Relevant bibliographies by topics / Water waves

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Water waves'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Water waves"

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Groves, M. D. "Steady Water Waves." Journal of Nonlinear Mathematical Physics 11, no. 4 (January 2004): 435–60. http://dx.doi.org/10.2991/jnmp.2004.11.4.2.

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Strauss, Walter A. "Steady water waves." Bulletin of the American Mathematical Society 47, no. 4 (2010): 671. http://dx.doi.org/10.1090/s0273-0979-2010-01302-1.

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Horikawa, K., H. Maruo, and A. D. D. Craik. "Nonlinear Water Waves." Journal of Applied Mechanics 56, no. 2 (June 1, 1989): 487. http://dx.doi.org/10.1115/1.3176115.

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Constantin, Adrian. "Nonlinear water waves." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1964 (April 13, 2012): 1501–4. http://dx.doi.org/10.1098/rsta.2011.0594.

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Noblesse, Francis, and Chi Yang. "Elementary water waves." Journal of Engineering Mathematics 59, no. 3 (January 10, 2007): 277–99. http://dx.doi.org/10.1007/s10665-006-9115-5.

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Hering, F., C. Leue, D. Wierzimok, and B. Jähne. "Particle tracking velocimetry beneath water waves. Part II: Water waves." Experiments in Fluids 24, no. 1 (January 26, 1998): 10–16. http://dx.doi.org/10.1007/s003480050145.

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Kogelbauer, Florian. "Symmetric irrotational water waves are traveling waves." Journal of Differential Equations 259, no. 10 (November 2015): 5271–75. http://dx.doi.org/10.1016/j.jde.2015.06.025.

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Wilkening, Jon. "Traveling-Standing Water Waves." Fluids 6, no. 5 (May 14, 2021): 187. http://dx.doi.org/10.3390/fluids6050187.

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We propose a new two-parameter family of hybrid traveling-standing (TS) water waves in infinite depth that evolve to a spatial translation of their initial condition at a later time. We use the square root of the energy as an amplitude parameter and introduce a traveling parameter that naturally interpolates between pure traveling waves moving in either direction and pure standing waves in one of four natural phase configurations. The problem is formulated as a two-point boundary value problem and a quasi-periodic torus representation is presented that exhibits TS-waves as nonlinear superpositions of counter-propagating traveling waves. We use an overdetermined shooting method to compute nearly 50,000 TS-wave solutions and explore their properties. Examples of waves that periodically form sharp crests with high curvature or dimpled crests with negative curvature are presented. We find that pure traveling waves maximize the magnitude of the horizontal momentum among TS-waves of a given energy. Numerical evidence suggests that the two-parameter family of TS-waves contains many gaps and disconnections where solutions with the given parameters do not exist. Some of these gaps are shown to persist to zero-amplitude in a fourth-order perturbation expansion of the solutions in powers of the amplitude parameter. Analytic formulas for the coefficients of this perturbation expansion are identified using Chebyshev interpolation of solutions computed in quadruple-precision.
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Alazard, Thomas, Pietro Baldi, and Daniel Han-Kwan. "Control of water waves." Journal of the European Mathematical Society 20, no. 3 (February 13, 2018): 657–745. http://dx.doi.org/10.4171/jems/775.

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Krishnan, E. V. "On shallow water waves." Acta Physica Hungarica 68, no. 3-4 (December 1990): 189–92. http://dx.doi.org/10.1007/bf03156162.

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Dissertations / Theses on the topic "Water waves"

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Gidel, Floriane Marie Pauline. "Variational water-wave models and pyramidal freak waves." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/21730/.

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A little-known fact is that, every week, two ships weighing over 100 tonnes sink in oceans, sometimes with tragic consequences. This alarming observation suggests that maritime structures may be struck by stronger waves than those they were designed to withstand. These are the legendary rogue (or freak) waves, i.e., suddenly appearing huge waves that have traumatised mariners for centuries and currently remain an unavoidable threat to ships, and to their crews and passengers. Thus motivated, an EU-funded collaboration between the Department of Applied Mathematics (Leeds University) and the Maritime Research Institute Netherlands (MARIN) supported this project, in which the ultimate goal, of importance to the international maritime sector, is to develop reliable damage-prediction tools, leading to beneficial impact in terms of both safety and costs. To understand the behaviour of rogue waves, cost-effective water-wave models are derived in both deep and shallow water. Novel mathematical and numerical strategies are introduced to capture the dynamic air-water interface and to ensure conservation of important properties. Specifically, advanced variational Galerkin finite-element methods are used to provide stable simulations of potential-flow water waves in a basin with wavemakers and seabed topography, which allows reliable simulations of rogue waves in a target area. For optimised computational speed, wave absorption is considered with a beach on which waves break and dissipate energy. Robust integrators are therefore introduced to couple the potential-flow model to shallow-water wave dynamics at the beach. Experimental validation of the numerical tank is conducted at Delft University of Technology to ensure accuracy of the simulations from the wavemaker to the beach. The numerical tank is designed for subsequent use by MARIN to investigate the damage caused by rogue waves on structures in order to update maritime design practice and to ensure safety of ships, therefore leading to a competitive commercial advantage across Europe.
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Bird, Charlotte C. "Nonlinear interactions of water waves, wave groups and beaches." Thesis, University of Bristol, 1999. http://hdl.handle.net/1983/c8fedc4e-9c73-4791-b1d8-b4ff14646025.

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Sampson, Joe. "Some solutions of the shallow water wave equations." Swinburne Research Bank, 2008. http://hdl.handle.net/1959.3/35957.

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Thesis (PhD) - Swinburne University of Technology, Faculty of Engineering and Industrial Sciences, 2008.
A thesis presented for the degree of Doctor of Philosophy, Mathematics discipline, Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, 2008. Typescript. Bibliography: p. 245-259.
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Jervis, Mark T. "Some effects of surface tension on water waves and water waves at a wall." Thesis, University of Bristol, 1996. http://hdl.handle.net/1983/d25e7f7d-bea4-4f94-a524-ebdeff698b95.

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The work presented here mainly concerns the effects of surface tension on steep gravity waves. These are investigated by extending a numerical program to include surface tension. The work has been influenced by contact with coastal engineers, and as a result the third chapter is devoted to the study of waves near a wall, in particular on shallow water. The two themes are brought together in the final substantial chapter which has significant implications for the extrapolation of results from small scale experiments to prototype scale. Chapter 1 introduces capillary waves. In chapter 2, results from the potential flow solver for nonlinear almost steady waves are compared with the theoretical work of Longuet-Higgins (1963,1995) and experiments Perlin, Ting & Lin (1993) and found generally to be in agreement. Some differences between our numerical results and the work of these authors are highlighted and explained. Chapter 3 relates to coastal engineering applications and considers a different type of surface wave, the gravity waves found in front of coastal structures. The study focuses on the hydrodynamic parameters on the bed under such waves. In particular, trends as the water depth is decreased and the failure of linear theory on shallow depths. Study of the interaction of such waves with coastal structures is continued in chapter 4. The flow of water due to the overtopping of a vertical wall by waves is modelled. Results for overtopping volume per wave are in general agreement with experimental data on overtopping rates. The model is used to investigate the effect of different shapes for bed geometry in front of the wall. The preceding chapters are brought together in the final sections. The inclusion of surface tension allows us to perform overtopping calculations for the small scale waves often used in wave experiments. We find that surface tension can significantly affect the overtopping volumes and run-up heights
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Marchant, Timothy Robert. "On short-crested water waves." Title page, contents and introduction only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phm3151.pdf.

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Baldock, Thomas Edward. "Non-linear transient water waves." Thesis, Imperial College London, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.432369.

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Metje, Nicole. "Sediment suspension under water waves." Thesis, University of Birmingham, 2002. http://etheses.bham.ac.uk//id/eprint/5264/.

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Data collected in a large scale laboratory wave flume by a research team using the autonomous bottom boundary layer rig, (STABLE) was the subject of this study. The near bed suspension processes were examined relating them to the hydrodynamics. The deployment of a number of sensors allowed the assessment of their individual performance including the analysis of the pump-sampling and acoustic concentration data. Wavelet analysis was applied to identify the influence of STABLE on the vortex ripples in the vicinity of the rig. It revealed that the modification of the ripple dimensions around STABLE's feet was very localised. Sediment suspension was found to be strongly correlated to wave groups. The measured concentrations and empirical models based on convective and diffusive entrainment mechanisms were compared. A model based on the jet like ejection of particles between a vortex pair was developed and showed that lifting of sediments up to ten ripple heights above the bed was possible. A second model, capable of simulating the pumping effect, included this entrainment process to simulate the suspension under wave groups taking the suspension history into account. The behaviour of neutrally buoyant particles in a laboratory wave flume was videoed and revealed jet like ejections and horizontal movement over two or more ripple wavelengths.
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Baumstein, Anatoly I. Saffman P. G. Saffman P. G. "Nonlinear water waves with shear /." Diss., Pasadena, Calif. : California Institute of Technology, 1997. http://resolver.caltech.edu/CaltechETD:etd-01042008-093737.

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Hunter, Samuel. "Waves in shallow water magnetohydrodynamics." Thesis, University of Leeds, 2015. http://etheses.whiterose.ac.uk/11475/.

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The dynamics of planetary and stellar objects are dominated by the fluid motions of electrically conducting media. Often, such fluid is confined to a shallow layer, perhaps in an atmosphere or bounded by stratification. One such layer is the solar tachocline: a thin layer of high velocity shear in the Sun, which is permeated by strong magnetic fields. The discovery of the solar tachocline has inspired the derivation of the equations of shallow water magnetohydrodynamics (SWMHD), in which the small aspect ratio of vertical to horizontal length scales is used to simplify the governing equations. This thesis takes these equations as a base, and aims to build on knowledge of the wave-like dynamics supported in the shallow water system. It will be shown that the analogy between the shallow water and 2D compressible hydrodynamic systems is broken with the introduction of magnetic field, and the differences between the two systems discussed. An energy conservation law will be derived and be used to infer stability properties of the SWMHD system. We will then construct a multi-layer system, and consider linear wave-like perturbations to a motionless basic state with a uniform magnetic field. Particular focus will be on the 2- and 3-layer models, and the effect of magnetic field strength on wave properties. A weakly nonlinear analysis reveals that the single layer and 2-layer rigid lid weakly non-hydrostatic models support solitary and cnoidal waves. The effect of magnetic field in the single layer case translates to a long-time rescaling, but has much more of an effect on the supported modes in the 2-layer model. The phenomenon of three-wave resonance is also supported in the single layer system, and magnetic influence is discussed. In rotating SWMHD, we find that resonant triad interactions are supported only in the presence of magnetic field. Weakly nonlinear predictions are found to be accurate at low disturbance amplitudes, when compared to the results from a fully nonlinear numerical scheme. Exact nonlinear solutions are derived and categorised, and their stability addressed using numerics.
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Zitti, Gianluca. "Avalanche-induced impact water waves." Doctoral thesis, Università Politecnica delle Marche, 2016. http://hdl.handle.net/11566/242980.

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Questa tesi propone un primo studio, mediante un modello bidimensionale semplificato, della generazione di tsunami in bacini d’acqua a causa dell’impatto di valanghe di neve. Uno studio analitico è stato effettuato mediante l’applicazione delle equazioni di bilancio ad un volume di controllo che include la zona di impatto della valanga e di formazione dell’onda. Le equazioni ottenute evidenziano quali sono i parametri fisici coinvolti nel problema. Inoltre, riscrivendo l’equazione di bilancio in termini di moto del baricentro della massa solida sommersa, si ottiene l’equazione di un oscillatore armonico. Lo studio mediate approccio grafico mostra una forma della soluzione simile al caso a coefficienti costanti, confrontabile con i dati sperimentali ed utilizzabile per la determinazione di funzioni predittive del moto della massa solida dopo l’impatto. Lo studio sperimentale è stato condotto mediante prove in canaletta variando le caratteristiche adimensionali della slavina che influenzano la formazione dell’onda e rilevando l’elevazione della superficie libera e il moto della massa solida impattata. Le caratteristiche dell’onda generata e del moto della massa impattata sono state confrontate, mediante regressioni non lineari (NLR), alle caratteristiche della slavina, arrivando a definire due coefficienti che mostrano eccellenti capacità previsionali delle caratteristiche dell’onda generata in prossimità dell’impatto. Il moto del baricentro della massa sommersa può essere efficacemente approssimato con le equazioni del moto dell’oscillatore armonico smorzato a coefficienti costanti. Mediante NLR, i coefficienti di tali equazioni sono stati scritti in termini dei coefficienti predittivi della slavina. Infine, lo studio delle caratteristiche dell’onda nello spazio suggerisce la presenza di una zona in prossimità dell’impatto in cui il comportamento dell’onda è fortemente non lineare, ma le sue caratteristiche posso essere valutate mediante le relazioni fornite.
In this thesis, a first study of the tsunamis generated by the impact of snow avalanches into water basin has been conducted, by means of a simplified two-dimensional (in the vertical plane) model. The problem has been first studied analytically, by applying the mass and momentum balance principles on a control volume, that includes the zones of avalanche impact and wave formation. The obtained equations have highlighted the physical parameters involved in the impulse waves generated by snow avalanches. Further, the balance equation has been written in terms of motion of the submerged solid mass barycentre, obtaining the equation of a simple damped harmonic oscillator (with non constant coefficients). The graphical study of the solution is consistent with the experimental data and has been used for the determination of predictive functions of the motion of the solid mass after the impact. The experiments have been conducted in a water flume, varying the dimensionless avalanche characteristics that affect the wave generation and acquiring the free surface elevation and the motion of the impacted solid mass. The characteristics of both the generated wave and the motion of the impacted mass have been related, using nonlinear regressions, to the avalanche characteristics, obtaining two impulse product parameters. The motion of the submerged mass barycentre has been approximated with the equations of the motion of a simple damped harmonic oscillator with constant coefficients obtaining and, by means of multiple nonlinear least square regressions, the coefficients of such equations have been related to the avalanche characteristics and to the impulse product parameters. Finally, the analysis of the space-depending avalanche characteristics suggests the existence of a zone in the proximity of the impact, where the wave has a strongly nonlinear behavior, but its characteristics can be predicted by the relations described in the present thesis.
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Books on the topic "Water waves"

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Stoker, J. J. Water Waves. Hoboken, NJ, USA: John Wiley & Sons, Inc., 1992. http://dx.doi.org/10.1002/9781118033159.

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Henry, David, Konstantinos Kalimeris, Emilian I. Părău, Jean-Marc Vanden-Broeck, and Erik Wahlén, eds. Nonlinear Water Waves. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-33536-6.

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Horikawa, Kiyoshi, and Hajime Maruo, eds. Nonlinear Water Waves. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-83331-1.

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Constantin, Adrian, Joachim Escher, Robin Stanley Johnson, and Gabriele Villari. Nonlinear Water Waves. Edited by Adrian Constantin. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31462-4.

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Debnath, Lokenath. Nonlinear water waves. Boston: Academic Press, 1994.

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Debnath, Lokenath. Nonlinear water waves. Boston: Academic Press, 1994.

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Oskar, Mahrenholtz, and Markiewicz M, eds. Nonlinear water wave interaction. Southampton: WIT Press, 1999.

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1945-, Dalrymple Robert A., ed. Water Wave Mechanics for Engineers and Scientists. Singapore: World Scientific, 1991.

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Khakimzyanov, Gayaz, Denys Dutykh, Zinaida Fedotova, and Oleg Gusev. Dispersive Shallow Water Waves. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46267-3.

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Galvin, Cyril J. Water waves and coastal processes. Springfield, Va: Cyril Galvin, 1995.

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Book chapters on the topic "Water waves"

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Shen, Samuel S. "Water Waves." In Nonlinear Topics in the Mathematical Sciences, 53–74. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2102-6_3.

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Gavrilyuk, S. L., N. I. Makarenko, and S. V. Sukhinin. "Water Waves." In Waves in Continuous Media, 77–136. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49277-3_3.

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Davis, Julian L. "Water Waves." In Wave Propagation in Solids and Fluids, 108–58. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3886-7_5.

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el Moctar, Bettar Ould, Thomas E. Schellin, and Heinrich Söding. "Water Waves." In Numerical Methods for Seakeeping Problems, 35–57. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-62561-0_4.

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Jain, Sudhir Ranjan, Bhooshan S. Paradkar, and Shashikumar M. Chitre. "Water Waves." In A Primer on Fluid Mechanics with Applications, 111–31. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-20487-6_8.

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Manasseh, Richard. "Water-surface waves." In Fluid Waves, 47–88. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9780429295263-3.

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Kjeldsen, Søren Peter. "Breaking Waves." In Water Wave Kinematics, 453–73. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0531-3_29.

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Gao, Ang, Xiufeng Wu, Shiqiang Wu, Hongpeng Li, Jiangyu Dai, and Fangfang Wang. "Study on Wind Waves Similarity and Wind Waves Spectrum Characteristics in Limited Waters." In Lecture Notes in Civil Engineering, 1220–35. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-6138-0_107.

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AbstractWind waves is an important factor affecting navigation safety and water environment in limited waters such as lakes and bays. Wind wave spectrum represents the frequency domain features of wind waves and has always been the focus of research. Based on the field observation and flume experimental method, the system analysis of similarity of two kinds of situations, discussed nonlinear response of the relationship of the spectral shape parameter of balance field α, β and wind waves basic frequency between factors like wind speed, wind blowing fetch and water depth. By means of wind tunnel flume and prototype observation data of nonlinear regression analysis, The relation formulas of wind wave frequency prediction considering the comprehensive influence of wind speed, wind blowing fetch and water depth is established. Relevant research is of great significance for revealing the evolution characteristics of wind waves in limited waters and guiding navigation safety and water environment management.
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Escher, Joachim. "Breaking Water Waves." In Lecture Notes in Mathematics, 83–119. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31462-4_2.

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Feldmeier, Achim. "Shallow Water Waves." In Theoretical and Mathematical Physics, 295–366. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31022-6_8.

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Conference papers on the topic "Water waves"

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Zou, Zhili, Yalong Zhou, and Kai Yan. "Crescent Waves on Finite Water Depth." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-11322.

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A laboratory experiment on generation and evolution of L2-type crescent waves was performed with focus on the effects of finite water depth on crescent waves. The new results include the critical wave steepness for triggering crescent waves, the characteristics of the wave surface pattern and amplitude spectrum, and the parameters of surface elevation.
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Lader, Pål F., Dag Myrhaug, and Bjo/rnar Pettersen. "Wave Crest Kinematics of Deep Water Breaking Waves." In 27th International Conference on Coastal Engineering (ICCE). Reston, VA: American Society of Civil Engineers, 2001. http://dx.doi.org/10.1061/40549(276)28.

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Yu, Lingyu, Zhenhua Tian, and Liuxian Zhao. "Gas Accumulation Detection in a Water Tank Using Lamb Waves." In ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/smasis2012-8110.

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According to U.S. Nuclear Regulatory Commission (NRC) Generic Letter 2008, the gas accumulation in the nuclear emergency core cooling systems is concerned since it may critically damage pipes, pumps and valves. There is a need to detect the inside gas accumulation including the quantification of gas location and volume. In this paper, we propose a in-situ technique for gas detection in a gas tank by using Lamb waves. Lamb wave propagation in a plate-like structure is affected by the boundary conditions. For structures in air or submerged in liquid, wave propagations are different. When the structure is in contact with liquid such as water, wave energy leaks into it from the solid material. Therefore, the way of gas detection is related to the detection of change in wave propagation characteristics. Experimental tests in a steel water tank were conducted and shown the Lamb wave’s response to the water presence. Theoretical study of Lamb waves propagation on a free plate in air and on a plate with one surface submerged in liquid were then conducted and compared. Further investigation to understand the change in Lamb wave propagation when water is present was conducted with frequency-wavenumber analysis. In the frequency-wavenumber space, it was found that a new plate wave mode, quasi-Scholte wave showed up. A0 Lamb mode showed a decreased propagation while S0 Lamb wave showed no changes. The change in the Lamb wave propagation is found to be frequency dependent.
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Jung, Tae-Hwa, and Changhoon Lee. "Supercritical Group Velocity for Dissipative Waves in Shallow Water." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83279.

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The group velocity for waves with energy dissipation in shallow water was investigated. In the Eulerian viewpoint, the geometric optics approach was used to get, at the first order, complex-valued wave numbers from given real-valued angular frequency, water depth, and damping coefficient. The phase velocity was obtained as the ratio of angular frequency to realvalued wave number. Then, at the second order, we obtained the energy transport equation which gives the group velocity. We also used the Lagrangian geometric optics approach which gives complex-valued angular frequencies from real-valued wave number, water depth, and damping coefficient. A noticeable thing was found that the group velocity is always greater than the phase velocity (i.e., supercritical group velocity) in the presence of energy dissipation which is opposite to the conventional theory for non-dissipative waves. The theory was proved through numerical experiments for dissipative bichromatic waves which propagate on a horizontal bed. Both the wave length and wave energy decrease for waves with energy dissipation. As a result, wave transformation such as shoaling, refraction, and diffraction are all affected by the energy dissipation. This implies that the shoaling, refraction, and diffraction coefficients for dissipative waves are different from the corresponding coefficients for non-dissipative waves. The theory was proved through numerical experiments for dissipative monochromatic waves which propagate normally or obliquely on a planar slope.
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SCHOBER, C. M. "ROGUE WAVES IN DEEP WATER." In Proceedings of the Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704467_0042.

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Dalrymple, Robert A., and Omar Knio. "SPH Modelling of Water Waves." In Fourth Conference on Coastal Dynamics. Reston, VA: American Society of Civil Engineers, 2001. http://dx.doi.org/10.1061/40566(260)80.

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Fenton, John D. "Polynomial Approximation and Water Waves." In 20th International Conference on Coastal Engineering. New York, NY: American Society of Civil Engineers, 1987. http://dx.doi.org/10.1061/9780872626003.015.

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Scheffner, Norman W. "Biperiodic Waves in Shallow Water." In 20th International Conference on Coastal Engineering. New York, NY: American Society of Civil Engineers, 1987. http://dx.doi.org/10.1061/9780872626003.055.

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Dalrymple, Robert A., Younes Nouri, and Zeynab Sabouri-Shargh. "WATER WAVES PROPAGATING OVER MUD." In Proceedings of the 31st International Conference. World Scientific Publishing Company, 2009. http://dx.doi.org/10.1142/9789814277426_0026.

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Osborne, Alfred R. "Nonlinear Fourier Analysis for Shallow Water Waves." In ASME 2021 40th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/omae2021-63933.

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Abstract I consider nonlinear wave motion in shallow water as governed by the KP equation plus perturbations. I have previously shown that broad band, multiply periodic solutions of the KP equation are governed by quasiperiodic Fourier series [Osborne, OMAE 2020]. In the present paper I give a new procedure for extending this analysis to the KP equation plus shallow water Hamiltonian perturbations. We therefore have the remarkable result that a complex class of nonlinear shallow water wave equations has solutions governed by quasiperiodic Fourier series that are a linear superposition of sine waves. Such a formulation is important because it was previously thought that solving nonlinear wave equations by a linear superposition principle was impossible. The construction of these linear superpositions in shallow water in an engineering context is the goal of this paper. Furthermore, I address the nonlinear Fourier analysis of experimental data described by shallow water physics. The wave fields dealt with here are fully two-dimensional and essentially consist of the linear superposition of generalized cnoidal waves, which nonlinearly interact with one another. This includes the class of soliton solutions and their associated Mach stems, both of which are important for engineering applications. The newly discovered phenomenon of “fossil breathers” is also characterized in the formulation. I also discuss the exact construction of Morison equation forces on cylindrical piles in terms of quasiperiodic Fourier series.
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Reports on the topic "Water waves"

1

Saffman, P. G. Research in Nonlinear Water Waves. Fort Belvoir, VA: Defense Technical Information Center, December 1989. http://dx.doi.org/10.21236/ada216996.

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Saffman, P. G. Research in Nonlinear Water Waves. Fort Belvoir, VA: Defense Technical Information Center, July 1990. http://dx.doi.org/10.21236/ada224065.

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Saffman, P. G. Research in Non-Linear Water Waves. Fort Belvoir, VA: Defense Technical Information Center, September 1991. http://dx.doi.org/10.21236/ada251919.

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4

Hammack, J. Multi-Periodic Waves in Shallow Water. Fort Belvoir, VA: Defense Technical Information Center, September 1992. http://dx.doi.org/10.21236/ada256521.

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5

Abdolmaleki, Kourosh. PR-453-134504-R05 On Bottom Stability Upgrade - MS III. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), November 2021. http://dx.doi.org/10.55274/r0012195.

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The extension of the PRCI on bottom stability (OBS) software's applicability to shallow water is assessed. Version 3 of the software has a limitation on water depth; only depths greater than 6 m (20 ft) are accepted. This limitation is likely related to the increasing inaccuracy of linear wave theory as the wave height to water depth ratio increases, as well as caution about breaking wave limits. The usage of linear wave theory inside the software can be categorized into two different types: � Linear regular waves - these are used in the Level 1 module to determine the motions of the water particles as part of the calculation of the hydrodynamic forces; � Linear irregular waves - these are present in the Level 2, Level 3 and ASM modules, where the surface wave energy spectra are converted to the near-seabed wave velocities through the use of a transfer function based on linear wave theory. It is noted that for irregular waves, all wave spectral formulations currently implemented in the OBS software, do not account for water depth. This document addresses the finite water depth and shallow water restrictions and presents a discussion and investigation in two categories: 1. The direct use of the linear theory to describe waves in the Level 1 calculation module; and 2. The direct use of linear spectral transfer functions in the Level 2, Level 3, and ASM modules. The scope of this activity is to prepare a solution for consideration by PRCI and implement the agreed course of action. The solution proposed will be based on the continued use of the linear wave theory. It is noted that higher order wave theories would be more appropriate for shallow water conditions, but due to the currently established methodology in the software, implementation of higher order wave theory is not included within this scope.
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6

Wei, Ge, and James T. Kirby. Simulation of Water Waves by Boussinesq Models. Fort Belvoir, VA: Defense Technical Information Center, March 1998. http://dx.doi.org/10.21236/ada344496.

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7

Dalrymple, Robert A. Modeling Water Waves with Smoothed Particle Hydrodynamics. Fort Belvoir, VA: Defense Technical Information Center, September 2013. http://dx.doi.org/10.21236/ada597658.

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Dalrymple, Robert A. Modeling Water Waves with Smoothed Particle Hydrodynamics. Fort Belvoir, VA: Defense Technical Information Center, September 2011. http://dx.doi.org/10.21236/ada557148.

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9

Holm, D. D., and R. A. Camassa. Dispersive water waves in one and two dimensions. Office of Scientific and Technical Information (OSTI), August 1997. http://dx.doi.org/10.2172/522263.

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Aranda, Iana, Alex Fairhart, Erin Peiffer, Marc Santos, Sahar Shamsi, and Tessa Greco. NREL Waves to Water Prize Program: Capability Matrix. Office of Scientific and Technical Information (OSTI), November 2022. http://dx.doi.org/10.2172/1897224.

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