Tesis sobre el tema "Water waves Mathematical models"
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1
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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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
3
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.
4
繆泉明 y 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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Liu, Xia y 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
6
Lai, Wing-chiu Derek y 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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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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Poon, Chun-Kin y 潘俊健. "Numerical simulation of coupled long wave-short wave system with a mismatch in group velocities". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B35381334.
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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.
10
Huang, Lingyan y 黃凌燕. "Mass transport due to surface waves in a water-mud system". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B35380457.
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Amenta, Pablo Marco. "On finite difference solutions for the ocean wave spectrum in regions of non-uniform water depth". Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/44698.
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This investigation is concerned with the determination of the sea state in terms of wave spectra. The phenomenum was calculated for two different bathymetries.
The purpose is to develop a finite difference method with an upwind differencing scheme to g solve several formulations of the wave action conservation equation. The computations were done in the wave number space and the frequency direction space. For the case of a beach with constant slope the results were compared with the analytical solution. For the case of an elliptical submerged shoal, they were compared with experimental data.
The results of the computer code showed a fairly good qualitative agreement with the actual
values for a smooth distribution of input energy.
Master of Science
12
Yang, Jie. "Spatial Coherence in a Shallow Water Waveguide". Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/14624.
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In shallow water environments, sound propagation experiences multiple interactions with the surface/bottom interfaces, with hydrodynamic disturbances such as internal waves, and with tides and fronts. It is thus very difficult to make satisfactory predictions of sound propagation in shallow water. Given that many of the ocean characteristics can be modeled as stochastic processes, the statistical measure, spatial coherence, is consequently an important quantity. Spatial coherence provides valuable information for array performance predictions. However, for the case of long-range, low frequency propagation, studies of spatial coherence influenced by various environmental parameters are limited insofar as having the appropriate environmental data with which to model and interpret the results.
The comprehensive Asian Seas International Experiment 2001 (ASIAEX01) examined acoustic propagation and scattering in shallow water. Environmental oceanographic data were taken simultaneously with the acoustic data. ASIAEX01 provided a unique data set which enabled separate study of the characteristics of the oceanographic features and their influence on long range sound propagation. In this thesis, the environmental descriptors considered include sediment sound speed and attenuation, background internal waves, episodic non-linear internal waves, and air-sea interface conditions. Using this environmental data, the acoustic data are analyzed to show the characteristics of spatial coherence in a shallow water waveguide. It is shown that spatial coherence can be used as an inversion parameter to extract geoacoustic information for the seabed. Environmental phenomena including internal waves and wind-generated surface waves are also studied. The spatial and temporal variations in the sound field induced by them are presented. In addition, a tank experiment is presented which simulates propagation in a shallow water waveguide over a short range. Based on the data model comparison results, the model proposed here is effective in addressing the major environmental effects on sound propagation in shallow water.
13
Zhang, Yi. "Numerical modeling of shock wave propagation and contaminant fate and transport in open channel networks". Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/20159.
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Ivanova, Kseniya. "Mathematical model of multi-dimensional shear shallow water flows : problems and solutions". Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0642/document.
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Cette thèse porte sur la résolution numérique du modèle multi-dimensionnel d'écoulement cisaillé en eau peu profonde. Dans le cas d'un mouvement unidimensionnel, ces équations coïncident avec les équations de la dynamique de gaz pour un choix particulier de l'équation d'état. Dans le cas multi-dimensionnel, le système est complètement différent du modèle de la dynamique de gaz. Il s'agit d'un système EDP hyperbolique 2D non-conservatif qui rappelle un modèle de turbulence barotrope. Le modèle comporte trois types d'ondes correspondant à la propagation des ondes de surface, des ondes de cisaillement et à celle de la discontinuité de contact. Nous présentons dans le cas 2D un schéma numérique basé sur une nouvelle approche de ``splitting" pour les systèmes d'équations non-conservatives. Chaque sous-système ne contient qu'une seule famille d'ondes: ondes de surface ou ondes de cisaillement, et discontinuité de contact. La précision d'une telle approche est testée sur des solutions exactes 2D décrivant l'écoulement lorsque la vitesse est linéaire par rapport aux variables spatiales, ainsi que sur des solutions décrivant des trains de rouleaux 1D. Finalement, nous modélisons un ressaut hydraulique circulaire formé dans un écoulement convergent radial d'eau. Les résultats numériques obtenus sont clairement similaires à ceux obtenus expérimentalement: oscillations du ressaut et son rotation avec formation du point singulier. L'ensemble des validations proposées dans ce manuscrit démontre les aptitudes du modèle et de la méthode numérique pour la résolution des problèmes complexes d'écoulements cisaillés en eau peu profonde multidimensionnelsThis thesis is devoted to the numerical modelling of multi-dimensional shear shallow water flows. In 1D case, the corresponding equations coincide with the equations describing non--isentropic gas flows with a special equation of state. However, in the multi-D case, the system differs significantly from the gas dynamics model. This is a 2D hyperbolic non-conservative system of equations which is reminiscent of a generic Reynolds averaged model of barotropic turbulent flows. The model has three families of characteristics corresponding to the propagation of surface waves, shear waves and average flow (contact characteristics). First, we show the ability of the one-dimensional conservative shear shallow water model to predict the formation of roll-waves from unstable initial data. The stability of roll waves is also studied.Second, we present in 2D case a new numerical scheme based on a splitting approach for non-conservative systems of equations. Each split subsystem contains only one family of waves (either surface or shear waves) and contact characteristics. The accuracy of such an approach is tested on exact 2D solutions describing the flow where the velocity is linear with respect to the space variables, and on the solutions describing 1D roll waves. Finally, we model a circular hydraulic jump formed in a convergent radial flow of water. Obtained numerical results are qualitatively similar to those observed experimentally: oscillation of the hydraulic jump and its rotation with formation of a singular point. These validations demonstrate the capability of the model and numerical method to solve challenging multi--dimensional problems of shear shallow water flows
15
Connell, R. J. "Unstable equilibrium : modelling waves and turbulence in water flow". Diss., Lincoln University, 2008. http://hdl.handle.net/10182/592.
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This thesis develops a one-dimensional version of a new data driven model of turbulence that uses the KL expansion to provide a spectral solution of the turbulent flow field based on analysis of Particle Image Velocimetry (PIV) turbulent data. The analysis derives a 2nd order random field over the whole flow domain that gives better turbulence properties in areas of non-uniform flow and where flow separates than the present models that are based on the Navier-Stokes Equations. These latter models need assumptions to decrease the number of calculations to enable them to run on present day computers or super-computers. These assumptions reduce the accuracy of these models. The improved flow field is gained at the expense of the model not being generic. Therefore the new data driven model can only be used for the flow situation of the data as the analysis shows that the kernel of the turbulent flow field of undular hydraulic jump could not be related to the surface waves, a key feature of the jump. The kernel developed has two parts, called the outer and inner parts. A comparison shows that the ratio of outer kernel to inner kernel primarily reflects the ratio of turbulent production to turbulent dissipation. The outer part, with a larger correlation length, reflects the larger structures of the flow that contain most of the turbulent energy production. The inner part reflects the smaller structures that contain most turbulent energy dissipation. The new data driven model can use a kernel with changing variance and/or regression coefficient over the domain, necessitating the use of both numerical and analytical methods. The model allows the use of a two-part regression coefficient kernel, the solution being the addition of the result from each part of the kernel. This research highlighted the need to assess the size of the structures calculated by the models based on the Navier-Stokes equations to validate these models. At present most studies use mean velocities and the turbulent fluctuations to validate a models performance. As the new data driven model gives better turbulence properties, it could be used in complicated flow situations, such as a rock groyne to give better assessment of the forces and pressures in the water flow resulting from turbulence fluctuations for the design of such structures. Further development to make the model usable includes; solving the numerical problem associated with the double kernel, reducing the number of modes required, obtaining a solution for the kernel of two-dimensional and three-dimensional flows, including the change in correlation length with time as presently the model gives instant realisations of the flow field and finally including third and fourth order statistics to improve the data driven model velocity field from having Gaussian distribution properties. As the third and fourth order statistics are Reynolds Number dependent this will enable the model to be applied to PIV data from physical scale models. In summary, this new data driven model is complementary to models based on the Navier-Stokes equations by providing better results in complicated design situations. Further research to develop the new model is viewed as an important step forward in the analysis of river control structures such as rock groynes that are prevalent on New Zealand Rivers protecting large cities.
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Morris-Thomas, Michael. "An investigation into wave run-up on vertical surface piercing cylinders in monochromatic waves". University of Western Australia. School of Oil and Gas Engineering, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0010.
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[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] Wave run-up is the vertical uprush of water when an incident wave impinges on a free- surface penetrating body. For large volume offshore structures the wave run-up on the weather side of the supporting columns is particularly important for air-gap design and ultimately the avoidance of pressure impulse loads on the underside of the deck structure. This investigation focuses on the limitations of conventional wave diffraction theory, where the free-surface boundary condition is treated by a Stokes expansion, in predicting the harmonic components of the wave run-up, and the presentation of a simplified procedure for the prediction of wave run-up. The wave run-up is studied on fixed vertical cylinders in plane progressive waves. These progressive waves are of a form suitable for description by Stokes' wave theory whereby the typical energy content of a wave train consists of one fundamental harmonic and corresponding phase locked Fourier components. The choice of monochromatic waves is indicative of ocean environments for large volume structures in the diffraction regime where the assumption of potential flow theory is applicable, or more formally A/a < Ο(1) (A and a being the wave amplitude and cylinder radius respectively). One of the unique aspects of this work is the investigation of column geometry effects - in terms of square cylinders with rounded edges - on the wave run-up. The rounded edges of each cylinder are described by the dimensionless parameter rc/a which denotes the ratio of edge corner radius to half-width of a typical column with longitudinal axis perpendicular to the quiescent free-surface. An experimental campaign was undertaken where the wave run-up on a fixed column in plane progressive waves was measured with wire probes located close to the cylinder. Based on an appropriate dimensional analysis, the wave environment was represented by a parametric variation of the scattering parameter ka and wave steepness kA (where k denotes the wave number). The effect of column geometry was investigated by varying the edge corner radius ratio within the domain 0 <=rc/a <= 1, where the upper and lower bounds correspond to a circular and square shaped cylinder respectively. The water depth is assumed infinite so that the wave run-up caused purely by wave-structure interaction is examined without the additional influence of a non-decaying horizontal fluid velocity and finite depth effects on wave dispersion. The zero-, first-, second- and third-harmonics of the wave run-up are examined to determine the importance of each with regard to local wave diffraction and incident wave non-linearities. The modulus and phase of these harmonics are compared to corresponding theoretical predictions from conventional diffraction theory to second-order in wave steepness. As a result, a basis is formed for the applicability of a Stokes expansion to the free-surface boundary condition of the diffraction problem, and its limitations in terms of local wave scattering and incident wave non-linearities. An analytical approach is pursued and solved in the long wavelength regime for the interaction of a plane progressive wave with a circular cylinder in an ideal fluid. The classical Stokesian assumption of infinitesimal wave amplitude is invoked to treat the free-surface boundary condition along with an unconventional requirement that the cylinder width is assumed much smaller than the incident wavelength. This additional assumption is justified because critical wavelengths for wave run-up on a fixed cylinder are typically much larger in magnitude than the cylinder's width. In the solution, two coupled perturbation schemes, incorporating a classical Stokes expansion and cylinder slenderness expansion, are invoked and the boundary value problem solved to third-order. The formulation of the diffraction problem in this manner allows for third-harmonic diffraction effects and higher-order effects operating at the first-harmonic to be found. In general, the complete wave run-up is not well accounted for by a second-order Stokes expansion of the free-surface boundary condition and wave elevation. This is however, dependent upon the coupling of ka and kA. In particular, whilst the modulus and phase of the second-harmonic are moderately predicted, the mean set-up is not well predicted by a second-order Stokes expansion scheme. This is thought to be caused by higher than second-order non-linear effects since experimental evidence has revealed higher-order diffraction effects operating at the first-harmonic in waves of moderate to large steepness when k < < 1. These higher-order effects, operating at the first-harmonic, can be partially accounted for by the proposed long wavelength formulation. For small ka and large kA, subsequent comparisons with measured results do indeed provide a better agreement than the classical linear diffraction solution of Havelock (1940). To account for the complete wave run-up, a unique approach has been adopted where a correction is applied to a first-harmonic analytical solution. The remaining non-linear portion is accounted for by two methods. The first method is based on regression analysis in terms of ka and kA and provides an additive correction to the first-harmonic solution. The second method involves an amplification correction of the first-harmonic. This utilises Bernoulli's equation applied at the mean free-surface position where the constant of proportionality is empirically determined and is inversely proportional to ka. The experimental and numerical results suggest that the wave run-up increases as rc/a--› 0, however this is most significant for short waves and long waves of large steepness. Of the harmonic components, experimental evidence suggests that the effect of a variation in rc/a on the wave run-up is particularly significant for the first-harmonic only. Furthermore, the corner radius effect on the first-harmonic wave run-up is well predicted by numerical calculations using the boundary element method. Given this, the proposed simplified wave run-up model includes an additional geometry correction which accounts for rc/a to first-order in local wave diffraction. From a practical view point, it is the simplified model that is most useful for platform designers to predict the wave run-up on a surface piercing column. It is computationally inexpensive and the comparison of this model with measured results has proved more promising than previously proposed schemes.
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Devkota, Bishnu Hari. "A new Lagrangian model for the dynamics and transport of river and shallow water flows". University of Western Australia. Centre for Water Research, 2005. http://theses.library.uwa.edu.au/adt-WU2005.0108.
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This study presents a new Lagrangian model for predicting dynamics and transport in rivers and shallow water flows. A hydrostatic model is developed for the prediction of rivers and floodplain flow and lateral interactions between them. The model is extended to the Boussinesq weakly non-linear, non-hydrostatic model for the simulation of solitary waves and undular bores. A model for advection-diffusion transport of tracers in open channel flow is also presented. The simulation results are compared against an analytical solution and published laboratory data, field data and theoretical results. It is demonstrated that the Lagrangian moving grid eliminates numerical diffusion and oscillations; the model is dynamically adaptive, providing higher resolution under the wave by compressing the parcels (grid). It also allows flow over dry beds and moving boundaries to be handled efficiently. The hydrostatic model results have shown that the model accurately simulates wave propagation and non-linear steepening until wave breaking. The model is successfully applied to simulate flow and lateral interactions in a compound channel and flood wave movement in a natural river. The non-hydrostatic model has successfully reproduced the general features of solitary waves such as the balance between non-linearity and wave dispersion and non-linear interactions of two solitary waves by phase-shift. Also, the model successfully reproduced undular bores (high frequency short waves) from a long wave and the predicted maximum height of the leading wave agreed very well with the published results. It is shown that the simple second order accurate Lagrangian scheme efficiently simulates dispersive waves without any numerical diffusion. Lagrangian modeling of advection-diffusion transport of Gaussian tracer distributions, top hat tracer distributions and steep fronts (step function) in steady, uniform flow has provided exact results and has shown that the scheme allows the use of a large time step without any numerical diffusion and oscillations, including for the advection of steep fronts. The scheme can handle large Courant numbers (results are presented for Cr = 0 to 20) and the entire range of grid Peclet numbers from zero to infinity. The model is successfully applied to tracer transport due to flow induced by simple waves, solitary waves and undular bores
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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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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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Karjanto, Natanael. "Mathematical aspects of extreme water waves". Enschede : University of Twente [Host], 2006. http://doc.utwente.nl/57607.
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Shipway, Ben. "Trapped modes in linear water waves and acoustics". Thesis, University of Bristol, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274610.
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Herterich, James George. "Mathematical models in water filtration". Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:73036408-fbc5-497a-a99f-b8da3dbca0a5.
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Membrane filtration is a simple concept for water purification: water containing particulate contaminants is forced through a semi-permeable membrane that rejects the particulates leaving clean water to flow out. Nevertheless, there are many complex features of membrane filtration, the most important of which is the accumulation of the particulates at the membrane surface. This leads ultimately to fouling of the membrane and a reduction in the efficiency of the process. Concentration polarization is the precursor of fouling, that is, a high concentration of contaminants develops in front of the membrane without the contaminants attaching to each other or the membrane surface. However, several types of acute membrane fouling develop from the layer formed in concentration polarization, including internal fouling, pore blocking and caking. Addressing these and related problems has been at the forefront of membrane research since the process' inception. In this thesis we develop mathematical models of aspects of crossflow and directflow filtration operating at constant flux. We begin by addressing questions related to the initial stages of concentration polarization in crossflow systems. In particular, we study the influence of particulates on the viscosity of the filtrate, and show how the filtration efficiency may be improved by tailoring the wall permeability to reduce the effects of osmosis. We then address the development of membrane fouling and caking in directflow systems: the transmembrane pressure difference, the possibility of elastic deformations during filtration, and the influence of these on the development of fouling and caking are all considered. We show that even small elastic effects can worsen fouling and suggest how the process can be operated to avoid this. We then discuss further opportunities for mathematical modelling in this area.
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Button, Peter. "Models for ocean waves". Master's thesis, University of Cape Town, 1988. http://hdl.handle.net/11427/14299.
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Includes bibliography.Ocean waves represent an important design factor in many coastal engineering applications. Although extreme wave height is usually considered the single most important of these factors there are other important aspects that require consideration. These include the probability distribution of wave heights, the seasonal variation and the persistence, or duration, of calm and storm periods. If one is primarily interested in extreme wave height then it is possible to restrict one's attention to events which are sufficiently separated in time to be effectively independently (and possibly even identically) distributed. However the independence assumption is not tenable for the description of many other aspects of wave height behaviour, such as the persistence of calm periods. For this one has to take account of the serial correlation structure of observed wave heights, the seasonal behaviour of the important statistics, such as mean and standard deviation, and in fact the entire seasonal probability distribution of wave heights. In other words the observations have to be regarded as a time series.
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Gidel, Floriane Marie Pauline. "Variational water-wave models and pyramidal freak waves". Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/21730/.
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A little-known fact is that, every week, two ships weighing over 100 tonnes sink in oceans, sometimes with tragic consequences. This alarming observation suggests that maritime structures may be struck by stronger waves than those they were designed to withstand. These are the legendary rogue (or freak) waves, i.e., suddenly appearing huge waves that have traumatised mariners for centuries and currently remain an unavoidable threat to ships, and to their crews and passengers. Thus motivated, an EU-funded collaboration between the Department of Applied Mathematics (Leeds University) and the Maritime Research Institute Netherlands (MARIN) supported this project, in which the ultimate goal, of importance to the international maritime sector, is to develop reliable damage-prediction tools, leading to beneficial impact in terms of both safety and costs. To understand the behaviour of rogue waves, cost-effective water-wave models are derived in both deep and shallow water. Novel mathematical and numerical strategies are introduced to capture the dynamic air-water interface and to ensure conservation of important properties. Specifically, advanced variational Galerkin finite-element methods are used to provide stable simulations of potential-flow water waves in a basin with wavemakers and seabed topography, which allows reliable simulations of rogue waves in a target area. For optimised computational speed, wave absorption is considered with a beach on which waves break and dissipate energy. Robust integrators are therefore introduced to couple the potential-flow model to shallow-water wave dynamics at the beach. Experimental validation of the numerical tank is conducted at Delft University of Technology to ensure accuracy of the simulations from the wavemaker to the beach. The numerical tank is designed for subsequent use by MARIN to investigate the damage caused by rogue waves on structures in order to update maritime design practice and to ensure safety of ships, therefore leading to a competitive commercial advantage across Europe.
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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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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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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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朱書堂 y 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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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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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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Burnham, Christian James. "Structural and dynamical properties of mathematical water models". Thesis, University of Salford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299208.
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Zhang, Shuangxi y 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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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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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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Varholm, Kristoffer. "Water waves with compactly supported vorticity : A functional-analytic approach to bifurcation theory and the mathematical theory of traveling water waves". Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-25748.
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We study the mathematical theory of water waves. Local bifurcation theory is also discussed, including the Crandall-Rabinowitz theorem; an abstract theorem used to establish the presence of bifurcation points in the zero set of maps on Banach spaces. A functional-analytic approach is used to prove the existence of a family of localized traveling waves with one or more point vortices, by bifurcating from a trivial solution. This is done in the setting of the incompressible Euler equations with gravity and surface tension, on finite depth. Our result is an extension of a recent result by Shatah, Walsh and Zeng, where existence was shown for a single point vortex on infinite depth. The properties of the resulting waves are also examined: We find that the properties depend significantly on the position of the point vortices in the water column.
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盧慧 y 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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El, Didy Sherif Mohamed Ahmed 1951. "Two-dimensional finite element programs for water flow and water quality in multi-aquifer systems". Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/191110.
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Multiple aquifer systems similar to those that exist at coal gasification sites are complicated groundwater situations. In these types of systems, the aquifers are separated by aquitards through which interaction between aquifers can occur. The movement of the products of combustion into the coal seam and adjacent aquifers is a serious problem of interest. This dissertation presents two-dimensional finite element models for water flow and water quality in multiple aquifer systems. These models can be applied for general problems as well as the problems associated with the burned cavities in coal gasification sites. The Galerkin weightedresidual method is used in both models. Eight-noded isoparametric elements are used. Spatial numerical integration is performed using Gaussian quadrature. A weighted finite difference scheme is used, in both of them, for time integration. The two models are written in FORTRAN V for the CDC CYBER 175. They are applicable to one- or two-dimensional problems involving steady-state or transient flow. Each aquifer can have different initial conditions and boundary conditions. Boundary conditions, pumping rates, and the recharge can be specified as a function of time. The output of the flow program-nodal heads and velocity components is used as an input to the quality program. The numerical models were validated for simple problems that have available analytical solutions.
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Barrett, Gary Edward. "Infiltration in water repellent soil". Thesis, University of British Columbia, 1988. http://hdl.handle.net/2429/28618.
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Observations made at Goat Meadows - a small sub-alpine basin located near Pemberton, British Columbia -demonstrated that a layer which is either water repellent or has only a limited affinity for water is present at most vegetated sites. The layer is typically a few centimetres in thickness, and is usually located at or near the top of the profile: it was present only in the zone of accumulation of organic matter. The spatial distribution of the layer did not appear to be related to the distribution of any particular species of plant. Sampling of sub-alpine sites in the Cascade, Selkirk, and Purcell Mountains indicated that such layers are common in the alpine - sub-alpine ecotone of southern British Columbia.
The relationship between ponding depth and infiltration rate was explored through experiments conducted on samples collected near Ash Lake, in Goat Meadows. These samples were chosen for analysis because the repellent layer was in excess of thirty centimetres thick at this site. Infiltration rates remained below 2x10⁻⁹ m/s for all samples, even given ponding depths of up to forty centimetres. Breakthrough of liquid water was not observed, even after one month, which implies that most of the infiltration occurred as vapour transfer.
In order to observe the movement of liquid water through water repellent media, a plexiglas cell was constructed. A synthetic water repellent sand with uniform surface properties was used as the medium. It was found that up to some critical depth, there was no entry of water into the medium. As the ponding depth was increased in steps, the front would advance in steps: it remained stationary between these step-increases in ponding depth. As the front advanced, protuberances or "fingers" began to develop. At some critical ponding depth, a finger would grow without bound. These observations pose a challenge to existing models of infiltration, since it appears that heterogeneity at the scale of individual pores must be invoked to explain them, but it is usually assumed that the properties of a porous medium are continuous at this scale.
The thermodynamics of filling and emptying of pores is considered with emphasis on the effects of pore shape and of variations in the physicochemical properties at the scale of the pore. This thermodynamic analysis provides the conceptual basis for development of a model of infiltration in which pore-scale heterogeneity is preserved. Although it was not developed as such, the model follows the approach of cellular automata, in which local relations between pores or "cells" govern the behaviour of the system. The model replicated the observations of infiltration into synthetic water repellent porous media well: both the halting advance of the front as the ponding depth was increased and the development of fingers were simulated. The fact that such complex behaviour was predicted using only a simple set of physically based rules confirms the power of the approach.Arts, Faculty of
Geography, Department of
Graduate
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Li, Ping y 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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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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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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Ye, Feng. "Derivation of a two-layer non-hydrostatic shallow water model". Thesis, Water Resources Research Center, University of Hawaii at Manoa, 1995. http://hdl.handle.net/10125/21919.
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A theoretical non-hydrostatic model is developed to describe the dynamics of a two-layer shallow water system in the presence of viscous and Coriolis effects. The Navier-Stokes equations are integrated over the water depth in each layer to obtain the layer-mean equations. To close the resulting equation set, perturbation expansions of the vertical momentum equation are used and the dynamic pressures are solved in terms of wave elevations and horizontal velocities. A preliminary analysis is also carried out and a result for the quasigeostrophic problems is given based on an previous study. Our final model is of the Bousinesq class which is nonlinear and dispersive, and includes the effects of surface wind stress, bottom friction, eddy diffusion and earth rotation. It is shown that our new model can be readily reduced to previous inviscid non-hydrostatic models. Our model can be used in numerical simulations to study real ocean problems such as hurricane generated waves, tidal induced current, and interactions among surface waves, internal waves and variable topographies.Thesis (M. S.)--University of Hawaii at Manoa, 1995.
Includes bibliographical references (leaves 55-59).
UHM: Has both book and microform.
U.S. Geological Survey; project no. 06; grant agreement no. 14-08-0001-G2015
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Kim, Jeong Hoon. "Stochastic turning point problem". Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40038.
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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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Barnes, Timothy. "The generation of low-frequency water waves on beaches". Thesis, University of Bristol, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319128.
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Thorell, Anton. "Surf Simulation with the Shallow Water Equations : Coupling of a surfer model to a shallow water wave". Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297697.
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This thesis covers the subject of deriving and solving the system of partial differential equations known as the Shallow Water Equations (SWE), and coupling the solutions of this equation system to a simplified model of a surfer - or any floating object, with the right choice of parameters. The SWE are generally used to analyze fluid movement on shallow areas, such as ocean waves nearing the shore, and are derived from the Navier-Stokes equations and restricted to conservation of mass and momentum in a fluid. In this project the solution to these equations was made to yield a propagating wave profile. From the solution, the steepening behaviour and the slow propagation speed of shallow water waves are explained - properties that are necessary for wave surfing. The SWE was solved with the first order accurate finite volume scheme known as the Lax Friedrichs Method (LxF), and a surfable wave is created with a suitable set of initial- and boundary conditions parameter values. LxF is also derived from the discretization of the conservation form of the SWE. The solver can also handle a non-horizontal seabed - bathymetry, but does not take into consideration friction from the seabed. A "surfer" was created as a point mass acted on by three forces: hydrodynamic drag, gravity and buoyancy. The "surfer" is made to move realistically by simulating the effect of these forces and updating position and velocity of the surfer accordingly. The surfer is made to move along with the wave.
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Putnam, Douglas Alan. "Forecasting for local water management". PDXScholar, 1985. https://pdxscholar.library.pdx.edu/open_access_etds/3540.
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Forecast models are investigated and developed for use in local water management to aid in determining short term water requirements and availability. The forecast models include precipitation occurrence and depth using a Markov chain model, temperature and solar radiation with a multivariate autoregressive model, and streamflow with autoregressive-moving average models. The precipitation, temperature, and solar radiation forecasts are used with a soil moisture model to determine water demands. A state space approach to the Muskingum-Cunge streamflow routing technique is developed. The forecast water demands and streamflow forecasts are used as inputs to this routing model. Forecast model errors and propagation of these errors from one model into the next are investigated.
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Vionnet, Leticia Beatriz, Thomas III Maddock y David C. Goodrich. "Investigations of stream-aquifer interactions using a coupled surface-water and ground-water flow model". Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1997. http://hdl.handle.net/10150/615700.
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A finite element numerical model is developed for the modeling of coupled
surface-water flow and ground-water flow. The mathematical treatment of subsurface
flows follows the confined aquifer theory or the classical Dupuit approximation for
unconfined aquifers whereas surface-water flows are treated with the kinematic wave
approximation for open channel flow. A detailed discussion of the standard approaches to
represent the coupling term is provided. In this work, a mathematical expression similar
to Ohm's law is used to simulate the interacting term between the two major hydrological
components. Contrary to the standard approach, the coupling term is incorporated
through a boundary flux integral that arises naturally in the weak form of the governing
equations rather than through a source term. It is found that in some cases, a branch cut
needs to be introduced along the internal boundary representing the stream in order to
define a simply connected domain, which is an essential requirement in the derivation of
the weak form of the ground-water flow equation. The fast time scale characteristic of
surface-water flows and the slow time scale characteristic of ground-water flows are
clearly established, leading to the definition of three dimensionless parameters, namely, a
Peclet number that inherits the disparity between both time scales, a flow number that
relates the pumping rate and the streamflow, and a Biot number that relates the
conductance at the river-aquifer interface to the aquifer conductance.
The model, implemented in the Bill Williams River Basin, reproduces the observed
streamflow patterns and the ground-water flow patterns. Fairly good results are obtained
using multiple time steps in the simulation process.
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Meeuwig, Jessica Jane. "All water is wet : predicting eutrophication in lakes and estuaries". Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=35918.
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Coastal eutrophication, defined as an increase in algal biomass (as chlorophyll (Chl)) is of increasing international concern. Although coastal eutrophication will likely increase as coastal populations grow, few models exist to support its management. Lake eutrophication has also long been recognized as an important environmental concern. However, effective lake eutrophication management exists, supported by regression and mass-balance models. Traditionally, these "Vollenweider" models link land-use to Chl via total phosphorus (TP), the nutrient considered to be limiting Chl. However, based on a data set of 63 lakes, Chl was more accurately predicted by models based on land-use than by those based on TP. This result provided the rationale to build Chl:land-use models for estuaries where the Chl:nutrient relations are unclear. Chl:land-use models were developed for 15 estuaries in PEI, 19 estuaries in Finland and 26 US estuaries. Land-use models predicted Chl more accurately than TP in the US estuaries and in some of the Finnish estuaries. In the Finnish estuaries, Chl was best predicted by a land-use model in estuaries dominated by nonpoint source loading whereas Chl was most accurately predicted by the Vollenweider approach in estuaries dominated by point-source loading. In the PEI estuaries, the accuracy of the land-use model was comparable to the accuracy of the TP model. The PEI estuaries had much lower yields of Chl per unit nutrient than lakes suggesting differences among systems. This Chl deficit (expected-observed Chl) was accounted for by herbivory and turbidity, neither of which factors are exclusive to estuaries. The comparison of Chl response to nutrients and land-use across lakes and estuaries demonstrated no systematic differences as a function of tidal energy, openness or salinity. The regression models based on the combined data accurately predicted Chl as a function of TP and percentage of the catchment forested and mean depth. These results sug
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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.
Texto completoResumen
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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Scholey, Kenneth Erwin. "Heat tranfser and crack formation in water-cooled zinc fuming furnace jackets". Thesis, University of British Columbia, 1991. http://hdl.handle.net/2429/30078.
Texto completoResumen
In the zinc slag fuming process, zinc is extracted from lead blast furnace slag by reduction with a coal/air mixture injected into the slag through submerged tuyeres. The furnace is constructed of water-cooled jackets to contain the molten bath and freeze a protective slag layer. The slag layer greatly reduces vessel wear caused by the corrosive and violently agitated bath. However, the jackets are known to develop cracks in the working face panel that initiate on the slag face and propagate towards the water cavity. If the cracks reach the water cavity explosions may result should the molten slag come into contact with the water.
In this study an analysis of heat transfer in the jacket has been carried out using in-plant measurements and mathematical modelling. The working face of a water jacket was instrumented with thermocouples and positioned in a fuming furnace at the Trail smelter of Cominco Ltd. Measurements revealed the presence of large thermal transients or temperature "spikes" in the panel approximately 20 cm above the tuyeres. The transients were observed during charging and tapping of the furnace and are likely associated with slag fall-off due to surface wave action and gas injection effects when the bath level is low. Temperatures at the mid-thickness were seen to rise by as much as 180 °C above the steady-state level. Under these conditions large compressive stresses are produced in the panel that are sufficient to cause yielding. Over time, the transients lead to low-cycle fatigue of the working face panel with crack formation initiating at pre-existing surface flaws.
A mathematical modelling analysis of the transient freezing phenomena has been carried out using the finite element method. The results indicate that the temperature spikes are associated with the sudden removal of patches of slag and molten slag
coming into direct contact with the jacket. The temperature spikes are large enough to generate compressive stresses that cause yielding of the material in the exposed area. In order to reduce the damage caused by the removal of the slag shell an increased number of anchoring studs should be used in critical areas and a higher water circulation velocity should be employed to increase the size of the frozen slag layer and its strength.Applied Science, Faculty of
Materials Engineering, Department of
Graduate
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Chen, Yongpin y 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.
Texto completoResumen
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