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Journal articles on the topic 'Non-linear water wave problems'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

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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2

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

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3

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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4

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 pol

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5

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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6

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 fo

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7

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 v

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8

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 exactl

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9

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 wav

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10

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.

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11

Chen, Cheng-Tsung, Jaw-Fang Lee, and Chun-Han Lo. "Mooring Drag Effects in Interaction Problems of Waves and Moored Underwater Floating Structures." Journal of Marine Science and Engineering 8, no. 3 (2020): 146. http://dx.doi.org/10.3390/jmse8030146.

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In contrast to either considering structures with full degrees of freedom but with wave force on mooring lines neglected or with wave scattering and radiation neglected, in this paper, a new analytic solution is presented for wave interaction with moored structures of full degrees of freedom and with wave forces acting on mooring lines considered. The linear potential wave theory is applied to solve the wave problem. The wave fields are expressed as superposition of scattering and radiation waves. Wave forces acting on the mooring lines are calculated using the Morison equation with relative m

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12

Evans, D. V. "Mathematical Techniques for Linear Wave–Structure Interactions." Journal of Ship Research 49, no. 04 (2005): 247–51. http://dx.doi.org/10.5957/jsr.2005.49.4.247.

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It is difficult not to be impressed by the sheer range of Touviah Miloh's research output, and it is all the more remarkable that he has found the time to become a regular contributor to the Water Wave Workshops over many years. Each of his contributions is characterized by the application of powerful mathematical techniques coupled with a keen sense of the underlying physics of the problem under consideration. In the spirit of this approach, this paper offers a review of some of the mathematical techniques that have been employed to tackle a variety of classical linear water-wave problems inv

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13

Scheffner, Norman W. "BIPERIODIC WAVES IN SHALLOW WATER." Coastal Engineering Proceedings 1, no. 20 (1986): 55. http://dx.doi.org/10.9753/icce.v20.55.

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The propagation of waves in shallow water is a phenomenon of significant practical importance. The ability to realistically predict the complex wave characteristics occurring in shallow water regions has always been an engineering goal which would make the development of solutions to practical engineering problems a reality. The difficulty in making such predictions stems from the fact that the equations governing the complex three-dimensional flow regime can not be solved without linearizing the problem. The linear equations are solvable; however, their solutions do not reflect the nonlinear

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14

Bihs, Hans, Kristina Heveling, and Arun Kamath. "REEF3D:NSEWAVE, A THREE-DIMENSIONAL NON-HYDROSTATIC WAVE MODEL ON A FIXED GRID." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 8. http://dx.doi.org/10.9753/icce.v36.waves.8.

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For coastal engineering problems, wave modeling is required for various spatial scales. In recent years, the development of high-resolution Computational Fluid Dynamics (CFD) based numerical wave tanks (NWT) has gained a lot of attention. Here, the Navier-Stokes equations are solved together with a two-phase interface capturing algorithm for the calculation of the free surface location. The interface capturing treatment of the free water surface is performed on fixed grids, allowing for the simulation of complex wave phenomena such as breaking waves. The CFD-based NWT are preferably used for n

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15

Kim, Jeong-Seok, Kyong-Hwan Kim, Jiyong Park, Sewan Park, and Seung Ho Shin. "A Numerical Study on Hydrodynamic Energy Conversions of OWC-WEC with the Linear Decomposition Method under Irregular Waves." Energies 14, no. 6 (2021): 1522. http://dx.doi.org/10.3390/en14061522.

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A numerical study was performed to investigate the applicability of the linear decomposition method for the hydrodynamic energy conversion of an oscillating-water-column type wave energy converter (OWC-WEC). Hydrodynamic problems of the OWC chamber were decomposed into the excitation and radiation problems with the time-domain numerical method based on the linear potential theory. A finite element method was applied to solve the potential flow in the entire fluid domain including OWC chamber structure. The validity of the linear decomposition method was examined by comparing with the direct in

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16

LINTON, C. M., and J. R. CADBY. "Scattering of oblique waves in a two-layer fluid." Journal of Fluid Mechanics 461 (June 25, 2002): 343–64. http://dx.doi.org/10.1017/s002211200200842x.

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We consider problems based on linear water wave theory concerning the interaction of oblique waves with horizontal cylinders in a fluid consisting of 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. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or lower layer are solved using multipole expansions.

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17

Lee, Kwang-Ho, and Yong-Hwan Cho. "Simple Breaker Index Formula Using Linear Model." Journal of Marine Science and Engineering 9, no. 7 (2021): 731. http://dx.doi.org/10.3390/jmse9070731.

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Breaking waves generated by wave shoaling in coastal areas have a close relationship with various physical phenomena in coastal regions. Therefore, it is crucial to accurately predict breaker indexes such as breaking wave height and breaking depth when designing coastal structures. Many studies on wave breaking have been carried out, and many experimental data have been documented. Representative studies on wave breaking provide many empirical formulas for the prediction of breaking index, mainly through hydraulic model experiments. However, the existing empirical formulas for breaking index d

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18

Ak, Turgut, S. Battal Gazi Karakoc, and Anjan Biswas. "Numerical Scheme to Dispersive Shallow Water Waves." Journal of Computational and Theoretical Nanoscience 13, no. 10 (2016): 7084–92. http://dx.doi.org/10.1166/jctn.2016.5675.

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This paper studies dispersive shallow water waves modeled by Rosenau Korteweg-de Vries (KdV) Regularized long wave (RLW) equation or R-KdV-RLW equation that is considered with power law nonlinearity. The numerical algorithm is based on collocation finite element method with quintic B-splines. Test problems including the motion of solitary waves and shock waves are studied to validate the suggested method. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and error norms L2 and L∞. A linear stability analysis based on a Fourier method shows t

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19

Abrahams, I. D., and P. A. Martin. "Fritz Joseph Ursell. 28 April 1923 — 11 May 2012." Biographical Memoirs of Fellows of the Royal Society 59 (January 2013): 407–21. http://dx.doi.org/10.1098/rsbm.2013.0005.

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Fritz Ursell was a singular and influential applied mathematician. He made seminal contributions to research in the mathematical analysis of linear water waves. This required the development of new techniques for the asymptotic evaluation of integrals, especially uniformly valid approximations. He made numerous contributions to the field; for example, he constructed a family of solutions for edge waves on a sloping beach that extended Stokes’s original result, he gave a detailed analysis of the Kelvin ship-wave pattern, and he was the first to prove the existence of trapped modes in water-wave

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20

Cerrato, Antonio, Luis Rodríguez-Tembleque, José A. González, and M. H. Ferri Aliabadi. "A coupled finite and boundary spectral element method for linear water-wave propagation problems." Applied Mathematical Modelling 48 (August 2017): 1–20. http://dx.doi.org/10.1016/j.apm.2017.03.061.

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21

Lee, D., and I. Son. "Optimal shape design of a floating body for minimal water wave forces." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 3 (2011): 752–62. http://dx.doi.org/10.1177/0954406211415200.

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Water waves are the most significant excitation source for floating vessels. The motion of floating vessels needs to be stable against a random water wave environment. In this study, the authors try to find an optimal shape for a floating body that gives minimal water wave excitation forces for a given water wave over a predefined frequency band. First, we propose a shape optimization formulation with a displacement constraint of which the objective function is to minimize water–structure interaction forces. For the calculation of water wave forces, high-order boundary-element analysis softwar

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22

BÜHLER, OLIVER. "Impulsive fluid forcing and water strider locomotion." Journal of Fluid Mechanics 573 (February 2007): 211–36. http://dx.doi.org/10.1017/s002211200600379x.

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This paper presents a study of the global response of a fluid to impulsive and localized forcing; it has been motivated by the recent laboratory experiments on the locomotion of water-walking insects reported in Hu, Chan & Bush (Nature, vol. 424, 2003, p. 663). These insects create both waves and vortices by their rapid leg strokes and it has been a matter of some debate whether either form of motion predominates in the momentum budget. The main result of this paper is to argue that generically both waves and vortices are significant, and that in linear theory they take up the horizontal m

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23

Linton, C. M., and N. G. Kuznetsov. "Non–uniqueness in two–dimensional water wave problems: numerical evidence and geometrical restrictions." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 453, no. 1966 (1997): 2437–60. http://dx.doi.org/10.1098/rspa.1997.0131.

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24

Linton, C. M., and M. McIver. "The interaction of waves with horizontal cylinders in two-layer fluids." Journal of Fluid Mechanics 304 (December 10, 1995): 213–29. http://dx.doi.org/10.1017/s002211209500440x.

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We consider two-dimensional problems based on linear water wave theory concerning the interaction of waves with horizontal cylinders in a fluid consisting of 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. These relations are systematically extended to the two-fluid case. It is shown that for symme

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25

Martinelli, Luca, Piero Ruol, and Giampaolo Cortellazzo. "ON MOORING DESIGN OF WAVE ENERGY CONVERTERS: THE SEABREATH APPLICATION." Coastal Engineering Proceedings 1, no. 33 (2012): 3. http://dx.doi.org/10.9753/icce.v33.structures.3.

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The design of a mooring system of a Wave Energy Converter is a challenging process that points out several unsolved technical problems, mostly related to the highly non-linear hydrodynamic phenomena occurring when high waves (e.g. 8 m high with 200 m wavelength) propagate in relatively shallow waters (e.g. 20 m). The aim of this note is to point out the relevance of the non-linear response of a WEC anchored in relatively shallow waters (shallow in the “non-linear” sense) in terms of loads applied to the mooring lines. Further, the effects of this cyclic load on the anchors is investigated. Not

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26

Harter, Robert, I. David Abrahams, and Michael J. Simon. "The effect of surface tension on trapped modes in water-wave problems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2088 (2007): 3131–49. http://dx.doi.org/10.1098/rspa.2007.0063.

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In this paper the effect of surface tension is considered on two two-dimensional water-wave problems involving pairs of immersed bodies. Both models, having fluid of infinite depth, support localized oscillations, or trapped modes, when capillary effects are excluded. The first pair of bodies is surface-piercing whereas the second pair is fully submerged. In the former case it is shown that the qualitative nature of the streamline shape is unaffected by the addition of surface tension in the free surface condition, no matter how large this parameter becomes. The main objective of this paper, h

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27

Kostense, J. K., K. L. Meijer, M. W. Dingemans, A. E. Mynett, and P. Van den Bosch. "WAVE ENERGY DISSIPATION IN ARBITRARILY SHAPED HARBOURS OF VARIABLE DEPTH." Coastal Engineering Proceedings 1, no. 20 (1986): 147. http://dx.doi.org/10.9753/icce.v20.147.

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A finite element model for combined refraction-diffraction problems of linear water waves has been extended to include the effect of various dissipative mechanisms on wave excitation response in harbours of arbitrary shape and variable depth. Especially, the effects of bottom friction, partial absorption along the harbour, contours, and transmission through permeable breakwaters have been considered. Although, within the mild slope approximation, the model is valid for arbitrary wave lengths, in this paper its effectiveness for harbour design applications is demonstrated for long wave induced

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Dyachenko, A. I., D. I. Kachulin, and V. E. Zakharov. "Super compact equation for water waves." Journal of Fluid Mechanics 828 (September 12, 2017): 661–79. http://dx.doi.org/10.1017/jfm.2017.529.

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Mathematicians and physicists have long been interested in the subject of water waves. The problems formulated in this subject can be considered fundamental, but many questions remain unanswered. For instance, a satisfactory analytic theory of such a common and important phenomenon as wave breaking has yet to be developed. Our knowledge of the formation of rogue waves is also fairly poor despite the many efforts devoted to this subject. One of the most important tasks of the theory of water waves is the construction of simplified mathematical models that are applicable to the description of th

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29

Gąsiorowski, Dariusz. "Modelling of Flood Wave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation." Archives of Hydro-Engineering and Environmental Mechanics 61, no. 3-4 (2014): 111–25. http://dx.doi.org/10.1515/heem-2015-0007.

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Abstract A full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of a moving wet-dry front, which lead to instability in numerical solutions. To overcome these difficulties, a simplified model in the form of a non-linear diffusi

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30

Nguyen, Thao Danh, and Duy The Nguyen. "SIMULATION OF WAVE PRESSURE ON A VERTICAL WALL BASED ON 2-D NAVIER-STOKES EQUATIONS." Science and Technology Development Journal 12, no. 18 (2009): 59–68. http://dx.doi.org/10.32508/stdj.v12i18.2384.

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This paper applies and develops a numerical model based on the two-dimensional vertical Navier-Stokes equations to simulate the temporal and spatial variations of wave parameters in front of vertical walls. A non-uniform grids system is performed in the numerical solution of the model by transforming a variable physical domain to a fixed computational domain. Through present model, beside some basic hydrodynamic problems of water waves such as wave profile and water particle velocities, standing wave pressures at the wall are examined. Numerical results of the present model are compared with l

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31

Konispoliatis, Dimitrios N., and Spyridon A. Mavrakos. "Diffraction and Radiation of Water Waves by a Heaving Absorber in Front of a Bottom-Mounted, V-shaped Breakwater of Infinite Length." Journal of Marine Science and Engineering 9, no. 8 (2021): 833. http://dx.doi.org/10.3390/jmse9080833.

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In the present study, the problems of diffraction and radiation of water waves by a cylindrical heaving wave energy converter (WEC) placed in front of a reflecting V-shaped vertical breakwater are formulated. The idea conceived is based on the possible exploitation of amplified scattered and reflected wave potentials originating from the presence of V-shaped breakwater, towards increasing the WEC’s wave power absorption due to the wave reflections. An analytical solution based on the method of images is developed in the context of linear water wave theory, taking into account the hydrodynamic

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32

Evans, D. V. "The wide-spacing approximation applied to multiple scattering and sloshing problems." Journal of Fluid Mechanics 210 (January 1990): 647–58. http://dx.doi.org/10.1017/s0022112090001434.

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Linear water-wave theor is used in conjuctin with a wide-spacing approximation to develop closed-form expressions for the reflection and transmission coeffcients appropriate to a plane wave incident upon any number of identical equally spaced obstacles in two dimensins, and also to derive a real expressin from which the sloshing requencies, which occur when the bodies are bounded by rigid walls, can be determined. In each case the solutin is in terms of known properties of radiation problems associated with any one of the bodies in isolation.

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33

Nazarov, S. A. "Concentration of the point spectrum on the continuous one in problems of linear water-wave theory." Journal of Mathematical Sciences 152, no. 5 (2008): 674–89. http://dx.doi.org/10.1007/s10958-008-9095-2.

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CHAMPNEYS, ALAN R., and MARK D. GROVES. "A global investigation of solitary-wave solutions to a two-parameter model for water waves." Journal of Fluid Mechanics 342 (July 10, 1997): 199–229. http://dx.doi.org/10.1017/s0022112097005193.

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The model equationformula herearises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravity–capillary water waves. Being Hamiltonian, reversible and depending upon two parameters, it shares the structure of the full steady water-wave problem. Moreover, all known analytical results for local bifurcations of solitary-wave solutions to the full water-wave problem have precise counterparts for the model equation.At the time of writing two major open problems for steady water waves are attracting particular attention. The first concerns the possible existence of

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35

Sclavounos, P. D. "Radiation and diffraction of second-order surface waves by floating bodies." Journal of Fluid Mechanics 196 (November 1988): 65–91. http://dx.doi.org/10.1017/s0022112088002617.

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The paper studies the radiation and diffraction by floating bodies of deep-water bichromatic and bidirectional surface waves subject to the second-order free-surface condition. A theory is developed for the evaluation of the second-order velocity potential and wave forces valid for bodies of arbitrary geometry, which does not involve the evaluation of integrals over the free surface or require an increased accuracy in the solution of the linear problem. Explicit sum- and difference-frequency ‘Green functions’ are derived for the radiation and diffraction problems, obtained from the solution of

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36

Tsai, Chia-Cheng, Tai-Wen Hsu, and Yueh-Ting Lin. "On Step Approximation for Roseau's Analytical Solution of Water Waves." Mathematical Problems in Engineering 2011 (2011): 1–20. http://dx.doi.org/10.1155/2011/607196.

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An indirect eigenfunction marching method (IEMM) is developed to provide step approximations for water wave problems. The bottom profile is in terms of successive flat shelves separated by abrupt steps. The marching conditions are represented by the horizontal velocities at the steps in the solution procedure. The approximated wave field can be obtained by solving a system of linear equations with unknown coefficients which represents the horizontal velocities under a proper basis. It is also demonstrated that this solution method can be exactly reduced to the transfer-matrix method (TM method

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37

Whitaker, Jeffrey S., and Sajal K. Kar. "Implicit–Explicit Runge–Kutta Methods for Fast–Slow Wave Problems." Monthly Weather Review 141, no. 10 (2013): 3426–34. http://dx.doi.org/10.1175/mwr-d-13-00132.1.

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Abstract Linear multistage (Runge–Kutta) implicit–explicit (IMEX) time integration schemes for the time integration of fast-wave–slow-wave problems for which the fast wave has low amplitude and need not be accurately simulated are investigated. The authors focus on three-stage, second-order schemes and show that a scheme recently proposed by one of them (Kar) is unstable for purely oscillatory problems. The instability is reduced if the averaging inherent in the implicit part of the scheme is decentered, sacrificing second-order accuracy. Two alternative schemes are proposed with better stabil

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38

Pierson, Willard J., and Azed Jean-Pierre. "Monte Carlo Simulations of Nonlinear Ocean Wave Records with Implications for Models of Breaking Waves." Journal of Ship Research 43, no. 02 (1999): 121–34. http://dx.doi.org/10.5957/jsr.1999.43.2.121.

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A Monte Carlo method for simulating nonlinear ocean wave records as a function of time is described. It is based on a family of probability density functions developed by Karl Pearson and requires additional knowledge of the dimensionless moments of a postulated nonlinear wave record, which are the skewness and kurtosis. A frequency spectrum is used to simulate a linear record. It is then transformed to a nonlinear record for the chosen values of the skewness and kurtosis. The result is not a perturbation expansion of the nonlinear equations that describe unbroken waves. It yields a simulated

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Smith, M. J. A., M. A. Peter, I. D. Abrahams, and M. H. Meylan. "On the Wiener–Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2242 (2020): 20200360. http://dx.doi.org/10.1098/rspa.2020.0360.

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A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener–Hopf technique. The derivation of the Wiener–Hopf equation is rather different from that which is used traditionally in water-waves problems, and it leads to the required equations directly. It is also shown how the solution can be computed straightforwardly using Cauchy-type integrals, which avoids the need to find the roots of the highly non-trivial dispersion equations. We illustrate the method with some numerical computation

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40

Santo, H., P. H. Taylor, E. Carpintero Moreno, et al. "Extreme motion and response statistics for survival of the three-float wave energy converter M4 in intermediate water depth." Journal of Fluid Mechanics 813 (January 17, 2017): 175–204. http://dx.doi.org/10.1017/jfm.2016.872.

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This paper presents both linear and nonlinear analyses of extreme responses for a multi-body wave energy converter (WEC) in severe sea states. The WEC known as M4 consists of three cylindrical floats with diameters and draft which increase from bow to stern with the larger mid and stern floats having rounded bases so that the overall system has negligible drag effects. The bow and mid float are rigidly connected by a beam and the stern float is connected by a beam to a hinge above the mid float where the rotational relative motion would be damped to absorb power in operational conditions. A ra

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El, Gennady A., Mark A. Hoefer, and Michael Shearer. "Expansion shock waves in regularized shallow-water theory." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2189 (2016): 20160141. http://dx.doi.org/10.1098/rspa.2016.0141.

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We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin–Bona–Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish

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Akrish, Gal, Oded Rabinovitch, and Yehuda Agnon. "Hydroelasticity and nonlinearity in the interaction between water waves and an elastic wall." Journal of Fluid Mechanics 845 (April 25, 2018): 293–320. http://dx.doi.org/10.1017/jfm.2018.207.

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The present study investigates the role of hydroelasticity and nonlinearity in the fundamental problem of the interaction between non-breaking water waves and an elastic wall. To this end, two interaction scenarios are considered: the interaction of a rigid wall supported by springs and a pulse-type wave, and the interaction of an elastic deformable wall and an incident wave group. Both of these scenarios are numerically simulated in a computational domain representing a two-dimensional wave flume. The simplicity of the domain enables one to perform highly efficient simulations using the high-

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ANNENKOV, SERGEI YU, and VICTOR I. SHRIRA. "Numerical modelling of water-wave evolution based on the Zakharov equation." Journal of Fluid Mechanics 449 (December 10, 2001): 341–71. http://dx.doi.org/10.1017/s0022112001006139.

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We develop a new approach to numerical modelling of water-wave evolution based on the Zakharov integrodifferential equation and outline its areas of application.The Zakharov equation is known to follow from the exact equations of potential water waves by the symmetry-preserving truncation at a certain order in wave steepness. This equation, being formulated in terms of nonlinear normal variables, has long been recognized as an indispensable tool for theoretical analysis of surface wave dynamics. However, its potential as the basis for the numerical modelling of wave evolution has not been adeq

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Konispoliatis, Dimitrios N., Ioannis K. Chatjigeorgiou, and Spyridon A. Mavrakos. "Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body." Fluids 6, no. 9 (2021): 320. http://dx.doi.org/10.3390/fluids6090320.

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In the present study, the diffraction and the radiation problems of water waves by a surface-piercing porous cylindrical body are considered. The idea conceived is based on the capability of porous structures to dissipate the wave energy and to minimize the environmental impact, developing wave attenuation and protection. In the context of linear wave theory, a three-dimensional solution based on the eigenfunction expansion method is developed for the determination of the velocity potential of the flow field around the cylindrical body. Numerical results are presented and discussed concerning

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Kim, Sung-Jae, and Weoncheol Koo. "Development of a Three-Dimensional Fully Nonlinear Potential Numerical Wave Tank for a Heaving Buoy Wave Energy Converter." Mathematical Problems in Engineering 2019 (September 19, 2019): 1–17. http://dx.doi.org/10.1155/2019/5163597.

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The hydrodynamic performance of a vertical cylindrical heaving buoy-type floating wave energy converter under large-amplitude wave conditions was calculated. For this study, a three-dimensional fully nonlinear potential-flow numerical wave tank (3D-FN-PNWT) was developed. The 3D-FN-PNWT was based on the boundary element method with Rankine panels. Using the mixed Eulerian–Lagrangian (MEL) method for water particle movement, nonlinear waves were produced in the PNWT. The PNWT can calculate the wave forces acting on the buoy accurately using an acceleration potential approach. The constant panel

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KNOBLES, D. P., S. A. STOTTS, R. A. KOCH, and T. UDAGAWA. "INTEGRAL EQUATION COUPLED MODE APPROACH APPLIED TO INTERNAL WAVE PROBLEMS." Journal of Computational Acoustics 09, no. 01 (2001): 149–67. http://dx.doi.org/10.1142/s0218396x01000449.

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A two-way coupled mode approach based on an integral equation formalism is applied to sound propagation through internal wave fields defined at the 1999 Shallow Water Acoustics Modeling Workshop. Solutions of the coupled equations are obtained using a powerful approach originally introduced in nuclear theory and also used to solve simple nonseparable problems in underwater acoustics. The basic integral equations are slightly modified to permit a Lanczos expansion to form a solution. The solution of the original set of integral equations is then easily recovered from the solution of the modifie

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Li, Hong Liang. "Far Field Solution of Circular Inclusion and Linear Crack by SH-Wave." Key Engineering Materials 462-463 (January 2011): 455–60. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.455.

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Circular inclusion exists widely in natural media, engineering materials and structures, and defects are usually found around the inclusion. When a composite material with circular inclusion and cracks is impacted by the dynamic load, on the one hand, the scattering field produced by the circular inclusion and cracks determines the dynamic stress concentration factor around the circular inclusion, and therefore determines whether the material is damaged or not; on the other hand, the scattering field also presents many characteristic parameters of the inclusion and cracks such as defect compos

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FONTELOS, M. A., and F. DE LA HOZ. "Singularities in water waves and the Rayleigh–Taylor problem." Journal of Fluid Mechanics 651 (April 30, 2010): 211–39. http://dx.doi.org/10.1017/s0022112009992710.

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We describe, by means of asymptotic methods and direct numerical simulation, the structure of singularities developing at the interface between two perfect, inviscid and irrotational fluids of different densities ρ1 and ρ2 and under the action of gravity. When the lighter fluid is on top of the heavier fluid, one encounters the water-wave problem for fluids of different densities. In the limit when the density of the lighter fluid is zero, one encounters the classical water-wave problem. Analogously, when the heavier fluid is on top of the lighter fluid, one encounters the Rayleigh–Taylor prob

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McIver, P., and R. Porter. "The motion of a freely floating cylinder in the presence of a wall and the approximation of resonances." Journal of Fluid Mechanics 795 (April 19, 2016): 581–610. http://dx.doi.org/10.1017/jfm.2016.201.

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A linear theory, based on wide-spacing and high-frequency approximations, is developed to describe resonant behaviour in two-dimensional water-wave problems involving a freely floating half-immersed cylinder in the presence of a vertical rigid wall. The theory is not able to describe the lowest-frequency resonance, but otherwise yields explicit approximations for the locations of resonances in the complex plane and for their corresponding residues. Two problems are investigated in detail: the time-domain motion following a vertical displacement of the cylinder from equilibrium, and the time-ha

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Lee, M. M., and A. T. Chwang. "Wave transformation by a vertical barrier between a single-layer fluid and a two-layer fluid." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 214, no. 6 (2000): 759–69. http://dx.doi.org/10.1243/0954406001523759.

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The reflection and transmission of water waves by a vertical barrier between a homogeneous fluid and a two-layer fluid are investigated for two different types of barrier: type I is a surface-piercing barrier and type II a bottom-standing barrier. For a type I barrier, the lower-layer fluid is the same as the homogeneous fluid and has a higher density than that of the upper-layer fluid. For a type II barrier, the upper layer fluid is the same as the homogeneous fluid and has a lower density than that of the lower-layer fluid. For any given finite thickness of the fluid layers, a hydrostatic eq

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