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1
King, Gregory B. (Gregory Blaine). "Explicit Multidimensional Solitary Waves". Thesis, University of North Texas, 1990. https://digital.library.unt.edu/ark:/67531/metadc504381/.
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In this paper we construct explicit examples of solutions to certain nonlinear wave equations. These semilinear equations are the simplest equations known to possess localized solitary waves in more that one spatial dimension. We construct explicit localized standing wave solutions, which generate multidimensional localized traveling solitary waves under the action of velocity boosts. We study the case of two spatial dimensions and a piecewise-linear nonlinearity. We obtain a large subset of the infinite family of standing waves, and we exhibit several interesting features of the family. Our solutions include solitary waves that carry nonzero angular momenta in their rest frames. The spatial profiles of these solutions also furnish examples of symmetry breaking for nonlinear elliptic equations.
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Chen, Hongqiu. "Solitary waves and other long-wave phenomena /". Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.
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Orszaghova, Jana. "Solitary waves and wave groups at the shore". Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:5b168bdc-4956-4152-a303-b23a6067bf42.
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A significant proportion of the world's population and physical assets are located in low lying coastal zones. Accurate prediction of wave induced run-up and overtopping of sea defences are important in defining the extent and severity of wave action, and in assessing risk to people and property from severe storms and tsunamis. This thesis describes a one-dimensional numerical model based on the Boussinesq equations of Madsen and Sorensen (1992) and the non-linear shallow water equations. The model is suitable for simulating propagation of weakly non-linear and weakly dispersive waves from intermediate to zero depth, such that any inundation and/or overtopping caused by the incoming waves is also calculated as part of the simulation. Wave breaking is approximated by locally switching to the non-linear shallow water equations, which can model broken waves as bores. A piston paddle wavemaker is incorporated into the model for complete reproduction of laboratory experiments. A domain mapping technique is used in the vicinity of the paddle to transform a time-varying domain into a fixed domain, so that the governing equations can be more readily solved. First, various aspects of the numerical model are verified against known analytical and newly derived semi-analytical solutions. The complete model is then validated with laboratory measurements of run-up and overtopping involving solitary waves. NewWave focused wave groups, which give the expected shape of extreme wave events in a linear random sea, are used for further validation. Simulations of experiments of wave group run-up on a plane beach yield very good agreement with the measured run-up distances and free surface time series. Wave-by-wave overtopping induced by focused wave groups is also successfully simulated with the model, with satisfactory agreement between the experimental and the predicted overtopping volumes. Repeated simulations, now driven by second order paddle displacement signals, give insight into second order error waves spuriously generated by using paddle signals derived from linear theory. Separation of harmonics reveals that the long error wave is significantly affecting the wave group shape and leading to enhanced runu-up distances and overtopping volumes. An extensive parameter study is carried out using the numerical model investigating the influence on wave group run-up of linear wave amplitude at focus, linear focus location, and wave group phase at focus. For a given amplitude, both the phase and the focus location significantly affect the wave group run-up. It is also found that the peak optimised run-up increases with the wave amplitude, but wave breaking becomes an inhibiting factor for larger waves. This methodology is proposed for extreme storm wave induced run-up analysis.
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Kim, Boguk Ph D. Massachusetts Institute of Technology. "Three-dimensional solitary waves in dispersive wave systems". Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/34543.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (p. 119-122).
Fully localized three-dimensional solitary waves, commonly referred to as 'lumps', have received far less attention than two-dimensional solitary waves in dispersive wave systems. Prior studies have focused in the long-wave limit, where lumps exist if the long-wave speed is a minimum of the phase speed and are described by the Kadomtsev-Petviashvili (KP) equation. In the water-wave problem, in particular, lumps of the KP type are possible only in the strong-surface-tension regime (Bond number, B > 1/3), a condition that limits the water depth to a few mm. In the present thesis, a new class of lumps is found that is possible under less restrictive physical conditions. Rather than long waves, these lumps bifurcate from infinitesimal sinusoidal waves of finite wavenumber at an extremum of the phase speed. As the group and phase velocities are equal there, small-amplitude lumps resemble fully localized wavepackets with envelope and crests moving at the same speed, and the wave envelope along with the induced mean-flow component are governed by a coupled Davey-Stewartson equation system of elliptic-elliptic type. The lump profiles feature algebraically decaying tails at infinity owing to this mean flow. In the case of water waves, lumps of the wavepacket type are possible when both gravity and surface tension are present on water of finite or infinite depth for B < 1/3.
(cont.) The asymptotic analysis of these lumps in the vicinity of their bifurcation point at the minimum gravity-capillary phase speed, is in agreement with recent fully numerical computations by Parau, Cooker & Vanden-Broeck (2005) as well as a formal existence proof by Groves & Sun (2005). A linear stability analysis of the gravity-capillary solitary waves that also bifurcate at the minimum gravity-capillary phase speed, reveals that they are always unstable to transverse perturbations, suggesting a mechanism for the generation of lumps. This generation mechanism is explored in the context of the two-dimensional Benjamin (2-DB) equation, a generalization to two horizontal spatial dimensions of the model equation derived by Benjamin (1992) for uni-directional, small-amplitude, long interfacial waves in a two-fluid system with strong interfacial tension. The 2-DB equation admits solitary waves and lumps of the wavepacket type analogous to those bifurcating at the minimum gravity-capillary phase speed in the water-wave problem. Based on unsteady numerical simulations, it is demonstrated that the transverse instability of solitary waves of the 2-DB equation results in the formation of lumps, which propagate stably and are thus expected to be the asymptotic states of the initial-value problem for fully localized initial conditions.
by Boguk Kim.
Ph.D.
5
Hoseini, Sayed Mohammad. "Solitary wave interaction and evolution". Access electronically, 2007. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20080221.110619/index.html.
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Mak, William Chi Keung Electrical Engineering & Telecommunications Faculty of Engineering UNSW. "Coupled Solitary Waves in Optical Waveguides". Awarded by:University of New South Wales. Electrical Engineering and Telecommunications, 1998. http://handle.unsw.edu.au/1959.4/17494.
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Soliton states in three coupled optical waveguide systems were studied: two linearly coupled waveguides with quadratic nonlinearity, two linearly coupled waveguides with cubic nonlinearity and Bragg gratings, and a quadratic nonlinear waveguide with resonant gratings, which enable three-wave interaction. The methods adopted to tackle the problems were both analytical and numerical. The analytical method mainly made use of the variational approximation. Since no exact analytical method is available to find solutions for the waveguide systems under study, the variational approach was proved to be very useful to find accurate approximations. Numerically, the shooting method and the relaxation method were used. The numerical results verified the results obtained analytically. New asymmetric soliton states were discovered for the coupled quadratically nonlinear waveguides, and for the coupled waveguides with both cubic nonlinearity and Bragg gratings. Stability of the soliton states was studied numerically, using the Beam Propagation Method. Asymmetric couplers with quadratic nonlinearity were also studied. The bifurcation diagrams for the asymmetric couplers were those unfolded from the corresponding diagrams of the symmetric couplers. Novel stable two-soliton bound states due to three-wave interaction were discovered for a quadratically nonlinear waveguide equipped with resonant gratings. Since the coupled optical waveguide systems are controlled by a larger number of parameters than in the corresponding single waveguide, the coupled systems can find a much broader field of applications. This study provides useful background information to support these applications.
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Melvin, Thomas R. O. "Travelling solitary waves in lattice equations". Thesis, University of Bristol, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.503947.
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This thesis is concerned with the existence and dynamics of travelling solitary waves in lattice equations, specifically a number of models of the discrete nonlinear Schrodinger equation (DNLS). The DNLS occurs in various forms when modelling a wide range of physical processes involving wave propagation. We provide a review of the literature and introduce some of the concepts that will be use to analyse the differential advance-delay equations which occur when posing lattice equations in a travelling frame. To show the existence of travelling solitary wave solutions to the DNLS three main methods are used, namely the pseudo-spectral method, Melnikov's method for the existence of homoclinic orbits and computation of the so-called Stokes constant for a beyond-all-orders asymptotic expansion. The pseudo-spectral method transforms the differential advance-delay equation into a large system of coupled algebraic equations which are solved numerically.
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Skryabin, Dmitry Vladimirovich. "Modulational instability of optical solitary waves". Thesis, University of Strathclyde, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366995.
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Moores, John Demeritt. "Collisions of orthogonally polarized solitary waves". Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/14420.
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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1989.Includes bibliographical references.
Support from the Office of Naval Research in the form of a 1986-1989 ONR Fellowship.
by John Demeritt Moores.
M.S.
10
Marchant, Anna Louise. "Formation of bright solitary matter-waves". Thesis, Durham University, 2012. http://etheses.dur.ac.uk/7279/.
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This thesis presents the development of an experimental apparatus to produce Bose-Einstein condensates (BECs) with tunable interparticle interactions. The ability to precisely control the strength of these interactions, and even to switch them from repulsive to attractive, allows one to probe novel regimes of condensate physics, from the collapse of attractively interacting BECs and the formation of solitary matter-waves to the observation of beyond mean-field effects in strongly repulsive condensates. The construction and characterisation of both a single and crossed beam optical dipole trap is presented. In the single beam case we develop a technique allowing the guided transport of atoms along the beam and up to a room-temperature surface; a technique which can be used to evaporatively cool the trapped atomic cloud. We produce Bose-Einstein condensates of 87Rb in the F=1, mF=-1 state in this trap, comparing the effect of beam waist on the evaporation trajectory. In the crossed beam trap Bose-Einstein condensation of 87Rb is realised in three distinct trapping configurations, along with a 1D optical lattice formed by changing the polarisation of the beams. A method of direct cooling of 85Rb atoms in the crossed trap is developed using a magnetic Feshbach resonance to precisely tune both the elastic and inelastic scattering properties of the atoms. The resonance used for this work occurs at 155G in collisions between atoms in the F=2, mF=-2 state of 85Rb. Bose-Einstein condensates of up to 40,000 85Rb atoms are formed in this trap and we demonstrate the presence of tunable interatomic interactions, exploring the collapse phenomenon associated with attractive condensates. By loading the 85Rb condensate into a quasi-1D waveguide we show that stable attractive condensates can be created, taking the form of bright solitary matter-waves. We observe a solitary wave of ~2,000 atoms which propagates, without dispersion, along the waveguide over a distance of ~1.1mm. The particle-like nature of the solitary wave is demonstrated by classical reflection of the wavepacket from a repulsive Gaussian barrier.
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Wiles, Timothy Peter. "Dynamics of bright solitary matter-waves". Thesis, Durham University, 2013. http://etheses.dur.ac.uk/7382/.
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This thesis describes the formation of a 85Rb Bose-Einstein condensate and the subsequent creation of a bright solitary matter-wave in a quasi-one-dimensional optical waveguide, with experiments investigating the dynamics of a solitary wave in comparison with a repulsive Bose-Einstein condensate. In the final chapters of this thesis, progress towards the interaction of a solitary wave with a narrow barrier and an attractive atom-surface potential is presented. Beyond the above, a review of recent soliton and solitary wave theory is presented from the perspective of an experimentalist, culminating in the numerical analysis of a variety of key areas, namely, quantum reflection, solitary wave size and solitary wave profile. The modelling and experimental results relating to the merging of ultracold gases of 85Rb and 87Rb, in order to create isotopic mixtures, is also described within this thesis. Such a scheme could be used as an initial step in the process of forming molecules or undertaking sympathetic cooling. Finally, the creation of a complex LabVIEW based experimental control system is also described within.
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Miyake, Taketoshi. "Computer Simulations of Electrostatic Solitary Waves". 京都大学 (Kyoto University), 2000. http://hdl.handle.net/2433/157008.
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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものであるKyoto University (京都大学)
0048
新制・課程博士
博士(情報学)
甲第8488号
情博第14号
新制||情||2(附属図書館)
UT51-2000-F392
京都大学大学院情報学研究科通信情報システム専攻
(主査)教授 松本 紘, 教授 橋本 弘蔵, 教授 大村 善治
学位規則第4条第1項該当
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Stastna, Marek. "Large fully nonlinear solitary and solitary-like internal waves in the ocean". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ65262.pdf.
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Johnston, Clifton Reed. "Solitary waves in fluid-filled elastic tubes". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq64866.pdf.
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Wattis, Jonathan A. D. "Analytic approximations to solitary waves on lattices". Thesis, Heriot-Watt University, 1993. http://hdl.handle.net/10399/1447.
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Cho, Yeunwoo 1973. "Nonlinear dynamics of three-dimensional solitary waves". Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/61595.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 105-108).
In problems of dispersive wave propagation governed by two distinct restoring-force mechanisms, the phase speed of linear sinusoidal wavetrains may feature a minimum, cmin, at non-zero wavenumber, kmin. Examples include waves on the surface of a liquid in the presence of both gravity and surface tension, flexural waves on a floating ice sheet, in which case capillarity is replaced by the flexural rigidity of the ice, and internal gravity waves in layered flows in the presence of interfacial tension. The focus here is on deep-water gravity-capillary waves, where cmin = 23 cm/s with corresponding wavelength Amin = 27r/kmin = 1.71 cm. In this instance, ignoring viscous dissipation, cmin is known to be the bifurcation point of two-dimensional (plane) and three-dimensional (fully localized) solitary waves, often referred to as "lumps"; these are nonlinear disturbances that propagate at speeds below cmin without change of shape owing to a perfect balance between the opposing effects of wave dispersion and nonlinear steepening. Moreover, Cmin is a critical forcing speed, as the linear inviscid response to external forcing moving at Cmin grows unbounded in time, and nonlinear effects as well as viscous dissipation are expected to play important parts near this resonance. In the present thesis, various aspects of the dynamics of gravity-capillary lumps are investigated theoretically. Specifically, it is shown that steep gravity-capillary lumps of depression can propagate stably and they are prominent nonlinear features of the forced response near resonant conditions, in agreement with companion experiment for the generation of gravity-capillary lumps on deep water. These findings are relevant to the generation of ripples by wind and to the wave drag associated with the motion of small bodies on a free surface.
by Yeunwoo Cho.
Ph.D.
17
Franklin, James. "Laboratory modelling of breaking internal solitary waves". Thesis, University of Dundee, 2014. https://discovery.dundee.ac.uk/en/studentTheses/bf2741dd-7183-4aa5-817e-f5d533269c95.
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Mamun, A. A. "Study of solitary waves in space plasmas". Thesis, University of St Andrews, 1997. http://hdl.handle.net/10023/13987.
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Theoretical investigations have been made of arbitrary amplitude electrostatic solitary waves in non-thermal plasmas, which may be of relevance to ionospheric and magnetospheric plasmas, and dusty plasmas, which are most common in earth's and cometary environments as well as in planetary rings, for understanding the nonlinear features of localised electrostatic disturbances in such space plasma systems. This thesis starts with an introductory chapter where a very brief historical review of solitary waves in plasmas has been presented. The study of arbitrary amplitude electrostatic solitary waves in non-thermal plasma has considered a plasma system consisting of warm adiabatic ions and non- thermal electrons. It is found that a non-thermal electron distribution may change the nature of ion-acoustic solitary waves. If the ions are assumed to respond as a fluid to perturbations in the potential, with no significant trapping in a potential well, then a thermal plasma only supports solitary waves with a density peak. However, with a suitable distribution of non-thermal electrons, solitary waves with both density peaks and density depressions may exist. This study has also included a numerical analysis showing how these electrostatic solitary structures evolve with time. The investigation has then been extended to magnetised plasmas to study the effects of magnetic field on obliquely propagating electrostatic solitary structures. This attempt first employed the reductive perturbation method and investigated the nonlinear properties of small but finite amplitude obliquely propagating solitary waves in this magnetised non-thermal plasma model. This study is then generalised to arbitrary amplitude solitary waves by the numerical solution of the full nonlinear system of equations. This numerical method has also been utilised to present a similar study in another popular plasma model, namely the two-electron-temperature plasma model. The study of arbitrary amplitude solitary waves in a dusty plasma has considered another plasma system which consists of an inertial dust fluid and ions with Maxwellian distribution and has investigated the nonlinear properties of dust- acoustic solitary waves. A numerical study has also been made to show how these dust-acoustic solitary waves evolve with time. The effects of non-thermal and vortex-like ion distributions are then incorporated into this study. The study of arbitrary amplitude electrostatic solitary waves in this thesis has finally been concluded with some brief discussion of our results and proposal for further studies, which are expected to generalise and develop our present work to some other extents, in this versatile area of research.
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Thomas, Alexandra Elizabeth. "The interaction of an internal solitary wave with surface gravity waves". Thesis, University of Edinburgh, 2002. http://hdl.handle.net/1842/13106.
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Solitary waves are nonlinear, non-oscillatory disturbances of permanent form. Recent advances in synthetic aperture radar imaging and analysis techniques have confirmed in situ observations and measurements that the passage of oceanic internal waves, and in particular internal solitary waves, is associated with modulations in sea surface roughness. It has not only revealed the ubiquity of this phenomenon but also highlighted the global existence of large amplitude, tidally induced, internal solitary waves. It appears, however, that little laboratory-based research has been carried out in this field. This work, therefore, focusses on the study of surface wavetrain modulations resulting from the passage of a single internal solitary wave. Digital Particle Image Velocimetry (DPIV) and Planar Laser Induced Fluorescence (PLIF) were employed to provide two-dimensional instantaneous velocity and density information respectively. Previous studies in this field have been performed with intrusive probe techniques, disturbing the fluid flow during measurement. Preliminary DPIV and PLIF experiments were performed on single internal solitary waves in a two-layer brine - fresh water stratification. To the author’s knowledge, the application of PLIF to the study of these waves had not been done previously. Results from the DPIV measurements concurred with previous research and highlighted the constraints of the DPIV system. The results were also compared to a recently developed and validated fully nonlinear numerical method. From the interaction investigations, both wavelength and amplitude modulations of the surface waves as a function of solitary wave phase were observed. In some cases, the shape of the internal wave was also affected. Velocity profiles were compared to the linear superposition of surface wave linear theory and the fully nonlinear numerical method. In addition, the PLIF analysis showed that, for the wave and stratification parameters investigated, there was no evidence for the compression and expansion of the density interface during the interaction.
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Yamazoe, Shotaro. "Bifurcations and Spectral Stability of Solitary Waves in Nonlinear Wave Equations". Kyoto University, 2020. http://hdl.handle.net/2433/259759.
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Ekeberg, Jonas. "Solitary waves and enhanced incoherent scatter ion lines". Doctoral thesis, Umeå universitet, Institutionen för fysik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-42955.
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This thesis addresses solitary waves and their significance for auroral particle acceleration, coronal heating and incoherent scatter radar spectra. Solitary waves are formed due to a balance of nonlinear and dispersive effects. There are several nonlinearities present in ideal magnetohydrodynamics (MHD) and dispersion can be introduced by including theHall termin the generalised Ohm’s law. The resulting system of equations comprise the classical ideal MHD waves, whistlers, drift waves and solitarywave solutions. The latter reside in distinct regions of the phase space spanned by the speed and the angle (to the magnetic field) of the propagating wave. Within each region, qualitatively similar solitary structures are found. In the limit of neglected electron intertia, the solitary wave solutions are confined to two regions of slow and fast waves, respectively. The slow (fast) structures are associated with density compressions (rarefactions) and positive (negative) electric potentials. Such negative potentials are shown to accelerate electrons in the auroral region (solar corona) to tens (hundreds) of keV. The positive electric potentials could accelerate solar wind ions to velocities of 300–800 km/s. The structure widths perpendicular to themagnetic field are in the Earth’s magnetosphere (solar corona) of the order of 1–100 km (m). This thesis also addresses a type of incoherent scatter radar spectra, where the ion line exhibits a spectrally uniform power enhancement with the up- and downshifted shoulder and the spectral region in between enhanced simultaneously and equally. The power enhancements are one order of magnitude above the thermal level and are often localised to an altitude range of less than 20 km at or close to the ionospheric F region peak. The observations are well-described by a model of ion-acoustic solitary waves propagating transversely across the radar beam. Two cases of localised ion line enhancements are shown to occur in conjunction with auroral arcs drifting through the radar beam. The arc passages are associated with large gradients in ion temperature, which are shown to generate sufficiently high velocity shears to give rise to growing Kelvin-Helmholtz (K-H) instabilities. The observed ion line enhancements are interpreted in the light of the low-frequency turbulence associated with these instabilities.Denna avhandling handlar om solitära vågor och deras roll i norrskensacceleration och koronaupphettning, samt deras signatur i spektra uppmätta med inkoherent spridningsradar. Solitära vågor bildas genom en balans mellan ickelinjära och dispersiva effekter. Ickelinjäriteter finns det gott om i ideal magnetohydrodynamik (MHD) och dispersion kan införas genom att inkludera Halltermen i den generaliserade Ohms lag. Det resulterande ekvationssystemet omfattar de klassiska vågorna inom ideal MHD, visslare, driftvågor och solitära vågor. De sistnämnda återfinns i väldefinierade områden i fasrummet som spänns upp av farten och vinkeln (mot magnetfältet) för den propagerande vågen. Inom varje sådant område återfinns kvalitativt lika solitära våglösningar. Om man försummar elektronernas tröghet begränsas de solitära våglösningarna till två områden med långsamma respektive snabba vågor. De långsamma (snabba) strukturerna är associerade med täthets-kompressioner (förtunningar) och positiva (negativa) elektriska potentialer. De negativa potentialerna visas kunna accelerera elektroner i norrskensområdet (solens korona) till tiotals (hundratals) keV medan de positiva potentialerna accelererar solvindsjoner till hastigheter på 300–800 km/s. Strukturbredderna vinkelrät mot magnetfältet är i jordens magnetosfär (solens korona) av storleksordningen 1–100 km (m). Denna avhandling tar även upp en typ av inkoherent spridningsradarspektra, där jonlinjen uppvisar en spektralt uniform förstärkning. Detta innebär att den upp- och nedskiftade skuldran och spektralbandet däremellan förstärks simultant och i lika hög grad. Effektförstärkningen är en storleksordning över den termiska nivån och är ofta lokaliserad till ett höjd-intervall av mindre än 20 km nära jonosfärens F-skiktstopp. Observationerna beskrivs väl av en modell med solitära vågor som propagerar transversellt genom radarstrålen. Två fall av lokaliserade jonlinjeförstärkningar visas sammanfalla med att norrskensbågar driver genom radarstrålen. I samband med bågarnas passage uppmäts stora gradienter i jontemperatur, vilket visas skapa tillräckligt kraftiga hastighetsskjuvningar för att Kelvin-Helmholtz-instabiliteter ska tillåtas växa. De observerade jonlinjeförstärkningarna tolkas i skenet av den lågfrekventa turbulensen som är kopplad till dessa instabiliteter.
22
Aigner, Andreas 1972. "Numerical simulations of internal and inertial solitary waves". Monash University, Dept. of Mathematics and Statistics, 2001. http://arrow.monash.edu.au/hdl/1959.1/8880.
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Calvo, David C. (David Christopher). "Dynamics and stability of gravity-capillary solitary waves". Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/88871.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2001.Includes bibliographical references (leaves 137-143).
Over the past several years, it has been recognized that a new class of solitary waves can propagate in nonlinear dispersive wave systems if the phase speed of linear waves attains a local extremum at some finite wavenumber. Near such a point, solitary waves in the form of small-amplitude wavepackets can be obtained for which the phase speed of the carrier oscillations matches the group speed of their envelope. Such an extremum is found in the analysis of water waves when the restoring forces of both gravity and surface tension are taken into account, and certain kinds of these gravity-capillary solitary waves have been observed in experiments. While past theoretical studies have focussed mainly on determining steady solitary wave profiles, very little work has been done on examining their stability properties which is the thrust of this thesis. Beginning in the weakly nonlinear regime, an asymptotic analysis of linear stability is presented and comparison is made with numerical computations. Contrary to predictions of the nonlinear Schrbdinger (NLS) equation, some free solitary wave types are found to be unstable owing to exponentially effects terms that lie beyond standard two-scale perturba- tion theory. Moreover, numerical simulations show that unstable gravity-capillary solitary waves may decompose into stable solitary waves that have soliton properties. Stability results are then extended to the fully nonlinear regime to treat both free and forced situa- tions using numerical techniques to solve the full hydrodynamic equations in steady form. A dramatic difference is found between the linear stability of free and forced waves in both weakly and fully nonlinear cases, and results obtained here are compared with laboratory experiments.
(cont.) The analysis followed in the free-surface problem is then generalized to examine the dynamics of gravity-capillary interfacial solitary waves in a layered two-fluid system. Here, the linear stability and limiting wave forms of free solitary waves are determined over a range of system parameters using the full hydrodynamic equations. Finally, a related problem of gravity-capillary envelope solitons is considered under the general situation of unequal phase and group speeds. By asymptotic and numerical techniques it is found that envelope solitons are generally nonlocal-tails are radiated owing to a resonance mechanism that is beyond the NLS equation.
by David C. Calvo.
Ph.D.
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Pirilla, Patrick Brian. "On the Trajectories of Particles in Solitary Waves". Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1311100628.
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Shen, Yifen. "The modulation of short waves riding on non-uniform velocity fields (solitary waves and long waves)". Thesis, University of Edinburgh, 1994. http://hdl.handle.net/1842/14405.
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This work studies the modulation and kinematics of short waves riding on non-uniform velocity fields (solitary waves and long waves) and achieves theoretical and experimental conclusions. For the interactions between short waves and solitary waves, short waves and long waves, this research shows that the wavenumber, frequency and amplitude of short waves riding on solitary waves and long waves are strongly modulated. It also demonstrates that the maximum values of the modulated short wavenumber, frequency, and amplitude always occur at the crests of solitary waves and long waves. By increasing either the amplitude of solitary waves or the steepnesses of long waves the main conclusion--- that the modulated short wavenumber, frequency, and amplitude increase on the crest of solitary waves and long waves--- is achieved. The kinematics of two component waves (short waves and long waves) has been measured by PIV (Particle Image Velocimetry). Comparison of the results with Fourier theory and various stretching methods is also carried out. The mechanisms of the modulation of short waves riding on solitary waves or long waves, as studied in this thesis, provides a useful base line for work on more general and complex local water wave breaking.
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Aközbek, Neset. "Optical solitary waves in a photonic band gap material". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0007/NQ35096.pdf.
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Bennett, Christopher James. "Solitary and transitional waves in two-layer microchannel flows". Thesis, University of Birmingham, 2015. http://etheses.bham.ac.uk//id/eprint/5922/.
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The understanding of wave dynamics in interfacial microchannel flows is important for many technological applications in the micro-device industry. Here, a theoretical and numerical study is undertaken in order to understand the propagation of interfacial waves in a two-layer flow. The flow is considered to be driven by, in separate cases, the force of gravity and a pressure gradient. The results may provide steps towards more efficiently designed microfluidic products, and a better understanding of experimentally observed waves.
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Yin, Chen Yun. "Solitary waves in immiscible two-component Bose-Einstein condensates". Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608650.
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Yu, Manfred Man Hoi. "Towards interferometry with bright solitary waves in a ring". Thesis, Durham University, 2016. http://etheses.dur.ac.uk/11441/.
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This thesis presents the work towards the realisation of an interferometer using bright solitary waves in a ring. The splitting of a bright solitary wave, which is created from a 85Rb Bose-Einstein condensate in an optical waveguide, is realised through scattering from a narrow potential well formed from a tightly focussed red detuned laser beam. We observe reflection of up to 25% of the atoms, along with the trapping of atoms at the position of the potential. Such a reflected fraction is much larger than the theoretical predictions for a single, narrow Gaussian potential. A more detailed model, which accounts for the diffraction pattern of the laser beam, suggests that the presence of these small subsidiary intensity maxima is the cause of the enhancement in quantum reflection. An upgrade of the apparatus sees a new set of magnetic coils, a compact coil mount, and a crossed optical dipole trap with independently controllable beams implemented. This enables the control of magnetic curvature and dipole trap position, and maximises the optical access to the science cell. To generate a ring trap for the interferometry scheme, a spatial light modulator (SLM) is incorporated into the experiment. Through underfilling the SLM panel with the laser beam, and the use of the analytical first phase guess prior to the error minimising Mixed Region Amplitude Freedom (MRAF) algorithm, we are able to generate speckle-free, high quality holograms of arbitrary shapes. Furthermore, we demonstrate atom trapping in a ring potential, which is formed at the intersection of the SLM beam and a red detuned horizontal light sheet.
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Chen, Li-Jen. "Bernstein-Greene-Kruskal electron solitary waves in collisionless plasmas /". Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/9644.
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Farnum, Edward D. "Stability and dynamics of solitary waves in nonlinear optical materials /". Thesis, Connect to this title online; UW restricted, 2005. http://hdl.handle.net/1773/6766.
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Höwing, Johannes [Verfasser]. "Spectral Stability of Solitary Waves and Undercompressive Shocks / Johannes Höwing". Konstanz : Bibliothek der Universität Konstanz, 2013. http://d-nb.info/1037917707/34.
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Tiong, Wei K. "Propagation of solitary waves and undular bores over variable topography". Thesis, Loughborough University, 2012. https://dspace.lboro.ac.uk/2134/10531.
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Description of the interaction of a shallow-water wave with variable topography is a classical and fundamental problem of fluid mechanics. The behaviour of linear waves and isolated solitary waves propagating over an uneven bottom is well understood. Much less is known about the propagation of nonlinear wavetrains over obstacles. For shallow-water waves, the nonlinear wavetrains are often generated in the form of undular bores, connecting two different basic flow states and having the structure of a slowly modulated periodic wave with a solitary wave at the leading edge. In this thesis, we examine the propagation of shallow-water undular bores over a nonuniform environment, and also subject to the effect of weak dissipation (turbulent bottom friction or volume viscosity). The study is performed in the framework of the variable-coefficient Korteweg-de Vries (vKdV) and variable-coefficient perturbed Korteweg-de Vries (vpKdV) equations. The behaviour of undular bores is compared with that of isolated solitary waves subject to the same external effects. We show that the interaction of the undular bore with variable topography can result in a number of adiabatic and non-adiabatic effects observed in different combinations depending on the specific bottom profile. The effects include: (i) the generation of a sequence of isolated solitons -- an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore; (ii) the generation of an extended weakly nonlinear wavetrain behind the bore; (iii) the formation of a transient multi-phase region inside the bore; (iv) a nonlocal variation of the leading solitary wave amplitude; (v) the change of the characteristics wavelength in the bore; and (vi) occurrence of a ``modulation phase shift" due to the interaction. The non-adiabatic effects (i) -- (iii) are new and to the best of our knowledge, have not been reported in previous studies. We use a combination of nonlinear modulation theory and numerical simulations to analyse these effects. In our work, we consider four prototypical variable topography profiles in our study: a slowly decreasing depth, a slowly increasing depth , a smooth bump and a smooth hole, which leads to qualitatively different undular bore deformation depending on the geometry of the slope. Also, we consider (numerically) a rapidly varying depth topography, a counterpart of the ``soliton fission" configuration. We show that all the effects mentioned above can also be observed when the undular bore propagates over a rapidly changing bottom . We then consider the modification of the variable topography effects on the undular bore by considering weak dissipation due to turbulent bottom friction or volume viscosity. The dissipation is modelled by appropriate right-hand side terms in the vKdV equation. The developed methods and results of our work can be extended to other problems involving the propagation of undular bores (dispersive shock waves in general) in variable media.
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Schmidt, Nathan Philip. "Generation, propagation and dissipation of second mode internal solitary waves". Thesis, University of Canterbury. Civil Engineering, 1998. http://hdl.handle.net/10092/7811.
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The behaviour of large amplitude second mode internal solitary waves has been investigated. Waves were generated in the laboratory by a variety of methods and were observed using dye and particle visualisation techniques. Observations of wave generation, propagation and dissipation were used to develop new theories about the behaviour of such waves.
Waves were generated by exchange flow, forced inflow and gravity collapse. The generation sequence was found to be similar for all three methods, with the gravity collapse technique allowing the most rapid and repeatable generation of second mode waves.
External propagation characteristics (wave celerity and geometry) were investigated using waves of dimensionless amplitude up to a/h = 11.6. It was found that wave geometry was described well by existing theory over the entire range of amplitudes, but the existing wave celerity relationships were only accurate up to a/h ≌ 3. A new analytical approach produced a relationship which is applicable to all large amplitude waves.
Internal propagation characteristics (internal circulation, entrainment and mass transport) were investigated using both particle visualisation and laser induced fluorescence techniques. It was found that internal circulation differs from the pattern suggested by existing numerical models. The interior of the wave is made up of an assemblage of vortices, symmetrical about the wave centreline, with a net flow rearwards along the centreline. These vortices are seen to play an important role in the entrainment of fluid into the wave. Entrainment appears to be caused by a non-symmetric Holmboe instability at the wave boundary. The entrainment into and expulsion of fluid from the wave results in the flushing of fluid from the wave. Measurements indicate that the rate of flushing is linearly proportional to distance and Richardson number during the primary flushing phase (from 100% to 10% tracer concentration). During the secondary flushing phase (from 10% to 1% tracer concentration) the flushing rate is lower but also linearly proportional to distance and Richardson number.
Wave dissipation experiments indicate that wave amplitude decay rate is constant for any wave but varies with densimetric factor. Waves with larger densimetric factors decay at a slower rate. An expression for wave energy was formulated and the wave energy decay rate was examined. It was found that the radiation of first mode waves does not provide a significant contribution to wave decay. Wall shear was quantified and found to vary with flume width. In this study it was responsible for approximately 9% of the dissipation rate. The remaining dissipation is due to fluid drag (interfacial shear, pressure drag and mixing) and was quantified by a drag coefficient. The drag coefficient varies with the inverse of the cube root of densimetric factor.
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Ilecki, Wojciech. "Theoretical study of spatial solitary waves in non-Kerr media". Thesis, University of Salford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.395747.
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MacNeil, John Michael Larratt. "Solitary waves in focussing and defocussing nonlinear, nonlocal optical media". Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20951.
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Nonlinear, nonlocal optical media has emerged as an ideal setting for experimentally observing and studying spatial optical solitary waves which otherwise cannot occur in Kerr media. Of particular interest is the eventual application to all-optical circuits. However, there is considerable work left to do on the theoretical end before this is a possibility. In this thesis we consider three problems. The first is how to solve the governing equations for optical beam propagation in the particular medium of the nematic liquid crystal (NLC), which is used as a prototypical example, exactly and approximately. In this respect we provide the first known, explicit solutions to the model as well as a comprehensive assessment on how to use variational, or modulation theory, in this context. This leads to the discovery of a novel form of bistability in the system, which shows there are two stable solitary wave solutions for a fixed power or L2 norm. We then consider how to approximate solutions for optical solitary waves propagating in a more general class of nonlocal nonlinear media using asymptotic methods. This is a long open problem and is resolved in the form of a simple to implement method with excellent accuracy and general applicability to previously intractable models. We conclude with the discovery and characterization of an instability mechanism in a coupled, defocussing nonlinear Schrodinger system. We show there is no stable, coupled, localized solution. This result is compared with the more well-studied bright solitary wave system and physical and mathematical explanations are offered.
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McSloy, John Michael. "Computationally determined existence and stability regimes of solitonic phenomena in nonlinear optics". Thesis, University of Strathclyde, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269899.
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Husrin, Semeidi [Verfasser], i Hocine [Akademischer Betreuer] Oumeraci. "Attenuation of Solitary Waves and Wave Trains by Coastal Forests / Semeidi Husrin ; Betreuer: Hocine Oumeraci". Braunschweig : Technische Universität Braunschweig, 2013. http://d-nb.info/1175821764/34.
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Preuße, Martina [Verfasser]. "Properties of Internal Solitary Waves in Deep Temperate Lakes / Martina Preuße". Konstanz : Bibliothek der Universität Konstanz, 2012. http://d-nb.info/1025637321/34.
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Marini, Andrea. "Theory of nonlinear and amplified surface plasmon polaritons". Thesis, University of Bath, 2011. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.547873.
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This thesis presents a study of Surface Plasmon Polaritons (SPPs) in hybrid metal-dielectric waveguides. The embedding of metal in nanostructured photonic components allows for manipulating and guiding light at the subwavelength scale. Such an extreme confinement enhances the nonlinear response of the dielectric medium, which is important for applications in optical processing of information, but is paid in terms of considerable ohmic loss in the metal. It is, however, possible to embed externally pumped active inclusions in the dielectric in order to compensate for the metal loss. A novel perturbative theory for Maxwell equations is introduced and applied to various nonlinear metal-dielectric structures, deriving the propagation equation for the optical field. The nonlinear dispersion law for amplified SPPs, filamentation and dissipative plasmon-soliton formation have been studied, revealing intrinsic core and tail instabilities that prevent solitons to propagate over long distances. Stable propagation of plasmon-solitons can be achieved in insulator-metal-insulator structures with active and passive interfaces. The active SPP is coupled with the passive SPP, which absorbs the perturbations destabilising the zero background of the soliton. Theoretical modelling of optical propagation in metal-dielectric stacks predicts a modified two-band structure, allowing for gap/discrete plasmon-soliton formation. Loss and nonlinear parameters in subwavelength nanowire waveguides are evaluated and compared to the results obtained by other research groups. In all calculations, particular attention is paid in considering boundary conditions accounting for loss and nonlinear corrections, which contribute to the propagation equation with a surface term that becomes significant in the subwavelength regime.
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Kim, Sungphil. "Internal Tides and Internal Solitary Waves in the Northern South China Sea". NCSU, 2009. http://www.lib.ncsu.edu/theses/available/etd-05152009-141246/.
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Large-amplitude internal solitary waves (ISWs) are frequently observed in the northern South China Sea (SCS). In a project sponsored by the US Office of Naval Research, four moorings were deployed between the Luzon Strait and the Chinese continental shelf by Steve Ramp of the Naval Postgraduate School and David Tang of National Taiwan University from late April 2005 to May 2006. Several CTD sections were taken during April and July in 2005. Satellite pictures were also collected during that period. In this study, these data were used to examine the characteristics, generation, and propagation of ISWs. In the satellite images, monthly change in stratification may cause northward shift of the propagation path, and ISWs are more frequently observed in July than in April and May. Speed estimation shows that ISWs propagate faster in the deep basin than over the continental margin and near the ridge. The generation of internal tides correlates with the eastward tidal flow over the ridge, while ISWs are produced by northwestward tidal currents over the ridges in the Luzon Strait.
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Billam, Thomas Paul. "Bright solitary waves and non-equilibrium dynamics in atomic Bose-Einstein condensates". Thesis, Durham University, 2012. http://etheses.dur.ac.uk/3561/.
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In this thesis we investigate the static properties and non-equilibrium dynamics of bright solitary waves in atomic Bose-Einstein condensates in the zero-temperature limit, and we investigate the non-equilibrium dynamics of a driven atomic Bose-Einstein condensate at finite temperature. Bright solitary waves in atomic Bose-Einstein condensates are non-dispersive and soliton-like matter-waves which could be used in future atom-interferometry experiments. Using the mean-field, Gross-Pitaevskii description, we propose an experimental scheme to generate pairs of bright solitary waves with controlled velocity and relative phase; this scheme could form an important part of a future atom interferometer, and we demonstrate that it can also be used to test the validity of the mean-field model of bright solitary waves. We also develop a method to quantitatively assess how soliton-like static, three-dimensional bright solitary waves are; this assessment is particularly relevant for the design of future experiments. In reality, the non-zero temperatures and highly non-equilibrium dynamics occurring in a bright solitary wave interferometer are likely to necessitate a theoretical description which explicitly accounts for the non-condensate fraction. We show that a second-order, number-conserving description offers a minimal self-consistent treatment of the relevant condensate -- non-condensate interactions at low temperatures and for moderate non-condensate fractions. We develop a method to obtain a fully-dynamical numerical solution to the integro-differential equations of motion of this description, and solve these equations for a driven, quasi-one-dimensional test system. We show that rapid non-condensate growth predicted by lower-order descriptions, and associated with linear dynamical instabilities, can be damped by the self-consistent treatment of interactions included in the second-order description.
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Li, Yile 1973. "Nonlinear shallow water three-dimensional solitary waves generated by high speed vessels". Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/91907.
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Hoq, Qazi Enamul. "Quantization Of Spin Direction For Solitary Waves in a Uniform Magnetic Field". Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4210/.
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It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data)and have nonzero spin (nonzero intrinsic angular momentum in the centre of momentum frame). In this paper we consider vector-valued solitary wave solutions to a nonlinear Klein-Gordon equation and investigate the behavior of these spinning solitary waves under the influence of an externally imposed uniform magnetic field. We find that the only stationary spinning solitary wave solutions have spin
parallel or antiparallel to the magnetic field direction.
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Choi, Wooyoung Wu Theodore Y. T. Wu Theodore Y. T. "Forced generation of solitary waves in a rotating fluid and their stability /". Diss., Pasadena, Calif. : California Institute of Technology, 1993. http://resolver.caltech.edu/CaltechETD:etd-08242007-075146.
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Wan, Bangjun. "A numerical study of conjugate flows and flat-centred internal solitary waves in a continuously stratified fluid". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/mq25896.pdf.
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Wang, Caixia. "Geophysical observations of nonlinear internal solitary-like waves in the Strait of Georgia". Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/17468.
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A novel observational method for studying internal features in the coastal ocean is devel-
oped and tested in a study of large nonlinear internal solitary-like waves. Observations were
carried out in the southern Strait of Georgia in the summers of 2001 and 2002. By quantitatively combining photogrammetrically rectified oblique photo images from a circling aircraft
with water column data we track a number of internal wave packets for periods of up to one
hour and obtain a more complete view of internal waves, including propagation, oblique
interaction, and generation. First, the applicability of various weakly nonlinear theories in
modeling propagation of these large waves is tested. Both two-layer and continuous linear,
KdV (Korteweg-de Vries), and BO (Benjamin-Ono) models are applied with and without
background shear currents. After background shear currents are included, it is found that
a continuously stratified BO equation can be used to model propagation speeds within ob-
servational error, and that this is not true for other theories. Second, four observed oblique
wave-wave interactions including two Mach interactions, one interaction which varied from
known interaction patterns, and one very shallow angle regular interaction are analyzed.
An existing small-amplitude theory is applied but is found to overestimate the likelihood of
Mach interaction at large amplitude. Finally, large-scale aerial surveys are mapped. Using
speeds typical of observed waves, their time and place of origin are predicted. It is found
that the observed waves are generated at the passes to the south of the Strait of Georgia
and are released into the Strait after ebb tides.
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Mohammadi, Siamak Malek. "Laboratory generation and physics of propagation of solitary waves and water surface depressions". Connect to this title online, 2009. http://etd.lib.clemson.edu/documents/1263400525/.
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Bisgard, Charlie. "Breaking and non-breaking solitary wave impact pressures on a cylinder over a 3-D bathymetry". Thesis, (4 MB), 2005. http://edocs.nps.edu/AR/topic/theses/2005/Jan/05Jan_Bisgard.pdf.
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Thesis (M.S.Civil and Environmental Engineering and Construction Management)--Oregon State University, 2005."January 2005." Description based on title screen as viewed on June 1, 2010 DTIC Descriptor(s): Three Dimensional, Bathymetry, Tsunamis, Earthquakes, Coastal Regions, Ocean Waves, Inertia, Landslides, Gravitational Fields, Seafloor Spreading, Long Wavelengths, Models, Energy, Theses, Time Includes bibliographical references (p. 84-85). Also available in print.
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El-Solh, Safinaz. "SPH Modeling of Solitary Waves and Resulting Hydrodynamic Forces on Vertical and Sloping Walls". Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/23778.
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Currently, the accurate prediction of the impact of an extreme wave on infrastructure located near shore is difficult to assess. There is a lack of established methods to accurately quantify these impacts. Extreme waves, such as tsunamis generate, through breaking, extremely powerful hydraulic bores that impact and significantly damage coastal structures and buildings located close to the shoreline. The damage induced by such hydraulic bores is often due to structural failure. Examples of devastating coastal disasters are the 2004 Indian Ocean Tsunami, 2005 Hurricane Katrina and most recently, the 2011 Tohoku Japan Tsunami. As a result, more advanced research is needed to estimate the magnitude of forces exerted on structures by such bores.
This research presents results of a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method which is used to simulate the impact of extreme hydrodynamic forces on shore protection walls. Typically, fluids are modeled numerically based on a Lagrangian approach, an Eulerian approach or a combination of the two. Many of the common problems that arise from using more traditional techniques can be avoided through the use of SPH-based models. Such challenges include the model computational efficiency in terms of complexity of implementation. The SPH method allows water particles to be individually modeled, each with their own characteristics, which then accurately depicts the behavior and properties of the flow field. An open source code, known as SPHysics, was used to run the simulations presented in this thesis. Several cases analysed consist of hydraulic bores impacting a flat vertical wall as well as a sloping seawall. The analysis includes comparisons of the numerical results with published experimental data. The model is shown to accurately reproduce the formation of solitary waves as well as their propagation and breaking. The impacting bore profiles as well as the resulting pressures are also efficiently simulated using the model.