Academic literature on the topic 'Non-linear water wave problems'
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Journal articles on the topic "Non-linear water wave problems"
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Akyildiz, Yilmaz. "Conservation laws for shallow water waves on a sloping beach." International Journal of Mathematics and Mathematical Sciences 9, no. 2 (1986): 387–96. http://dx.doi.org/10.1155/s0161171286000480.
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Shallow water waves are governed by a pair of non-linear partial differential equations. We transfer the associated homogeneous and non-homogeneous systems, (corresponding to constant and sloping depth, respectively), to the hodograph plane where we find all the non-simple wave solutions and construct infinitely many polynomial conservation laws. We also establish correspondence between conservation laws and hodograph solutions as well as Bäcklund transformations by using the linear nature of the problems on the hodogrpah plane.
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Evans, D. V., and C. M. Linton. "On step approximations for water-wave problems." Journal of Fluid Mechanics 278 (November 10, 1994): 229–49. http://dx.doi.org/10.1017/s002211209400368x.
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The scattering of water waves by a varying bottom topography is considered using two-dimensional linear water-wave theory. A new approach is adopted in which the problem is first transformed into a uniform strip resulting in a variable free-surface boundary condition. This is then approximated by a finite number of sections on which the free-surface boundary condition is assumed to be constant. A transition matrix theory is developed which is used to relate the wave amplitudes at ±∞. The method is checked against examples for which the solution is known, or which can be computed by alternative means. Results show that the method provides a simple accurate technique for scattering problems of this type.
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Liu, Philip L. F., H. W. Hsu, and Meng H. Lean. "Applications of boundary integral equation methods for two-dimensional non-linear water wave problems." International Journal for Numerical Methods in Fluids 15, no. 9 (1992): 1119–41. http://dx.doi.org/10.1002/fld.1650150912.
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Fenton, John D. "POLYNOMIAL APPROXIMATION AND WATER WAVES." Coastal Engineering Proceedings 1, no. 20 (1986): 15. http://dx.doi.org/10.9753/icce.v20.15.
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A different approach to the solution of water wave problems is considered. Instead of using an approximate wave theory combined with highly accurate global spatial approximation methods, as for example in many applications of linear wave theory, a method is developed which uses local polynomial approximation combined with the full nonlinear equations. The method is applied to the problem of inferring wave properties from the record of a pressure transducer, and is found to be capable of high accuracy for waves which are not too short, even for large amplitude waves. The general approach of polynomial approximation is well suited to problems of a rather more general nature, especially where the geometry is at all complicated. It may prove useful in other areas, such as the nonlinear interaction of long waves, shoaling of waves, and in three dimensional problems, such as nonlinear wave refraction and diffraction.
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KASHIYAMA, Kazuo, and Mutsuto KAWAHARA. "Adaptive finite element method for linear water wave problems." Doboku Gakkai Ronbunshu, no. 387 (1987): 115–24. http://dx.doi.org/10.2208/jscej.1987.387_115.
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Karunakar, Perumandla, and Snehashish Chakraverty. "Solution of interval shallow water wave equations using homotopy perturbation method." Engineering Computations 35, no. 4 (2018): 1610–24. http://dx.doi.org/10.1108/ec-12-2016-0449.
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Purpose This paper aims to present solutions of uncertain linear and non-linear shallow water wave equations. The uncertainty has been taken as interval and one-dimensional interval shallow water wave equations have been solved by homotopy perturbation method (HPM). In this study, basin depth and initial conditions have been taken as interval and the single parametric concept has been used to handle the interval uncertainty. Design/methodology/approach HPM has been used to solve interval shallow water wave equation with the help of single parametric concept. Findings Previously, few authors found solution of shallow water wave equations with crisp basin depth and initial conditions. But, in actual sense, the basin depth, as well as initial conditions, may not be found in crisp form. As such, here these are considered as uncertain in term of intervals. Hence, interval linear and non-linear shallow water wave equations are solved in this study using single parametric concept-based HPM. Originality/value As mentioned above, uncertainty is must in the above-titled problems due to the various parametrics involved in the governing differential equations. These uncertain parametric values may be considered as interval. To the best of the authors’ knowledge, no work has been reported on the solution of uncertain shallow water wave equations. But when the interval uncertainty is involved in the above differential equation, then direct methods are not available. Accordingly, single parametric concept-based HPM has been applied in this study to handle the said problems.
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Groves, Mark D. "Theoretical aspects of gravity–capillary waves in non-rectangular channels." Journal of Fluid Mechanics 290 (May 10, 1995): 377–404. http://dx.doi.org/10.1017/s0022112095002552.
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This article reports the results of theoretical research concerning linear waves propagating on the surface of water in a uniform horizontal channel of arbitrary crosssection. Three different versions of the problem are considered. The first is the hydrodynamic problem when surface tension is neglected. The second and third include capillary effects, necessitating the use of edge conditions at the points of contact of the free edges and the channel walls. Two sets of edge constraints are used: pinned edges, where the lines of contact are fixed, and free edges, where the surface meets locally vertical walls orthogonally. These choices are physically realistic and have certain advantages for mathematical analysis.The hydrodynamic problems are shown to have a Hamiltonian structure in which the non-local operators inherent in the water-wave problem are explicitly exhibited. The existence, properties and applications of normal-mode solutions are discussed, and a qualitative comparison of those obtained for each problem is given. Explicit and numerical calculations of the dispersion relations for the normal modes are also carried out. A long-wave theory based upon a decomposition of the hydrodynamic problems in Fourier-transform space is developed. Finally a bifurcation theory for linear travelling waves is discussed, a potential application of which is the construction of an existence theory for periodic travelling-wave solutions of the corresponding nonlinear problems.
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Liu, Z., D. L. Xu, and S. J. Liao. "Finite amplitude steady-state wave groups with multiple near resonances in deep water." Journal of Fluid Mechanics 835 (November 27, 2017): 624–53. http://dx.doi.org/10.1017/jfm.2017.787.
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In this paper, finite amplitude steady-state wave groups with multiple nearly resonant interactions in deep water are investigated theoretically. The nonlinear water wave equations are solved by the homotopy analysis method (HAM), which imposes no constraint on either the number or the amplitude of the wave components, to resolve the small-divisor problems caused by near resonances. A new kind of auxiliary linear operator in the framework of the HAM is proposed to transform the small divisors associated with the non-trivial nearly resonant components to singularities associated with the exactly resonant ones. Primary components, exactly resonant components together with nearly resonant components are considered as the initial non-trivial components, since all of them are homogeneous solutions to the auxiliary linear operator. For wave groups with weak nonlinearity, the energy transfer between nearby nearly resonant components is remarkable. As the nonlinearity increases, the number of steady-state wave groups increases as more components join the near resonance. This indicates that the probability of existence of steady-state resonant waves increases with the nonlinearity of wave groups. The frequency band broadens and spectral asymmetry becomes more and more pronounced. The amplitude of each component may either increase or decrease with the nonlinearity of wave groups, while the amplitude of the whole wave group increases continuously and finite amplitude wave groups are obtained. This work shows the wide existence of steady-state waves when multiple nearly resonant interactions are considered.
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CADBY, J. R., and C. M. LINTON. "Three-dimensional water-wave scattering in two-layer fluids." Journal of Fluid Mechanics 423 (November 3, 2000): 155–73. http://dx.doi.org/10.1017/s0022112000002007.
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We consider, using linear water-wave theory, three-dimensional problems concerning the interaction of waves with structures in a fluid which contains a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise, and these relations are systematically extended to the two-fluid case. The particular problems of wave radiation and scattering by a submerged sphere in either the upper or lower layer are then solved using multipole expansions.
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Єфремова, Н. В., A. Є. Нильва, Н. Н. Котовська, and М. В. Дрига. "Theoretical and experimental investigations of wave field around vessel in shallow water." Herald of the Odessa National Maritime University, no. 62 (August 11, 2020): 72–89. http://dx.doi.org/10.47049/2226-1893-2020-2-72-89.
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Un-running vessel at the shallow-water road anchorage is under exposure to waves that come at arbitrary angle from the high sea. 3D waves from deep-sea area become practically 2D when entering shallow water. While mean periods are kept, waves become shorter and their crests become higher and sharpener than for deep-water ones. As a result of diffraction of waves that come from the deep-water sea at the vessel, a transformation zone appears where waves become 3D again. Dimensions of the waves’ transformation zone, character and height of waves in this zone specify safety of auxiliary crafts, e.g. tugboats, bunker vessels, pilot and road crafts, oil garbage collectors and boom crafts. In the complex 3D waves the trajectory of auxiliary vessel’s movement has to be safe, vessel’s motions have to be moderate. Besides waves’ height is one of the parameters that are used for forecast of movement of spilled oil. Last years the biggest part examination of waves’ problems was devoted to estimation of waves’ impact onto stationary or floating shelf facilities. For validity estimation, waves’ characteristics defined due to different theories, are compared with experimental ones. But characteristics of the waves around shelf facilities are hardly able to be compared to same ones of waves around bodies with vessel-type shape. At the experiments with vessels’ models, waves’ impact onto vessel was examined, but not the transformation of the waves themselves. So, comparing of waves area’s characteristics defined by both theoretical experimental ways is an actual problem. Aim of the paper is verification of results of wave area investigation; wave area is located around a vessel that is exposed of arbitrary angle waves at shallow water conditions. Description of experimental investigations of transformed waves in the towing tank is done; transformation zone appears around vessel’s model while running waves diffract on it. Distribution of waves’ amplitudes at the designated points was fixed by the special designed and manufactured unit. Experimental data is compared with computation results both of linear and non-linear theories. It was assumed that experimental results and theoretical data satisfactory meet each other; also that non-linear computations define the maximal values of waves’ amplitudes at all cases.
Dissertations / Theses on the topic "Non-linear water wave problems"
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Han, F. S. "Non-linear free surface problems using the boundary element method." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378300.
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Jeyakumaran, R. "Some scattering and sloshing problems in linear water wave theory." Thesis, Brunel University, 1993. http://bura.brunel.ac.uk/handle/2438/5390.
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Using the method of matched asymptotic expansions the reflection and transmission coefficients are calculated for scattering of oblique water waves by a vertical barrier. Here an assumption is made that the barrier is small compared to the wavelength and the depth of water. A number of sloshing problems are considered. The eigenfrequencies are calculated when a body is placed in a rectangular tank. Here the bodies considered are a vertical surface-piercing or bottom-mounted barrier, and circular and elliptic cylinders. When the body is a vertical barrier, the eigenfunction expansion method is applied. When the body is either a circular or elliptic cylinder, and the motion is two-dimensional, the boundary element method is applied to calculate the eigenfrequencies. For comparison, two approximations, "a wide-spacing", and "a small-body" are used for a vertical barrier and circular cylinder. In the wide-spacing approximation, the assumption is made that the wavelength is small compared with the distance between the body and walls. The small-body approximation means that a typical dimension of the body is much larger than the cross-sectional length scale of the fluid motion. For an elliptic cylinder, the method of matched asymptotic expansions is used and compared with the result of the boundary- element method. Also a higher-order solution is obtained using the method of matched asymptotic expansions, and it is compared with the exact solution for a surface-piercing barrier. Again the assumption is made that the length scale of the motion is much larger than a typical body dimension. Finally, the drift force on multiple bodies is considered the ratio of horizontal drift force in the direction of wave advance on two cylinders to that on an isolated cylinder is calculated. The method of matched asymptotic expansions is used under the assumption that the wavelength is much greater than the cylinder spacing.
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McNatt, James Cameron. "Cylindrical linear water waves and their application to the wave-body problem." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20378.
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The interaction between water waves and a floating or fixed body is bi-directional: wave forces act on and cause motion in the body, and the body alters the wave field. The impact of the body on its wave field is important to understand because: 1) it may have positive or negative consequences on the natural or built environment; 2) multiple bodies in proximity interact via the waves that are scattered and radiated by them; and 3) in ocean wave energy conversion, by conservation of energy, as a device absorbs energy, so too must the energy be removed from the wave field. Herein, the cylindrical solutions to the linear wave boundary-value problem are used to analyze the floating body wave field. These solutions describe small-amplitude, harmonic, potential-flow waves in the form of a Fourier summation of incoming and outgoing, partial, cylindrical, wave components. For a given geometry and mode of motion, the scattered or radiated waves are characterized by a particular set of complex cylindrical coefficients. A novel method is developed for finding the cylindrical coefficients of a scattered or radiated wave field by making measurements, either computationally or experimentally, over a circular-cylindrical surface that circumscribes the body and taking a Fourier transform as a function of spatial direction. To isolate evanescent modes, measurements are made on the free-surface and as a function of depth. The technique is demonstrated computationally with the boundary-element method software, WAMIT. The resulting analytical wave fields are compared with those computed directly by WAMIT and the match is found to be within 0.1%. A similar measurement and comparisons are made with experimental results. Because of the difficulty in making depth-dependent measurements, only free-surface measurements were made with a circular wave gauge array, where the gauges were positioned far from the body in order to neglect evanescent modes. The experimental results are also very good. However, both high-order harmonics and wave reflections led to difficulties. To compute efficiently the wave interactions between multiple bodies, a well-known multiple-scattering theory is employed, in which waves that are scattered and radiated by one body are considered incident to another body, which in turn radiates and scatters waves, sending energy back to the first. Wave fields are given by their cylindrical representations and unknown scattered wave amplitudes are formulated into a linear system to solve the problem. Critical to the approach is the characterization of, for each unique geometry, the cylindrical forces, the radiated wave coefficients, and the scattered waves in the form of the diffraction transfer matrix. The method developed herein for determining cylindrical coefficients is extended to new methods for finding the quantities necessary to solve the interaction problem. The approach is demonstrated computationally with WAMIT for a simple cylinder and a more complex wave energy converter (WEC). Multiple-scattering computations are verified against direct computations from WAMIT and are performed for spectral seas and a very large array of 101 WECs. The multiple-scattering computation is 1,000- 10,000 times faster than a direct computation because each body is represented by 10s of wave coefficients, rather than 100s to 1,000s of panels. A new expression for wave energy absorption using cylindrical coefficients is derived, leading to a formulation of wave energy absorption efficiency, which is extended to a nondimensional parameter that relates to efficiency, capture width and gain. Cylindrical wave energy absorption analysis allows classical results of heaving and surging point absorbers to be easily reproduced and enables interesting computations of a WEC in three-dimensions. A Bristol Cylinder type WEC is examined and it is found that its performance can be improved by flaring its ends to reduce "end effects". Finally, a computation of 100% wave absorption is demonstrated using a generalized incident wave. Cylindrical representations of linear water waves are shown to be effective for the computations of wave-body wave fields, multi-body interactions, and wave power absorption, and novel methods are presented for determining cylindrical quantities. One of the approach's greatest attributes is that once the cylindrical coefficients are found, complex representations of waves in three dimensions are stored in vectors and matrices and are manipulated with linear algebra. Further research in cylindrical water waves will likely yield useful applications such as: efficient computations of bodies interacting with short-crested seas, and continued progress in the understanding of wave energy absorption efficiency.
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Ruggeri, Felipe. "A higher order time domain panel method for linear and weakly non linear seakeeping problems." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/3/3135/tde-09122016-074844/.
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This thesis addresses the development of a weakly non-linear Higher Order Time Domain Rankine Panel Method (TDRPM) for the linear and weakly non-linear seakeeping analysis of floating offshore structures, including wave-current interaction effects. A higher order boundary elements method is adopted based on the body geometry description using Non-uniform Rational B-splines (NURBS) formulation, which can be generated by many standard Computed Aided Design (CAD) softwares widely available, and the several computed quantities (velocity potential, free surface elevation and others) are described using a B-spline formulation of arbitrary degree. The problem is formulated considering wave-current-body interactions up to second order effects, these ones considering the terms obtained by interaction of zero/first order quantities. In order to provide numerical stability, the Initial Boundary Value Problem (IBVP) is formulated in terms of the velocity potential and the local acceleration potential, the later used to predict the hydrodynamic pressure accurately. The zeroth order problem is solved using the double-body linearization instead of the Neumman-Kelvin one in order to allow bluff bodies simulation, leading to very complex expressions regarding the m-terms computation. The method adopts the Rankine sources as Green\'s function, which are integrated using Gauss quadrature in the entire domain, but for the self-influence terms that are integrated using a desingularized procedure. The numerical method is verified initially considering simplified geometries (sphere and circular cylinder) for both, first and second-order computations, with and without current effects. The derivatives of the velocity potential are verified by comparing the numerical m-terms to the analytical solutions for a hemisphere under uniform flow. The mean and double frequency drift forces are computed for fixed and floating structures and the quantities involved in these computations (wave runup, velocity field) are also compared to literature results, including the free floating response of a sphere under current effects. Two practical cases are also studied, namely the wave-induced second order responses of a semi-submersible platform and the wavedrift-damping effect evaluated through the equilibrium angle of a turret moored FPSO. For the former, some specific model tests were designed and conducted in a wave-basin.<br>Essa tese aborda o desenvolvimento de um método de Rankine de ordem alta no domínio do tempo (TDRPM) para o estudo de problemas lineares e fracamente não lineares, incluindo o efeito de corrente, envolvendo sistemas flutuantes. O método de ordem alta desenvolvido considera a geometria do corpo como descrita pelo padrão Non-uniform Rational Basis Spline (NURBS), que está disponível em diverso0s softwares de Computed Aided Design (CAD) disponíveis, sendo as diversas funções (potencial de velocidades, elevação da superfície-livre e outros) descritos usando B-splines de grau arbitrário. O problema é formulado considerando interações onda-corrente-estrutura para efeitos de até segunda ordem, os de ordem superior sendo calculados considerando as interações somente dos termos de ordem inferior. Para garantir a estabilidade numérica, o problema de contorno com valor inicial é formulado0 com relação ao potencial de velocidade e de parcela local do potencial de acelerações, este para garantir cálculos precisos da pressão dinâmica. O problema de ordem zero é resolvido usando a linearização de corpo-duplo ao invés da linearização de Neumman-Kelvin para permitir a análise de corpos rombudos, o que requer o cálculo de termos-m de grande complexidade. O método adota fontes de Rankine como funções de Green, que são integradas através de quadratura de Gauss-Legendre no domínio todo, exceto com relação aos termos de auto-influência que adotasm um procedimento de dessingularização. O método numérico é inicialmente verificado considerando corpos de geometria simplificada (esfera e cilindro), considerando efeitos de primeira e segunda ordens, com e sem corrente. As derivadas do potencial de velocidade são verificadas comparando os termos-m obtidos numericamente com soluções analíticas disponíveis para a esfera em fluído infinito. As forças de deriva média e dupla-frequência são calculadas para estruturas fixas e flutuantes, sendo as funções calculadas (elevação da superfície, campo de velocidade) comparadas com resultados disponíveis na literatura, incluindo o movimento da esfera flutuante sob a ação de corrente e ondas. São também estudados dois casos de aplicação prática, a resposta de segunda ordem de uma plataforma semi-submersível e o efeito de wave-drift damping para o ângulo de equilíbrio de uma plataforma FPSO ancorada através de sistema turred. No caso da semi-submersível, os ensaios foram projetados e realizados em tanque de provas.
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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 multidimensionnels<br>This 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
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Clamond, Didier. "Amplitudes et phases dans la théorie des ondes de gravité." Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1994GRE10152.
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Dans cette these, la propagation d'une onde courte sur une onde solitaire est etudiee d'un point de vue theorique et experimental. Les equations des ondes de gravite sont non lineaires et la solution generale est inconnue. Alors, des methodes de perturbations sont utilisees pour obtenir une approximation de la solution et une description qualitative des phenomenes. Il y a principalement deux theories de ce type: la theorie de stokes et la theorie de l'eau peu profonde. La theorie de stokes decrit les ondes courtes, et la theorie de l'eau peu profonde les ondes longues. Ces deux theories ne sont jamais valides dans pour les memes valeurs des parametres caracteristiques. Nous etudions l'interaction entre une onde courte et une onde longue, choisir l'une de ces theories est donc impossible: il est necessaire d'en developper une nouvelle. Une methode de perturbation de type wkb, adaptee aux equations non lineaires, donne une theorie capable de decrire des ondes courtes et longues simultanement. Les principaux resultats sont des dephasages et des variations de frequences (effets doppler). La partie experimentale donne des mesures du dephasage subit par l'onde courte. L'accord entre theorie et experience est excellent
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Watson, Francis Maurice. "Better imaging for landmine detection : an exploration of 3D full-wave inversion for ground-penetrating radar." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/better-imaging-for-landmine-detection-an-exploration-of-3d-fullwave-inversion-for-groundpenetrating-radar(720bab5f-03a7-4531-9a56-7121609b3ef0).html.
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Humanitarian clearance of minefields is most often carried out by hand, conventionally using a a metal detector and a probe. Detection is a very slow process, as every piece of detected metal must treated as if it were a landmine and carefully probed and excavated, while many of them are not. The process can be safely sped up by use of Ground-Penetrating Radar (GPR) to image the subsurface, to verify metal detection results and safely ignore any objects which could not possibly be a landmine. In this thesis, we explore the possibility of using Full Wave Inversion (FWI) to improve GPR imaging for landmine detection. Posing the imaging task as FWI means solving the large-scale, non-linear and ill-posed optimisation problem of determining the physical parameters of the subsurface (such as electrical permittivity) which would best reproduce the data. This thesis begins by giving an overview of all the mathematical and implementational aspects of FWI, so as to provide an informative text for both mathematicians (perhaps already familiar with other inverse problems) wanting to contribute to the mine detection problem, as well as a wider engineering audience (perhaps already working on GPR or mine detection) interested in the mathematical study of inverse problems and FWI.We present the first numerical 3D FWI results for GPR, and consider only surface measurements from small-scale arrays as these are suitable for our application. The FWI problem requires an accurate forward model to simulate GPR data, for which we use a hybrid finite-element boundary-integral solver utilising first order curl-conforming N\'d\'{e}lec (edge) elements. We present a novel `line search' type algorithm which prioritises inversion of some target parameters in a region of interest (ROI), with the update outside of the area defined implicitly as a function of the target parameters. This is particularly applicable to the mine detection problem, in which we wish to know more about some detected metallic objects, but are not interested in the surrounding medium. We may need to resolve the surrounding area though, in order to account for the target being obscured and multiple scattering in a highly cluttered subsurface. We focus particularly on spatial sensitivity of the inverse problem, using both a singular value decomposition to analyse the Jacobian matrix, as well as an asymptotic expansion involving polarization tensors describing the perturbation of electric field due to small objects. The latter allows us to extend the current theory of sensitivity in for acoustic FWI, based on the Born approximation, to better understand how polarization plays a role in the 3D electromagnetic inverse problem. Based on this asymptotic approximation, we derive a novel approximation to the diagonals of the Hessian matrix which can be used to pre-condition the GPR FWI problem.
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Simon, Amélie. "Modélisation des phénomènes de films liquides dans les turbines à vapeur." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEC001/document.
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Dans la production d'électricité, un des leviers centraux pour réduire les détériorations et les pertes causées par l'humidité dans les turbines à vapeur est l'étude des films liquides. Ces films minces, sont créés par la déposition de gouttes et sont fortement cisaillés. Des gouttes peuvent ensuite être arrachées du film. A l'heure actuelle, aucun modèle complet et valide n'existe pour décrire ce phénomène. Un modèle 2D à formulation intégrale associé à des lois de fermetures a été dérivé pour représenter ce film. Comparé aux équations classiques de Saint-Venant, le modèle prend en compte davantage d'effets : le transfert de masse, l'impact des gouttes, le cisaillement à la surface libre, la tension de surface, le gradient de pression et la rotation. Une analyse des propriétés du modèle (hyperbolicité, entropie, conservativité, analyse de stabilité linéaire, invariance par translation et par rotation) est réalisée pour juger de la pertinence du modèle. Un nouveau code 2D est implémenté dans un module de développement libre du code EDF Code Saturne et une méthode de volumes finis pour un maillage non-structure a été développée. La vérification du code est ensuite effectuée avec des solutions analytiques dont un problème de Riemann. Le modèle, qui dégénère en modèle classique de Saint-Venant pour le cas d'un film tombant sur un plan inclinée, est validé par l'expérience de Liu and Gollub, 1994, PoF et comparé à des modèles de références (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Un autre cas d'étude met en scène un film cisaillé en condition basse-pression de turbine à vapeur et, est validé par l'expérience de Hammitt et al., 1981, I. Enfin, le code film est couplé aux données 3D du champ de vapeur autour d'un stator d'une turbine basse-pression du parc EDF, issues de Blondel, 2014, PhD thesis. Cette application industrielle montre la faisabilité d'une simulation d'un film en condition réelle du turbine à vapeur<br>In the electricity production, one central key to reduce damages and losses due to wetness in steam turbines is the study of liquid films. These thin films are created by the deposition of droplets and are highly sheared. This film may then be atomized into coarse water. At the moment, no comprehensive and validated model exists to describe this phenomenon. A 2D model based on a integral formulation associated with closure laws is developed to represent this film. Compared to classical Shallow-Water equation, the model takes into account additional effect : mass transfer, droplet impact, shearing at the free surface, surface tension, pressure gradient and the rotation. The model properties (hyperbolicity, entropy, conservativity, linear stability, Galilean invariance and rotational invariance) has been analyzed to judge the pertinence of the model. A new 2D code is implemented in a free module of the code EDF Code Saturne and a finite volume method for unstructured mesh has been developed. The verification of the code is then carried out with analytical solutions including a Riemann problem. The model, which degenerates into classical Shallow-Water equations for the case of a falling liquid film on a inclined plane, is validated by the experiment of Liu and Gollub, 1994, PoF and compared to reference models (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Another study depicts a sheared film under low-pressure steam turbine conditions and is validated by the experiment of Hammitt et al., 1981, FiI. Lastly, the code film is coupled to 3D steam data around a fixed blade of a BP100 turbine, from Blondel, 2014, PhD thesis. This industrial application shows the feasibility of liquid film's simulation in real steam turbine condition
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Yang, Po Chuan, and 楊博全. "Application of the Thermal Wave Theory to Analyze Non-linear Bio-heat Transfer Problems." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/48124089905253247971.
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碩士<br>國立成功大學<br>機械工程學系<br>89<br>With the recent of advance in the biomedical engineering, the research of the bio-heat transfer for human body is increasingly from qualitative analysis to quantitative analysis. Therefore people have to know thoroughly the characteristic and theory of heat transfer for human body. The classical Fourier heat flux model assumes the infinite propagation velocity of thermal wave, which is definitely permitted for the majority of thermal problems. However, the Fourier law breaks down when the heat conduction process in living tissues involves low temperature. Under this circumstance, a finite propagation velocity should be required for such problem. Up to date, the published paper concerning the advanced study of the heat conduction problems with the thermal wave effect for living tissues is limited so this is the main reason why this project is proposed.
This hybrid numerical method is the combination of the Laplace transform technique and the control volume method in conjunction with the least square scheme to analyze the thermal wave phenomena in living tissues. Various examples are illustrated to evidence the precision.
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Izadparast, Amir Hossein. "Semi-empirical Probability Distributions and Their Application in Wave-Structure Interaction Problems." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-12-8763.
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In this study, the semi-empirical approach is introduced to accurately estimate
the probability distribution of complex non-linear random variables in the field of wavestructure
interaction. The structural form of the semi-empirical distribution is developed
based on a mathematical representation of the process and the model parameters are
estimated directly from utilization of the sample data. Here, three probability
distributions are developed based on the quadratic transformation of the linear random
variable. Assuming that the linear process follows a standard Gaussian distribution, the
three-parameter Gaussian-Stokes model is derived for the second-order variables.
Similarly, the three-parameter Rayleigh-Stokes model and the four-parameter Weibull-
Stokes model are derived for the crests, troughs, and heights of non-linear process
assuming that the linear variable has a Rayleigh distribution or a Weibull distribution.
The model parameters are empirically estimated with the application of the conventional
method of moments and the newer method of L-moments. Furthermore, the application
of semi-empirical models in extreme analysis and estimation of extreme statistics is discussed. As a main part of this research study, the sensitivity of the model statistics to
the variability of the model parameters as well as the variability in the samples is
evaluated. In addition, the sample size effects on the performance of parameter
estimation methods are studied.
Utilizing illustrative examples, the application of semi-empirical probability
distributions in the estimation of probability distribution of non-linear random variables
is studied. The examples focused on the probability distribution of: wave elevations and
wave crests of ocean waves and waves in the area close to an offshore structure, wave
run-up over the vertical columns of an offshore structure, and ocean wave power
resources. In each example, the performance of the semi-empirical model is compared
with appropriate theoretical and empirical distribution models. It is observed that the
semi-empirical models are successful in capturing the probability distribution of
complex non-linear variables. The semi-empirical models are more flexible than the
theoretical models in capturing the probability distribution of data and the models are
generally more robust than the commonly used empirical models.
Books on the topic "Non-linear water wave problems"
1
Jeyakumaran, R. Some scattering and sloshing problems in linear water wave theory. Brunel University, 1993.
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Yousuff, Hussaini M., and Institute for Computer Applications in Science and Engineering., eds. Non-linear evolution of a second mode wave in supersonic boundary layers. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1989.
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Yousuff, Hussaini M., and Institute for Computer Applications in Science and Engineering., eds. Non-linear evolution of a second mode wave in supersonic boundary layers. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1989.
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Steward, David R. Analytic Element Method. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198856788.001.0001.
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The Analytic Element Method provides a foundation to solve boundary value problems commonly encountered in engineering and science. The goals are: to introduce readers to the basic principles of the AEM, to provide a template for those interested in pursuing these methods, and to empower readers to extend the AEM paradigm to an even broader range of problems. A comprehensive paradigm: place an element within its landscape, formulate its interactions with other elements using linear series of influence functions, and then solve for its coefficients to match its boundary and interface conditions with nearly exact precision. Collectively, sets of elements interact to transform their environment, and these synergistic interactions are expanded upon for three common types of problems. The first problem studies a vector field that is directed from high to low values of a function, and applications include: groundwater flow, vadose zone seepage, incompressible fluid flow, thermal conduction and electrostatics. A second type of problem studies the interactions of elements with waves, with applications including water waves and acoustics. A third type of problem studies the interactions of elements with stresses and displacements, with applications in elasticity for structures and geomechanics. The Analytic Element Method paradigm comprehensively employs a background of existing methodology using complex functions, separation of variables and singular integral equations. This text puts forth new methods to solving important problems across engineering and science, and has a tremendous potential to broaden perspective and change the way problems are formulated.
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Bouchet, Freddy, Tapio Schneider, Antoine Venaille, and Christophe Salomon, eds. Fundamental Aspects of Turbulent Flows in Climate Dynamics. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198855217.001.0001.
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This book collects the text of the lectures given at the Les Houches Summer School on “Fundamental aspects of turbulent flows in climate dynamics”, held in August 2017. Leading scientists in the fields of climate dynamics, atmosphere and ocean dynamics, geophysical fluid dynamics, physics and non-linear sciences present their views on this fast growing and interdisciplinary field of research, by venturing upon fundamental problems of atmospheric convection, clouds, large-scale circulation, and predictability. Climate is controlled by turbulent flows. Turbulent motions are responsible for the bulk of the transport of energy, momentum, and water vapor in the atmosphere, which determine the distribution of temperature, winds, and precipitation on Earth. Clouds, weather systems, and boundary layers in the oceans and atmosphere are manifestations of turbulence in the climate system. Because turbulence remains as the great unsolved problem of classical physics, we do not have a complete physical theory of climate. The aim of this summer school was to survey what is known about how turbulent flows control climate, what role they may play in climate change, and to outline where progress in this important area can be expected, given today’s computational and observational capabilities. This book reviews the state-of-the-art developments in this field and provides an essential background to future studies. All chapters are written from a pedagogical perspective, making the book accessible to masters and PhD students and all researchers wishing to enter this field. It is complemented by online video of several lectures and seminars recorded during the summer school.
Book chapters on the topic "Non-linear water wave problems"
1
Tomita, H. "On Non-Linear Water Wave Groups and the Induced Mean Flow." In The Ocean Surface. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-015-7717-5_7.
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Teruo, Ushijima, and Matsuki Mihoko. "Fully discrete approximation of a second order linear evolution equation related to the water wave problem." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0085492.
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Alexeyeva, Lyudmila, and Yergali Kurmanov. "Generalized and Fundamental Solutions of Motion Equations of Two-Component Biot’s Medium." In Mathematical Theorems - Boundary Value Problems and Approximations. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92064.
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Here processes of wave propagation in a two-component Biot’s medium are considered, which are generated by arbitrary forces actions. By using Fourier transformation of generalized functions, a fundamental solution, Green tensor, of motion equations of this medium has been constructed in a non-stationary case and in the case of stationary harmonic oscillation. These tensors describe the processes of wave propagation (in spaces of dimensions 1, 2, 3) under an action of power sources concentrated at coordinates origin, which are described by a singular delta-function. Based on them, generalized solutions of these equations are constructed under the action of various sources of periodic and non-stationary perturbations, which are described by both regular and singular generalized functions. For regular acting forces, integral representations of solutions are given that can be used to calculate the stress-strain state of a porous water-saturated medium.
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"The Neumann–Kelvin Problem for a Submerged Body." In Linear Water Waves. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511546778.009.
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"Two-Dimensional Problem for a Surface-Piercing Body." In Linear Water Waves. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511546778.010.
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Ide, Shinji, Takao Sekine, and Masao Fujiu. "NON-LINEAR PROGRAMMING PROBLEMS OF WASTEWATER TREATMENT PROCESSES." In Instrumentation, Control and Automation of Water and Wastewater Treatment and Transport Systems. Elsevier, 1990. http://dx.doi.org/10.1016/b978-0-08-040776-0.50015-9.
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Pradhan, Moumita, Provas Kumar Roy, and Tandra Pal. "Multi-Objective Short-Term Hydro-Thermal Scheduling Using Meta-Heuristic Approaches." In Handbook of Research on Advancements of Swarm Intelligence Algorithms for Solving Real-World Problems. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-3222-5.ch016.
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Every day humans face new challenges to survive in this world. It is a big challenge to utilize hydro and thermal generating unit properly. Researchers are trying to explore new techniques to improve scheduling of generating units. Environmental matter is a big issue to modern society. This chapter suggests a well-organized and effective approach using concept of grey wolf optimization (GWO) to deal with non-linear, multi-objective, short-term, hydro-thermal scheduling (MOHTS) problem. Moreover, authors have incorporated oppositional based learning (OBL) to enhance characteristics of GWO to achieve solution more consistently and accurately. To explore authenticity of our proposed algorithms, GWO and OGWO (oppositional based GWO) are applied to multi-chain cascade of 4-hydro and 3-thermal test system. Effective constraints like valve-point loading, water discharge, water storage, etc., are considered here. Statistical comparisons with other enlisted heuristic methods are done. The projected methods solve MOHTS problem quickly and efficiently.
Conference papers on the topic "Non-linear water wave problems"
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Buchner, Bas, Joris van den Berg, Joop Helder, and Tim Bunnik. "Non-Linear Wave Runup Along the Side of Ships Causing Green Water Problems: Experiments and First CFD Calculations." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-23022.
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Large relative wave motions along the side of a ship can lead to green water on the deck. With a simplified test setup of a thin plate under an angle with the wave direction (to separate non-linear wave run up from motion effects), the non-linear wave reflection along the side of ships is studied in the present paper. These pilot tests with regular and irregular waves gave new insight in the process of non-linear wave run up with plunging and spilling breakers close to the plate. The complex processes observed made clear that linear or second order models will not be able to predict this behavior accurately. Previously [1] it was concluded that CFD methods that allow wave breaking are necessary for a prediction of these important effects. In the present paper a first pilot study is presented with an improved Volume of Fluid (VoF) Method. It is concluded that the method is in principle able to present these relative wave motions, but that a finer gridding is necessary to study the detailed flows.
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Ferreira González, Daniel, Jonas Bechthold, and Moustafa Abdel-Maksoud. "Application of a Boundary Element Method for Wave-Body Interaction Problems Considering the Non-Linear Water Surface." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61852.
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In this paper an existing time domain panel method, which was originally developed for propeller flow simulations, is extended by implementing the mixed Eulerian-Lagrangian approach for the computation of the non-linear free water surface. The three-dimensional panel method uses a constant source and doublet density distribution on each panel and a Dirichlet boundary condition to solve the velocity potential in every time step. Additionally, a formulation for the acceleration potential is included in order to determine the hydrodynamic forces accurately. The paper gives an overview on the governing equations and introduces the numerical approach. Validation results of the developed method are presented for the wave resistance of a submerged spheroid and a wigley hull. Additionally, the wave diffraction due to a surface piercing cylinder in regular waves is validated regarding the forces and the water surface elevation around the body. Here, the computations are compared with other numerical methods as well as tank test results. Apart from this, the paper deals with an application example showing simulations of an artificial service vessel catamaran in waves. The forces on the hull with and without forward speed are presented. The paper concludes with a discussion of the presented results and a brief outlook on further work.
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Luo, Yi, Torgeir Vada, and Marilena Greco. "Numerical Investigation of Wave-Body Interactions in Shallow Water." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-23042.
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Present investigation is based on a numerical study using a time-domain Rankine panel method. The effort and novelty is to extend the applicability of the solver to shallower waters and to steeper waves by including additional non-linear effects, but in a way so to limit the increase in computational costs. The challenge is to assess the improvement with respect to the basic formulation and the recovery of linear theory in the limit of small waves. The wave theories included in the program are Airy, Stokes 5th order and Stream function. By their comparison the effect of the incoming-wave non-linearities can be investigated. For the free-surface boundary conditions two alternative formulations are investigated, one by Hui Sun [1] and one developed here. The two formulations combined with the above-mentioned wave theories are applied to two relevant problems. The first case is a fixed vertical cylinder in regular waves, where numerical results are compared with the model tests by Grue & Huseby [2]. The second case is a freely floating model of a LNG carrier (with zero forward speed) in regular waves, where computations are compared with the experimental results from the EC project “Extreme Seas”. This comparison revealed several challenges such as how to interpret/post process the experimental data. Some of these are described in the paper. After careful handling of both computed and measured data the comparisons show reasonable agreement. It is proven that including more non-linear effects in the free-surface boundary conditions can significantly improve the results. The formulation by Hui Sun gives better results compared to the linear condition, but the present formulation is shown to provide a further improvement, which can be explained through the nonlinear terms included/retained in the two approaches.
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Kim, J. W., R. C. Ertekin, and K. J. Bai. "Linear and Non-Linear Wave Models Based on Hamilton’s Principle and Stream-Function Theory: CMSE and IGN." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29747.
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Recently, two wave models based on the stream-function theory have been derived from Hamilton’s principle for gravity waves. One is the Irrotational Green-Naghdi (IGN) equation and the other is the Complementary Mild-Slope Equation (CMSE). The IGN equation has been derived to describe refraction and diffraction of nonlinear gravity waves in the time domain and in water of finite but arbitrary bathymetry. The CMSE has been derived to consider the same problem in the (linear) frequency domain. In this paper, we first describe the discuss the two models from the viewpoint of Hamilton’s principle. Then the two models are applied to a resonant scattering of Stokes waves over periodic undulations, or the Bragg scattering problem. The numerical results are compared with existing numerical predictions and experimental data. It is found here that Level 3 IGN equation can describe Bragg scattering well for arbitrary bathymetry.
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Abdolmaleki, K., K. P. Thiagarajan, and J. J. Monaghan. "On the Non-Linear Decay Motion of an Oscillatory Plate." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67095.
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We study the non-linear decay motion of a 2D plate experimentally and analytically. The plate was hinged to the bottom of a wave flume and was positioned at a certain initial angle. The restoring force on the plate was derived from two horizontal pre-tensioned springs. To maintain the system characteristics linear, the springs were selected to allow a maximum 18 degrees of rotation for the plate. The position, velocity and the acceleration of the plate were retrieved from the load cells attached to the springs. The plate was released from its initial position at t = 0 and allowed to oscillate. The free-surface elevation was captured using a high frame per second (200 fps) digital camera. In addition, two wave probes on either side of the plate were installed. It was observed that the high stiffness of the springs produced a mild impact to the water that caused a relatively large water run-up and water jet. This event, consequently, made the decay motion very non-linear. A formulation based on the linear theory was developed to help with the understanding and interpreting the physics of the problem. The presented experiment aims to benchmark various numerical techniques such as Smoothed Particle Hydrodynamics (SPH) that intend to simulate free-surface and water impact problems. Although the setup did not model a green water incident, most of the features in the problem, like initial water impact, run up and water jet resemble the physics of green water. In the designed experiment, not only body 3D effects were minimum, but also the system characteristics were linear. Moreover, in contrast to the dam break experiments, perfect initial conditions were achieved. Therefore, the effects of the flow nonlinearities such as the plate impact to the water, water run up-down and water jet were studied without interference of the body nonlinearities. The impact of these effects on the damping and the added mass were highlighted.
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Tang, Tianning, Margaret J. Yelland, and Thomas A. A. Adcock. "The Average Shape of Large Waves in the Norwegian Sea: Is Non-Linear Physics Important?" In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95068.
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Abstract Linear wave theory predicts that in a random sea, the shape of the average wave is given by the scaled autocorrelation function — the “NewWave”. However, the gravity wave problem is non-linear. Numerical simulations of waves on deep water have suggested that their average shape can become modified in a number of ways, including the largest wave in a group tending to move to the front of the group through non-linear dispersion. In this paper we examine whether this occurs for waves in the Norwegian Sea. Field data measured from the weather ship Polarfront is analysed for the period 2000 to 2009. We find that, at this location, the effect of non-linearity is small due to the moderate steepness of the sea-states.
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Jensen, Jo̸rgen Juncher. "Conditional Short-Crested Waves in Shallow Water and With Superimposed Current." In ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/omae2002-28399.
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For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes’ wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean waves is poorly represented, as the shape of the wave spectrum does not enter the wave kinematics. To overcome this problem and still keep the simplicity of a deterministic approach, Tromans, Anaturk and Hagemeijer (1991) suggested the use of a deterministic wave, defined as the expected linear Airy wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected linear short-crested wave riding on a uniform current is given. The analysis is based on the conventional shallow water Airy wave theory and the direction of the main wind direction can make any direction with the current. A consistent derivation of the wave spectrum taking into account current and finite water depth is used. The numerical results show a significant effect of the water depth, the directional spreading and the current on the conditional mean wave profile. Extensions to higher order waves are finally discussed.
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Jensen, Jo̸rgen Juncher. "Conditional Short-Crested Second Order Waves in Shallow Water and With Superimposed Current." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51243.
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For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes’ wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean waves is poorly represented, as the shape of the wave spectrum does not enter the wave kinematics. To overcome this problem and still keep the simplicity of a deterministic approach, Tromans, Anaturk and Hagemeijer (1991) suggested the use of a deterministic wave, defined as the expected linear Airy wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected second order short-crested wave riding on a uniform current is given. The analysis is based on the second order Sharma and Dean shallow water wave theory and the direction of the main wind direction can make any direction with the current. Numerical results showing the importance of the water depth, the directional spreading and the current on the conditional mean wave profile and the associated wave kinematics are presented. A discussion of the use of the conditional wave approach as design waves is given.
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Lye, Jim L., David T. Brown, and Fraser Johnson. "An Investigation Into the Non-Linear Effects Resulting From Air Cushions in the Orecon Oscillating Water Column (OWC) Device." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79115.
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When designing an Oscillating Water Column (OWC) device, the motions and structural responses in waves are of great interest. However, predictions of these motions are complicated by the presence of air chambers above a large proportion of the waterplane area. Modeling the stiffness provided by air cushions at model scale presents a number of problems as air stiffness does not scale according to the laws of Froude scaling. To-date, the closest analogy might be an air-lifted gravity base structure, or crane vessel. However, in an OWC device, the air is not trapped as it is allowed to vent through a turbine. As a result, in still water, none of the mass of the buoy is supported by the air column. However, as the buoy is subjected to waves of increasing height the influence of the air chambers on the motions response becomes more pronounced. Experiments into the behavior of structures with trapped air springs have focused largely on benign sea conditions as the air cushions are generally used in vessels or structures involved with installation operations or similar. In contrast, the behavior of an OWC device must be predicted in all conditions up to, and including, survival conditions. BPP-TECH are providing technical support to the designers of the Orecon MRC wave energy buoy. This buoy uses chambers of varying drafts to generate electricity from the waves. The buoy is tension moored to the sea bed in order to constrain the heave motions to maximize the air pressure within the chambers as waves pass. A series of tank tests were undertaken at the OCEANIDE facility in order to investigate the motions of the buoy while tension moored and also measure the mooring line tensions. This paper will focus on the methods used to represent the air chambers at model scale and will present the results of the tests. A variety of different orifice sizes were used in the test campaign in order to provide a spread of values that would offer an insight into the effect of the air chambers on the motions of the structure in waves.
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Hayatdavoodi, Masoud, and R. Cengiz Ertekin. "A Comparative Study of Nonlinear Shallow-Water Wave Loads on a Submerged Horizontal Box." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-24572.
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This paper is concerned with calculations of the two-dimensional nonlinear vertical and horizontal forces and overturning moment due to the unsteady flow of an inviscid, incompressible fluid over a fully-submerged horizontal, fixed box. The problem is approached on the basis of the Level I Green-Naghdi (GN) theory of shallow-water waves. The main objective of this paper is to present a comparison of the solitary and cnoidal wave loads calculated by use of the GN equations, with those computed by Euler’s equations and the recent laboratory measurements, and also with a linear solution of the problem for small-amplitude waves. The results show a remarkable similarity between the GN and Euler’s models and the laboratory measurements. In particular, the calculations predict that the thickness of the box has no effect on the vertical forces and only a slight influence on the two-dimensional horizontal positive force. The calculations also predict that viscosity of the fluid has a small effect on these loads. The results have applications to various physical problems such as wave forces on submerged coastal bridges and submerged breakwaters.