear one-dimensional composite regions are then investigated in detail. The general temperature and flux formulations are developed for the three standard orthogonal coordinate systems. The general solution for the flux and temperature distributions are obtained in the flux domain using a generalized integral transform technique. Additional features associated with hyperbolic heat conduction are displayed through examples with various thermal disturbances. A generalized expression for temperature dependent thermal conductivity is introduced and incorporated into the one-dimensional hyperbolic heat equation. An approximate analytical solution is obtained and compared with a standard numerical method. Finally, recommendations for future analytical and experimental investigations are suggested.
Ph. D.

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24

Zhang, Wenjun. "Waves in mathematical models of intracellular calcium and other excitable systems". Thesis, University of Auckland, 2011. http://hdl.handle.net/2292/14482.

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Oscillations in cytoplasmic calcium concentration are a crucial control mechanism in almost every cell type. Two important classes of oscillation are of particular interest: solitary and periodic waves. Both types of waves are commonly observed in physical experiments and found in mathematical models of calcium dynamics and other excitable systems. In this thesis, we try to understand these two classes of wave solutions. We first investigate wave solutions of the canonical excitable model, the FitzHugh-Nagumo (FHN) equations. We analyze the FHN equations using geometric singular perturbation theory and numerical integration, and find some new codimension-two organizing centres of the overall dynamics. Many analytical results about the FHN model in its classical form have already been established. We devise a transformation to change the form of the FHN equations we study into the classical form to make use of the results. This enables us to show how basic features of the bifurcation structure of the FHN equations arise from the singular limit. We then study waves of a representative calcium model. We analyze the dynamics of the calcium model in the singular limit, and show how homoclinic and Hopf bifurcations of the full system arise as perturbations of singular homoclinic and Hopf bifurcations. We compare the wave solutions in the FHN model and the calcium model, and show that the dynamics of the two models differ in some respects (most importantly, in the way in which diffusion enters the equations). We conclude that the FHN model should not uniformly be used as a prototypical model for calcium dynamics. Motivated by phenomena seen in the FHN and calcium models, we then investigate reduction techniques for excitable systems, including the quasi-steady state approximation and geometric singular perturbation theory, and show that criticality of Hopf bifurcations may be changed when applying these reduction methods to slow-fast biophysical systems. This suggests that great care should be taken when using reduction techniques such as these, to ensure that spurious conclusions about the dynamics of a model are not drawn from the dynamics of a reduced version of the model. Finally, we describe the class of numerical algorithms used to compute features of the detailed bifurcation sets for the FHN and calcium models, and show how these were used to locate a non-structurally stable heteroclinic connection between periodic orbits in a calcium model; this is the first time such a global bifurcation has been computed.

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25

Zhang, Shuangxi, e 張雙喜. "Numerical study of rayleigh waves in anisotropic media". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B31245092.

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26

Marasli, Barsam. "Spatially traveling waves in a two-dimensional turbulent wake". Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184811.

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Abstract (sommario):

Hot-wire measurements taken in the turbulent wake of a flat plate are presented. Symmetrical and antisymmetrical perturbations at various amplitudes and frequencies were introduced into the wake by small flap oscillations. As predicted by linear stability theory, the sinuous (antisymmetric) mode was observed to be more significant than the varicose (symmetric) mode. When the amplitude of the perturbation was low, the spatial development of the introduced coherent perturbation was predicted well by linear stability theory. At high forcing levels, the wake spreading showed dramatic deviations from the well known square-root behavior of the unforced case. Measured coherent Reynolds stresses changed sign in the neighborhood of the neutral point of the perturbation, as predicted by the linear theory. However, the linear theory failed to predict the disturbance amplitude and transverse shapes close to the neutral point. Some nonlinear aspects of the evolution of instabilities in the wake are discussed. Theoretical predictions of the mean flow distortion and the generation of the first harmonic are compared to experimental measurements. Given the unforced flow and the amplitude of the fundamental wave, the mean flow distortion and the amplitude of the first harmonic are predicted remarkably well.

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27

盧慧 e Hui Loo. "Effect of surface waves on pollutant dispersion". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31224866.

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28

Pinilla, Camilo Ernesto. "Numerical simulation of shear instability in shallow shear flows". Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115697.

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The instabilities of shallow shear flows are analyzed to study exchanges processes across shear flows in inland and coastal waters, coastal and ocean currents, and winds across the thermal-and-moisture fronts. These shear flows observed in nature are driven by gravity and governed by the shallow water equations (SWE). A highly accurate, and robust, computational scheme has been developed to solve these SWE. Time integration of the SWE was carried out using the fourth-order Runge-Kutta scheme. A third-order upwind bias finite difference approximation known as QUICK (Quadratic Upstream Interpolation of Convective Kinematics) was employed for the spatial discretization. The numerical oscillations were controlled using flux limiters for Total Variation Diminishing (TVD). Direct numerical simulations (DNS) were conducted for the base flow with the TANH velocity profile, and the base flow in the form of a jet with the SECH velocity profile. The depth across the base flows was selected for the' balance of the driving forces. In the rotating flow simulation, the Coriolis force in the lateral direction was perfectly in balance with the pressure gradient across the shear flow during the simulation. The development of instabilities in the shear flows was considered for a range of convective Froude number, friction number, and Rossby number. The DNS of the SWE has produced linear results that are consistent with classical stability analyses based on the normal mode approach, and new results that had not been determined by the classical method. The formation of eddies, and the generation of shocklets subsequent to the linear instabilities were computed as part of the DNS. Without modelling the small scales, the simulation was able to produce the correct turbulent spreading rate in agreement with the experimental observations. The simulations have identified radiation damping, in addition to friction damping, as a primary factor of influence on the instability of the shear flows admissible to waves. A convective Froude number correlated the energy lost due to radiation damping. The friction number determined the energy lost due to friction. A significant fraction of available energy produced by the shear flow is lost due the radiation of waves at high convective Froude number. This radiation of gravity waves in shallow gravity-stratified shear flow, and its dependence on the convective Froude number, is shown to be analogous to the Mach-number effect in compressible flow. Furthermore, and most significantly, is the discovery from the simulation the crucial role of the radiation damping in the development of shear flows in the rotating earth. Rings and eddies were produced by the rotating-flow simulations in a range of Rossby numbers, as they were observed in the Gulf Stream of the Atlantic, Jet Stream in the atmosphere, and various fronts across currents in coastal waters.

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29

繆泉明 e Quanming Miao. "Effect of submerged vertical structures on ship waves". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B3025176X.

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30

Arbic, Brian K. "Generation of mid-ocean eddies : the local baroclinic instability hypothesis". Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/53047.

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Abstract (sommario):

Thesis (Ph.D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences and the Woods Hole Oceanographic Institution), 2000.
Includes bibliographical references (p. 284-290).
by Brian Kenneth Arbic.
Ph.D.

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31

Li, Ping, e 李平. "Numerical methodologies for electromagnetic parasitic system modeling and simulation". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/202361.

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In this thesis, to efficiently and accurately model the electromagnetic radiations from electronic and antenna systems, and to analyze the hybrid electromagnetic (EM)-circuit system and the interactions between EM waves and multi-physics systems, a plethora of full-wave approaches are developed. Specifically, a set of frequency-domain methods are proposed in the first part of this thesis to characterize the electromagnetic radiations from device under test (DUT) based on the sampled near-field data. For the first approach, the dyadic Green function (DGF) in the presence of perfectly conducting sphere is expanded by spherical vector wave functions, which is mathematically rigorous. Based on this DGF and the reciprocity theorem, the radiation outside the spherical sampling surface can be accurately predicted with only the tangential components of the electric near-field over this sampling surface. Sometimes for situations where electronic devices are placed in good conductive shielding enclosures with apertures or ventilation slots, only partially planar electric near-field sampling over the apertures or the slots is sufficient according to Schelkunoff’s principle. Due to the unavailability of analytical DGF and the prohibitively computational cost for the numerical DGF, a novel two-step process approach by considering the radiation problem as a scattering issue with incident waves from the equivalent magnetic currents derived from the sampled electric near-field is proposed. However, the very near-field radiation inside the sampling surface cannot be retrieved with the above two approaches. To overcome this limitation, the equivalent source reconstruction based methods are introduced by replacing the radiators with equivalent current sources that are capable of reproducing the original radiation. Due to the difficulty of acquiring the phase information of the near-field data, a fully new iterative phaseless source reconstruction method (SRM) which only needs the amplitude of the electric field is developed. To reduce the computational cost of traditional SRM for broadband radiators, a wideband SRM based on a Stoer-Bulirsh (SB) recursive tabular algorithm is proposed. Enhanced by an adaptive frequency sampling strategy, only a very small number of frequency samples are required. With the purpose to capture the nonlinear response of EM-circuit systems, transient scattering from penetrable objects, surface plasmon polarization (SPP) of grapheme below the terahertz range, and the impacts of random parameters on the physical behavior of stochastic systems, various novel discontinuous Galerkin time-domain (DGTD) based methods and their extensions are developed. For a practical electronic system, apart from the EM part, the presence of lumped elements must be considered. Therefore, a hybrid EM-circuit solver is indispensable. For the EM subsystem governed by Maxwell’s equations, it is solved by DGTD with an explicit time-marching scheme. For the lumped subsystem, circuit equations are constructed based on either the modified nodal analysis (MNA) derived from Kirchoff’s current law or the basic I-V relations. By introducing a port voltage and current, the EM and circuit solvers are synchronized in the temporal sequence at the lumped port. This synchronized EM-circuit solver is free of instabilities even though nonlinear circuit elements are involved. For open-region scattering problem analysis, a novel approach by integrating the time-domain boundary integral (TDBI) algorithm with DGTD is developed. At the truncation boundary, the fields required for the incoming flux in DGTD is calculated using the TDBI from the equivalent currents over a Huygens’ surface enclosing the scatterer. The hybrid DGTD-BI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer’s shape. By considering the one atom-thick graphene as an infinitesimally thin conductive sheet, a surface impedance boundary condition (SIBC) augmented DGTD algorithm is developed to model the graphene. With this SIBC, straightforward volumetric discretization is avoided, thus significantly reducing the memory cost and meanwhile alleviating the restriction on the minimum time marching size. Due to the complex relation between the surface conductivity σg (comprising contributions from both intraband and interband) and the angular frequency ω, direct mapping the numerical flux from the frequency to the time-domain via inverse Fourier transform is not available. To address this issue, a fast-relaxing vector-fitting (FRVF) technique is used to approximate the σg by rational functions in the Laplace-domain. Via inverse Laplace transform, the time-domain matrix equations are obtained in integral forms of time t. Resorting to finite integral technique (FIT), a fully-discrete matrix system can be achieved. Finally, to consider the impact of random parameters on realistic electronic systems, a stochastic solver based on DGTD and sparse-grid collocation method is developed. To reduce the number of supporting, an adaptive strategy is utilized by using the local hierarchical surplus as error indicator. To improve the flexibility of the proposed algorithm, both piecewise linear and Lagrange polynomial basis functions are employed to handle different stochastic systems. Particularly, the piecewise linear basis function is more efficient for non-smoothly observables while Lagrange polynomials are more suitable for smoothly observables. With these strategies, the singularities and quick variations can be efficiently captured but with very small number of collocation points. The above proposed algorithms are demonstrated by various examples, the accuracy, efficiency, and robustness of these algorithms are clearly observed.
published_or_final_version
Electrical and Electronic Engineering
Doctoral
Doctor of Philosophy

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32

Kwon, Sun Hong. "Directional growth of wind generated waves". Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49816.

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33

Weaver, Anthony T. "On assimilating sea surface temperature data into an ocean general circulation model". Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/29204.

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The feasibility of sea surface temperature (SST) data improving the performance of an ocean general circulation model (OGCM) is investigated through a series of idealized numerical experiments. The GFDL Bryan-Cox-Semtner primitive equation model is set-up as an eddy resolving, unforced, flat bottomed channel of uniform depth. 'Observed' SST data taken from a reference ocean established in a control run are continuously assimilated into an 'imperfect' model using a simple 'nudging' scheme based on a surface relaxation condition of the form Q = C(SST — T₁) where Q is the heat flux and T₁ is the temperature at the top level of the model. The rate of assimilation is controlled by adjusting the constant inverse relaxation time parameter C. Numerical experiments indicate that the greatest improvement in the model fields is achieved in the extreme case of infinite assimilation (i.e., C = ᅇ) in which the 'observed' SST is directly inserted into the model. This improvement is quantified by monitoring the reduction in the root mean square (RMS) errors relative to the simulated reference ocean. Assimilation with longer relaxation time-scales (i.e., smaller C's) proves quite ineffective in reducing the RMS errors. The improvement in the direct insertion numerical experiment stems from the model's ability to transfer assimilated SST into subsurface information through strong advective processes. The assimilation of cool surface data induces convective overturning which transfers the 'cool' information downward rapidly but adversely affects the vertical thermal structure by an unrealistic deepening of the mixed layer. By contrast, warm surface data do not penetrate downward readily. Thus, the systematically biased downward flux of coolness gradually produces unrealistically cool subsurface waters.
Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate

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34

Elsden, Tom. "Numerical modelling of ultra low frequency waves in Earth's magnetosphere". Thesis, University of St Andrews, 2016. http://hdl.handle.net/10023/15663.

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Ultra Low Frequency (ULF) waves are a ubiquitous feature of Earth's outer atmosphere, known as the magnetosphere, having been observed on the ground for almost two centuries, and in space over the last 50 years. These waves represent small oscillations in Earth's magnetic field, most often as a response to the external influence of the solar wind. They are important for the transfer of energy throughout the magnetosphere and for coupling different regions together. In this thesis, various features of these oscillations are considered. A detailed background on the history and previous study of ULF waves relevant to our work is given in the introductory chapter. In the following chapters, we predominantly use numerical methods to model ULF waves, which are carefully developed and thoroughly tested. We consider the application of these methods to reports on ground and spaced based observations, which allows a more in depth study of the data. In one case, the simulation results provide evidence for an alternative explanation of the data to the original report, which displays the power of theoretical modelling. An analytical model is also constructed, which is tested on simulation data, to identify the incidence and reflection of a class of ULF wave in the flank magnetosphere. This technique is developed with the aim of future applications to satellite data. Further to this, we develop models both in Cartesian and dipole geometries to investigate some of the theoretical aspects of the coupling between various waves modes. New light is shed on the coupling of compressional (fast) and transverse (Alfvén) magnetohydrodynamic (MHD) wave modes in a 3D dipole geometry. Overall, this thesis aims to develop useful numerical models, which can be used to aid in the interpretation of ULF wave observations, as well as probing new aspects of the existing wave theory.

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35

Wu, Lichuan. "Introducing Surface Gravity Waves into Earth System Models". Doctoral thesis, Uppsala universitet, Luft-, vatten och landskapslära, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-314760.

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Surface gravity waves alter the turbulence of the bottom atmosphere and the upper ocean. Accordingly, they can affect momentum flux, heat fluxes, gas exchange and atmospheric mixing. However, in most state-of-the-art Earth System Models (ESMs), surface wave influences are not fully considered or even included. Here, applying surface wave influences into ESMs is investigated from different aspects. Tuning parameterisations for including instantaneous wave influences has difficulties to capture wave influences. Increasing the horizontal resolution of models intensifies storm simulations for both atmosphere-wave coupled (considering the influence of instantaneous wave-induced stress) and stand-alone atmospheric models. However, coupled models are more sensitive to the horizontal resolution than stand-alone atmospheric models. Under high winds, wave states have a big impact on the sea spray generation. Introducing a wave-state-dependent sea spray generation function and Charnock coefficient into a wind stress parameterisation improves the model performance concerning wind speed (intensifies storms). Adding sea spray impact on heat fluxes improves the simulation results of air temperature. Adding sea spray impact both on the wind stress and heat fluxes results in better model performance on wind speed and air temperature while compared to adding only one wave influence. Swell impact on atmospheric turbulence closure schemes should be taken into account through three terms: the atmospheric mixing length scale, the swell-induced momentum flux at the surface, and the profile of swell-induced momentum flux. Introducing the swell impact on the three terms into turbulence closure schemes shows a better performance than introducing only one of the influences. Considering all surface wave impacts on the upper-ocean turbulence (wave breaking, Stokes drift interaction with the Coriolis force, Langmuir circulation, and stirring by non-breaking waves), rather than just one effect, significantly improves model performance. The non-breaking-wave-induced mixing and Langmuir circulation are the most important terms when considering the impact of waves on upper-ocean mixing. Accurate climate simulations from ESMs are very important references for social and biological systems to adapt the climate change. Comparing simulation results with measurements shows that adding surface wave influences improves model performance. Thus, an accurate description of all important wave impact processes should be correctly represented in ESMs, which are important tools to describe climate and weather. Reducing the uncertainties of simulation results from ESMs through introducing surface gravity wave influences is necessary.

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36

Lee, Craig M. "Observations and models of upper ocean response to atmospheric forcing : wind driven flow, surface heating and near-inertial wave interactions with mesoscale currents /". Thesis, Connect to this title online; UW restricted, 1995. http://hdl.handle.net/1773/11039.

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37

Santoso, Agus Mathematics &amp Statistics Faculty of Science UNSW. "Evolution of climate anomalies and variability of Southern Ocean water masses on interannual to centennial time scales". Awarded by:University of New South Wales. School of Mathematics and Statistics, 2005. http://handle.unsw.edu.au/1959.4/33355.

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In this study the natural variability of Southern Ocean water masses on interannual to centennial time scales is investigated using a long-term integration of the Commonwealth Scientic and Industrial Research Organisation (CSIRO) coupled climate model. We focus our attention on analysing the variability of Antarctic IntermediateWater (AAIW), Circumpolar DeepWater (CDW), and Antarctic Bottom Water (AABW). We present an analysis of the dominant modes of temperature and salinity (T - S) variability within these water masses. Climate signals are detected and analysed as they get transmitted into the interior from the water mass formation regions. Eastward propagating wavenumber-1, -2, and -3 signals are identied using a complex empirical orthogonal function (CEOF) analysis along the core of the AAIW layer. Variability in air-sea heat uxes and ice meltwater rates are shown by heat and salt budget analyses to control variability of Antarctic Surface Water where density surfaces associated with AAIW outcrop. The dominant mode in the CDW layer is found to exhibit an interbasin-scale of variability originating from the North Atlantic, and propagating southward into the Southern Ocean. Salinity dipole anomalies appear to propagate around the Atlantic meridional overturning circulation with the strengthening and weakening of North Atlantic Deep Water formation. In the AABW layer, T - S anomalies are shown to originate from the southwestern Weddell Sea, driven by salinity variations and convective overturning in the region. It is also demonstrated that the model exhibits spatial patterns of T - S variability for the most part consistent with limited observational record in the Southern Hemisphere. However, some observations of decadal T - S changes are found to be beyond that seen in the model in its unperturbed state. We further assess sea surface temperature (SST) variability modes in the Indian Ocean on interannual time scales in the CSIRO model and in reanalysis data. The emergence of a meridional SST dipole during years of southwest Western Australian rainfall extremes is shown to be connected to a large-scale mode of Indian Ocean climate variability. The evolution of the dipole is controlled by variations in atmospheric circulation driving anomalous latent heat uxes with wind-driven ocean transport moderating the impact of evaporation and setting the conditions favourable for the next generation phase of an opposite dipole.

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38

Bailey, J. S. L. "Experimentally verified fluid loading models for slender horizontal cylinders in waves". Thesis, University of Sussex, 2000. http://sro.sussex.ac.uk/id/eprint/737/.

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This thesis reports on research work aimed at improving methods for predicting the fluid loading on fixed- and compliant offshore structures in waves. In focusing on slender member fluid-interaction models, the limitations and uncertainties associated with the widely-used Morison equation are examined. An improved empirical model has been developed and tested extensively alongside the Morison equation, using real experimental data. This improved model gives a better representation of the frequency dependency of the fluid-loading coefficients: this is particularly important in compliant motion conditions where the so-called relative velocity concept still needs to be verified under carefully controlled experimental conditions. The model is based entirely on the use of linear wave kinematics, thus simplifying calibration in irregular conditions and avoiding the need for a consistent non-linear wave theory (which is still lacking). By appropriate adaptation the improved model can also be extended to include amplitude dependency in the loading coefficients. The Improved Model has been developed through an analysis of experimental data. For this purpose the experimental work was focused on a horizontal cylinder, at model scale, located in a wave tank at the University of Sussex. The fluid loading experienced by a fixed cylinder, in both regular and irregular waves conditions, was measured and examined in detail. In addition, a comprehensive study of the loading on compliant cylinders, in both regular and irregular waves, was undertaken. Extensive use was made of appropriate parameter estimation techniques with initial attention (using simulated data) given to their accuracy for use with noisy experimental measurements. The effects of subtle (but undesirable) tank characteristics were also carefully taken into account. The study shows that, for fixed horizontal cylinders, benefits can be clearly identified in using the improved model, with frequency dependent coefficients, over the frequency dependent Morison equation. Moreover, the study shows that the relative velocity concept is more appropriate for use with the improved model than with the Morison model.

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39

Jung, Kyung Tae. "On three-dimensional hydrodynamic numerical modelling of wind induced flows in stably stratified waters : a Galerkin-finite difference approach". Title page, contents and summary only, 1989. http://web4.library.adelaide.edu.au/theses/09PH/09phj95.pdf.

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40

Kim, Jeong Hoon. "Stochastic turning point problem". Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40038.

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Abstract (sommario):

A one-dimensional refractive, randomly-layered medium is considered in an acoustic context. A time harmonic plane wave emitted by a source is incident upon it and generates totally reflected fields which consist of "signal" and "noise". The statistical properties, i.e., mean and correlation functions, of these fields are to be obtained. The variations of the medium structure are assumed to have two spatial scales; microscopic random fluctuations are superposed upon slowly varying macroscopic variations. With an intermediate scale of the wavelength, the interplay of total internal reflection (geometrical acoustics) and random multiple scattering (localization phenomena) is analyzed for the turning point problem. The problem, in particular, above the turning point is formulated in terms of a transition scale. Two limit theorems for stochastic differential equations with multiple spatial scales, called Theorem 1 and Theorem 2, are derived. They are applied to the stochastic initial value problems for reflection coefficients in the regions above and below the turning point, respectively. Theorem 1 is an extension of a limit theorem on O( 1) scaled interval to infinite scale and provides uniformly-valid approximate statistics for random multiple scattering in the region above the turning point (transition as well as outer regions). Theorem 2 deals with stochastic problems with a rapidly varying deterministic component and approximates the reflection process in the region below the turning point which is characterized by the random noise. Finally, the evolution of the reflection coefficient statistics in the whole region is described by combining the two results as a product of a transformation at the turning point and two evolution operators corresponding to the two regions.
Ph. D.

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41

Lai, Wing-chiu Derek, e 黎永釗. "The propagation of nonlinear waves in layered and stratified fluids". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B29750441.

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42

Liu, Xia, e 刘霞. "Numerical modeling of landslide-induced waves and their effects on downstream structures". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B48199412.

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Impulse waves in reservoirs, lakes, bays and oceans may be generated by landslides. The resulting impulse waves can propagate and cause disaster to the downstream. Some studies are carried out to investigate such phenomenon but most of them were based on either experimental observations or empirical/semiempirical relationships in simulating the waves generated by landslides. Therefore, the fundamental mechanism of such hazard is not got fully understood (complex motions of landslides with arbitrary geometry and interactions of fluid with landslides or shorelines). In addition, the effects of landslide-induced waves on downstream structures are rarely reported. Therefore, it appears necessary that the coupling numerical model is developed to simulate landslide-induced waves and to investigate generated wave characteristics. Furthermore, their effects on downstream structures should be investigated for mitigating hazard, such as the estimations of wave run-up, rundown and wave overtopping. This thesis presents the numerical modeling of landslide-induced waves and their effects on the downstream structures based on the computational fluid dynamics (CFD) package FLUENT. As there is no existing module to simulate water waves, the redevelopment of FLUENT by the user defined function (UDF) is necessary. For the problem of landslide-induced wave, two simplified numerical models are developed, including piston-type model and inlet boundary-type model. These two numerical models can rapidly assess the landslide-induced waves but be appropriate for the simple cases, such as a vertical wall moving horizontally or slump-type landslide whose particle velocities and free surface displacements at the inlet boundary are known. In order to expand the available range of numerical modeling, the block models aiming for rockslide are developed to investigate landslide-induced waves. Four categories of landslides are considered, such as horizontal landslide, vertical landslide, subaerial landslide and submarine landslide. Except of horizontal landslide, the coupled block model is employed to investigate water waves generated by vertical, subaerial and submarine landslides. The coupling is based on an iterative procedure enforcing the principle of the dynamic equilibrium of the fluid, the slide and their interfaces, and the interaction between landslide and fluid are considered. The wave characteristics generated by above-mentioned different types of landslides are investigated and discussed. For their effects of landslide-induced wave on downstream structures, the focuses of numerical modeling are the run-up and rundown of waves generated by subaerial and submarine landslides and wave overtopping on the downstream structures. The detailed numerical modeling illustrates that the present models can predict fairly well landslide-induced waves and their effects on downstream structures. The results of parametric study indicate that slide volume and impact Froude number ( v / gh ) play important roles on generated wave characteristics. The wave characteristics, propagation distance and geometric characteristics of seaward structural wall (slope and crest freeboard) are major factors in determining the characteristics of wave run-up, rundown and overtopping. Several useful prediction relationships are provided.
published_or_final_version
Civil Engineering
Doctoral
Doctor of Philosophy

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43

Boegman, Leon. "The degeneration of internal waves in lakes with sloping topography". University of Western Australia. Centre for Water Research, 2004. http://theses.library.uwa.edu.au/adt-WU2005.0043.

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[Truncated abstract] Observations are presented from Lake Biwa (Japan) and Lake Kinneret (Israel) showing the ubiquitous and often periodic nature of high-frequency internal waves in large stratified lakes. In both lakes, high-frequency wave events were observed within two distinct categories: (1) Vertical mode one solitary waves with wavelength ˜100-500 m and frequency near 103 Hz and (2) sinusoidal vertical mode one waves with wavelength ˜5-30 m and frequency just below the local maximum buoyancy frequency near 102 Hz. The sinusoidal waves were associated with shear instability and were shown to dissipate their energy sporadically within the lake interior. Conversely, the solitary waves were found to be capable of propagating to the lake perimeter where they may break upon sloping topography, each releasing ˜1% of the total basin-scale internal wave energy to the benthic boundary layer.

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44

Lin, Zaibin. "Integrated numerical model for wave induced seabed response around offshore structures". Thesis, University of Aberdeen, 2017. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=232272.

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Seabed stability in the vicinity of those offshore structure, which has been one of the particular concerns in engineering practice, can be compromised by the action of energetic waves. This project investigates the mechanisms of wave-induced soil response and liquefaction in a porous seabed near offshore structures. For this purpose both 2-Dimensional (2-D) and 3-Dimensional (3-D) integrated Wave-Seabed-Structure Interaction (WSSI) models have been developed within the project. They were used to simulate the effect of nonlinear wave-structure interaction on dynamic soil response in the neighbourhood of offshore pipelines, mono-pile structures, and multi-cylinder structures. Prior to applying the proposed WSSI models to practical engineering cases, several validations, mainly including wave and soil validations, were conducted. Excellent agreements between numerical and experimental results indicate the capacity of proposed WSSI models to simulate nonlinear wave-induced seabed response around offshore structures. Hereafter, the verified WSSI models are adopted to explore the mechanism of storm wave-induced soil response near offshore structures. The study of the offshore pipeline partially or fully buried in the seabed has shown that the leewake vortex can be sufficiently avoided with enough embedment, which also leads to lower possibility of the onset of scour in adjacent area of pipeline and the reduction of possible momentary liquefaction depth under pipeline bottom. Nonlinear wave-induced seabed response around a mono-pile structure, was investigated using the 3-D WSSI model developed in OpenFOAM, which allows to run numerical WSSI simulations in parallel. It was shown that, for waves propagating in a given longitudinal direction, the liquefaction occurs with greater depth at the lateral sides of mono-pile structure than at the front and back sides of mono-pile structure. Increasing penetration depth of the mono-pile structure slightly reduces the adjacent liquefaction depth. By adopting the same 3-D WSSI model, the numerical investigation of wave-induced soil response in the proximity of a multi-cylinder structure has been conducted. As found in the analysis by using same wave parameters in the case of a mono-pile structure, the nonlinear interaction between waves and multi-cylinder structure may significantly alter the distribution of liquefaction depth around each cylinder, compared to that for a single cylinder. Moreover, considering the effect of incident wave angles, such as 0° and 45° wave headings, it can be noted that the downstream cylinders are better protected from liquefaction threat due to the presence of upstream cylinders.

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45

PRUETT, CHARLES DAVID. "NUMERICAL SIMULATION OF NONLINEAR WAVES IN FREE SHEAR LAYERS (MIXING, COMPUTATIONAL, FLUID DYNAMICS, HYDRODYNAMIC STABILITY, SPATIAL, FLUID FLOW MODEL)". Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183869.

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A numerical model has been developed which simulates the three-dimensional stability and transition of a periodically forced free shear layer in an incompressible fluid. Unlike previous simulations of temporally evolving shear layers, the current simulations examine spatial stability. The spatial model accommodates features of free shear flow, observed in experiments, which in the temporal model are precluded by the assumption of streamwise periodicity; e.g., divergence of the mean flow and wave dispersion. The Navier-Stokes equations in vorticity-velocity form are integrated using a combination of numerical methods tailored to the physical problem. A spectral method is adopted in the spanwise dimension in which the flow variables, assumed to be periodic, are approximated by finite Fourier series. In complex Fourier space, the governing equations are spatially two-dimensional. Standard central finite differences are exploited in the remaining two spatial dimensions. For computational efficiency, time evolution is accomplished by a combination of implicit and explicit methods. Linear diffusion terms are advanced by an Alternating Direction Implicit/Crank-Nicolson scheme whereas the Adams-Bashforth method is applied to convection terms. Nonlinear terms are evaluated at each new time level by the pseudospectral (collocation) method. Solutions to the velocity equations, which are elliptic, are obtained iteratively by approximate factorization. The spatial model requires that inflow-outflow boundary conditions be prescribed. Inflow conditions are derived from a similarity solution for the mean inflow profile onto which periodic forcing is superimposed. Forcing functions are derived from inviscid linear stability theory. A numerical test case is selected which closely parallels a well-known physical experiment. Many of the aspects of forced shear layer behavior observed in the physical experiment are captured by the spatial simulation. These include initial linear growth of the fundamental, vorticity roll-up, fundamental saturation, eventual domination of the subharmonic, vortex pairing, emergence of streamwise vorticity, and temporary stabilization of the secondary instability. Moreover, the spatial simulation predicts the experimentally observed superlinear growth of harmonics at rates 1.5 times that of the fundamental. Superlinear growth rates suggest nonlinear resonances between fundamental and harmonic modes which are not captured by temporal simulations.

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46

Chen, Yongpin, e 陈涌频. "Surface integral equation method for analyzing electromagnetic scattering in layered medium". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B4775283X.

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Surface integral equation (SIE) method with the kernel of layered medium Green's function (LMGF) is investigated in details from several fundamental aspects. A novel implementation of discrete complex image method (DCIM) is developed to accelerate the evaluation of Sommerfeld integrals and especially improve the far field accuracy of the conventional one. To achieve a broadband simulation of thin layered structure such as microstrip antennas, the mixed-form thin-stratified medium fast-multipole algorithm (MF-TSM-FMA) is developed by applying contour deformation and combining the multipole expansion and plane wave expansion into a single multilevel tree. The low frequency breakdown of the integral operator is further studied and remedied by using the loop-tree decomposition and the augmented electric field integral equation (A-EFIE), both in the context of layered medium integration kernel. All these methods are based on the EFIE for the perfect electric conductor (PEC) and hence can be applied in antenna and circuit applications. To model general dielectric or magnetic objects, the layered medium Green's function based on pilot vector potential approach is generalized for both electric and magnetic current sources. The matrix representation is further derived and the corresponding general SIE is setup. Finally, this SIE is accelerated with the DCIM and applied in quantum optics, such as the calculation of spontaneous emission enhancement of a quantum emitter embedded in a layered structure and in the presence of nano scatterers.
published_or_final_version
Electrical and Electronic Engineering
Doctoral
Doctor of Philosophy

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47

Alias, Azwani B. "Mathematical modelling of nonlinear internal waves in a rotating fluid". Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15861.

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Large amplitude internal solitary waves in the coastal ocean are commonly modelled with the Korteweg-de Vries (KdV) equation or a closely related evolution equation. The characteristic feature of these models is the solitary wave solution, and it is well documented that these provide the basic paradigm for the interpretation of oceanic observations. However, often internal waves in the ocean survive for several inertial periods, and in that case, the KdV equation is supplemented with a linear non-local term representing the effects of background rotation, commonly called the Ostrovsky equation. This equation does not support solitary wave solutions, and instead a solitary-like initial condition collapses due to radiation of inertia-gravity waves, with instead the long-time outcome typically being an unsteady nonlinear wave packet. The KdV equation and the Ostrovsky equation are formulated on the assumption that only a single vertical mode is used. In this thesis we consider the situation when two vertical modes are used, due to a near-resonance between their respective linear long wave phase speeds. This phenomenon can be described by a pair of coupled Ostrovsky equations, which is derived asymptotically from the full set of Euler equations and solved numerically using a pseudo-spectral method. The derivation of a system of coupled Ostrovsky equations is an important extension of coupled KdV equations on the one hand, and a single Ostrovsky equation on the other hand. The analytic structure and dynamical behaviour of the system have been elucidated in two main cases. The first case is when there is no background shear flow, while the second case is when the background state contains current shear, and both cases lead to new solution types with rich dynamical behaviour. We demonstrate that solitary-like initial conditions typically collapse into two unsteady nonlinear wave packets, propagating with distinct speeds corresponding to the extremum value in the group velocities. However, a background shear flow allows for several types of dynamical behaviour, supporting both unsteady and steady nonlinear wave packets, propagating with the speeds which can be predicted from the linear dispersion relation. In addition, in some cases secondary wave packets are formed associated with certain resonances which also can be identified from the linear dispersion relation. Finally, as a by-product of this study it was shown that a background shear flow can lead to the anomalous version of the single Ostrovsky equation, which supports a steady wave packet.

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48

BRIKOWSKI, TOM HARRY. "A QUANTITATIVE ANALYSIS OF HYDROTHERMAL CIRCULATION AROUND MID-OCEAN RIDGE MAGMA CHAMBERS". Diss., The University of Arizona, 1987. http://hdl.handle.net/10150/184128.

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Hydrothermal activity is one of the dominant processes affecting the chemical and thermal evolution of oceanic crust at the mid-ocean ridge (MOR), but little is known about the sub-surface portions of ridge hydrothermal systems. These systems can be investigated using numerical modeling techniques, and models of two-dimensional cross-sections are utilized in this study to investigate the behavior of MOR hydrothermal systems. The influence of magma chamber geometry is explored by modeling two extremes of proposed geometry. Seismological evidence supports a dike-like 2 km half-width chamber, and models of this chamber indicate that: (1) complete crystallization of the magma requires 30,000 years, (2) hydrothermal upflow and hot springs are concentrated in a narrow band within 1.5 km of the ridge axis for the lifetime of the system, (3) a large hydrothermal cell forms and remains centered above the distal tip of the intrusion for the lifetime of the system, (4) effective hydrothermal activity ends by 70,000 yrs. Petrological evidence supports a wide sill-like chamber 15 km in half-width, and models of this chamber indicate that: (1) complete crystallization of the magma requires 100,000 yrs, (2) hydrothermal vents are present at the ridge axis, but most of the vents are located 5-10 km away from the axis, (3) a large hydrothermal cell develops at the distal tip of the magma chamber, while a series of small but vigorous cells develops directly above the intrusion, both features migrate toward the ridge axis as the magma solidifies, (4) effective hydrothermal activity ends by 170,000 yrs. Substantially different hydrothermal systems develop around these two chamber geometries and comparison of the models shows this is because different patterns of near-critical P-T conditions developed around them. The fundamental influence on the nature and pattern of hydrothermal circulation at MOR is the distribution of near-critical conditions.

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49

Nugroho, Widijanto Satyo. "Waves generated by a load moving on an ice sheet over water". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ32720.pdf.

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50

Caccavano, Adam. "Optics and Spectroscopy in Massive Electrodynamic Theory". PDXScholar, 2013. https://pdxscholar.library.pdx.edu/open_access_etds/1485.

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The kinematics and dynamics for plane wave optics are derived for a massive electrodynamic field by utilizing Proca's theory. Atomic spectroscopy is also examined, with the focus on the 21 cm radiation due to the hyperfine structure of hydrogen. The modifications to Snell's Law, the Fresnel formulas, and the 21 cm radiation are shown to reduce to the familiar expressions in the limit of zero photon mass.

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Tesi sul tema "Ocean waves – – Mathematical models"

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