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1
Lundgren, H., and Torben Sorensen. "A PULSATING WATER TUNNEL." Coastal Engineering Proceedings 1, no. 6 (January 29, 2011): 21. http://dx.doi.org/10.9753/icce.v6.21.
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Since the basic mechanism of sand transportation in wave motion is so far unknown, there is a great need for observations of such transportation in large waves, especially, because of the possible difference of transportation in prototype wave motion from that in small model waves. By means of the apparatus described in the present paper the water and sediment motion near the bed can be reproduced on a prototype scale with the only modification that velocities at all points are in phase.
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Iversen, H. W. "WAVES AND BREAKERS IN SHOALING WATER." Coastal Engineering Proceedings 1, no. 3 (January 1, 2000): 1. http://dx.doi.org/10.9753/icce.v3.1.
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Wiegel and Johnson (1950) summarized useable wave theories for deep and shallow water. Mason (1950) discussed waves in shoaling water and compared theoretical predictions with measurements. The theories are shown to apply, within practical limits, to periodic systems of deep water waves, and to periodic waves progressing over a shoaling bottom to wave positions near the breaking point.
Near and at the breaking position the wave features are not predicted from theory with desired accuracies and measured characteristics are used to describe breakers. The available measurements are limited and do not show the effects of variables such as the beach slope.
Recent work at the University of California has resulted in information on the limits of applicability of the linearized wave theories as applied to wave transformation in shoaling water, and on breaker shapes and motion; including the effect of beach slope.
3
Fang, Ming-Chung, Ming-Ling Lee, and Chwang-Kuo Lee. "Time Simulation of Water Shipping for a Ship Advancing in Large Longitudinal Waves." Journal of Ship Research 37, no. 02 (June 1, 1993): 126–37. http://dx.doi.org/10.5957/jsr.1993.37.2.126.
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The technique of time-domain numerical simulation for the occurrence of water shipping on board in head waves is presented. The nonlinear effects of the large-amplitude motion are treated. These nonlinear factors include the effect of large wave amplitude, large ship motion, the change of hull configuration below the free surface and the nonlinear resultant wave. Therefore, the variation of the potentials and the hydrodynamic coefficients for a ship at each time step must be carefully treated. While handling the determination of the instantaneous wave surface around the ship hull, the complete incident, diffracted, and radiated wave system is used rather than the incident wave only. The complexity of the ship speed effect on the related terms is also treated at each time step, especially for the radiation problems. An experimental setup is also designed to measure the motion response and the relative motion, and comparisons are made. The results show excellent agreement and the validity of the theory is confirmed. The successful development of the present technique can be extended to analyze the dynamic stability, capsize phenomena, and ship motion in irregular waves
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Ramsden, Jerald D., and John H. Nath. "KINEMATICS AND RETURN FLOW IN A CLOSED WAVE FLUME." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 31. http://dx.doi.org/10.9753/icce.v21.31.
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Stokes (1847) showed that finite amplitude progressing waves cause a net drift of fluid, in the direction of wave motion, which occurs in the upper portion of the water column. In a closed wave flume this drift must be accompanied by a return flow toward the wave generator to satisfy the conservation of mass. This study presents Eulerian velocity and water surface measurements soon after the onset of wave motion from 12 locations in a large scale flume. Waves with .67 < kh < 2.29 and .09 < H/h < .39 were produced in a water depth of 3.5 meters. Superimposing the return flow theory of Kim (1984) with seventh order stream function theory is shown to improve the velocity predictions. The measured return flows are a function of time and depth and agree with Kim's theory as a first approximation. The mean water surface set-down agrees with the theory of Brevik (1979) except for the nearly deep water waves.
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Jamali, Mirmosadegh, and Gregory A. Lawrence. "Viscous Wave Interaction Due to Motion of a Surface Wave Over a Sediment Bed." Journal of Offshore Mechanics and Arctic Engineering 128, no. 4 (April 28, 2006): 276–79. http://dx.doi.org/10.1115/1.2217753.
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The results of a flume experiment and a theoretical study of surface wave motion over a fluidized bed are presented. It is shown that a resonant wave interaction between a surface wave and two interfacial waves at the interface of the fresh water and the fluidized bed is a strong mechanism for instability of the interface and the subsequent mixing of the layers. The interfacial waves are subharmonic to the surface wave and form a standing wave at the interface. The interaction is investigated theoretically using a viscous interaction analysis. It is shown that surface wave height and viscous effects are the determining factors in the instability mechanism. The results indicate that the net effect of viscosity on the interaction is to suppress the interfacial waves.
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Bendykowska, Genowefa, and Gosta Werner. "TRANSFORMATION OF SHALLOW WATER WAVE SPECTRA." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 44. http://dx.doi.org/10.9753/icce.v21.44.
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Investigations are presented, on some effects of nonlinearity in the motion of shallow water wave spectra. The waves were generated, mechanically in a laboratory wave flume with fixed bottom. Essential differences with the linear dispersion relation are found, showing vanishing dispersivity of higher frequency spectral components in strongly nonlinear spectra. The mean frequency increases with decreasing water depth. The relation of the peak frequency to the mean frequency varied in the experiments from 0.9 to 0.5, for deep to shallow water wave spectra respectively.
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Onu, Kristjan, and N. Sri Namachchivaya. "Stochastically forced water waves in a circular basin." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2120 (March 10, 2010): 2363–81. http://dx.doi.org/10.1098/rspa.2009.0665.
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An analysis of wave motion under stochastic excitation is presented. The starting point is a Hamiltonian model of surface wave motion. This model is augmented with linear damping and stochastic forcing terms. An asymptotic scaling parameter is then introduced to show that the problem has three time scales. Integrability of the system is established for the case of two wave modes near 1:1 resonance. Stochastic averaging is used to reduce the dimensions of the system from four to two and the evolution of surface waves is now described, over long time scales and small amplitude stochastic forcing, by the evolution of the integrals of motion, as a random process. The domain of the generator of this random process is characterized and it includes a ‘gluing’ boundary condition. The adjoint of the generator yields the Fokker–Planck partial-differential equation (FPE). This equation governs the time evolution of the joint probability density of the two integrals of motion. The coefficients of the FPE are calculated numerically and the steady-state solution is found using the finite-element method. Results of the analysis show a distinct peak in the probability density along one edge of the reduced domain.
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Yuan, Peiyin, Pingyi Wang, and Yu Zhao. "Innovative Method for Ship Navigation Safety Risk Response in Landslide-Induced Wave." Advances in Civil Engineering 2021 (May 27, 2021): 1–10. http://dx.doi.org/10.1155/2021/6640548.
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When the bank of a reservoir slope slides along a weak structural plane at a high speed, “landslide slamming” will occur in the nearby water. The formation of landslide-induced waves is a serious threat to the safety of wharfs, shore marks, buildings in the water, and vessels navigating in reservoir areas. To ensure the safety of navigating ships, this study proposes a landslide-induced wave water ship navigation safety risk response technology. The propagation characteristics of landslide-induced waves are analysed based on a physical model experiment, and the characteristics of a ship's motion response and mooring cable tensions are studied under conditions of bow and stern mooring and multipoint mooring. The influences of the landslide-induced wave direction and ship navigation position on the ship rolling motion characteristics are discussed. The results of this study can further improve the navigation safety of ships in landslide-induced wave waters.
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Umeyama, Motohiko. "Dynamic-pressure distributions under Stokes waves with and without a current." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2111 (December 11, 2017): 20170103. http://dx.doi.org/10.1098/rsta.2017.0103.
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To investigate changes in the instability of Stokes waves prior to wave breaking in shallow water, pressure data were recorded vertically over the entire water depth, except in the near-surface layer (from 0 cm to −3 cm), in a recirculating channel. In addition, we checked the pressure asymmetry under several conditions. The phase-averaged dynamic-pressure values for the wave–current motion appear to increase compared with those for the wave-alone motion; however, they scatter in the experimental range. The measured vertical distributions of the dynamic pressure were plotted over one wave cycle and compared to the corresponding predictions on the basis of third-order Stokes wave theory. The dynamic-pressure pattern was not the same during the acceleration and deceleration periods. Spatially, the dynamic pressure varies according to the faces of the wave, i.e. the pressure on the front face is lower than that on the rear face. The direction of wave propagation with respect to the current directly influences the essential features of the resulting dynamic pressure. The results demonstrate that interactions between travelling waves and a current lead more quickly to asymmetry. This article is part of the theme issue ‘Nonlinear water waves’.
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Kilner, F. A. "MODEL TESTS ON THE MOTION OF MOORED SHIPS PLACED ON LONG WAVES." Coastal Engineering Proceedings 1, no. 7 (January 29, 2011): 40. http://dx.doi.org/10.9753/icce.v7.40.
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The equation of motion for a moored ship, subject to stationary wave action, is presented and discussed. The moorings are longitudinal, the ship is considered to be aligned to the direction of wave motion and positioned at a node, and the wave length is assumed long compared with the ship length. If the motion of the ship is assumed to be simple harmonic, and frictional forces between the ship and the water are neglected, an elementary analysis gives the required relation between the amplitudes of the ship's movement and of the water particle motion associated with the wave, A description is given of some tests carried out on model ships moored in a flume where stationary waves can be generated, and the amplitude and period can be varied independently. In these experiments, the amplitude of ship movement could be measured visually, or inferred from strain gauge readings, and the water motion was also observed. The results of these tests are compared with the simple theory. A table tilting harmonically is shown to be a mechanical analogy to stationary wave action on ships. The hydrodynamic mass for a ship moving in surge or sway motion is measured and is found to depend on the depth of water in which the ship is moored.
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Takano, Yasuhide, Goji T. Etoh, and Gozo Tsujimoto. "MEASUREMENTS OF VORTEX GENERATION AND MOTION AT WIND WAVE SURFACES." Coastal Engineering Proceedings 1, no. 33 (October 15, 2012): 28. http://dx.doi.org/10.9753/icce.v33.waves.28.
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Vortices generated at water surface under wind wave condition are most important phenomena for mass exchange between atmosphere and ocean. To extract vortices from randomly distributed velocity vectors obtained by a PTV, a new method to accurately estimate vorticity is proposed. The proposed method uses the Moving Least Square method which has been developed for grid-less numerical simulation. The optimal size of fitting area is derived theoretically and is confirmed by Monte Carlo simulation. Comparison of the accuracy between the proposed method and the commonly used method shows the advantage of the proposed method. The developed method is applied to the measurements of vorticity near the wind wave interfaces. The results show the generation and movements of the vortices at water surfaces.
12
Rahman, Matiur, and Lokenath Debnath. "Nonlinear diffraction of water waves by offshore stuctures." International Journal of Mathematics and Mathematical Sciences 9, no. 4 (1986): 625–52. http://dx.doi.org/10.1155/s0161171286000807.
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This paper is concerned with a variational formulation of a nonaxisymmetric water wave problem. The full set of equations of motion for the problem in cylindrical polar coordinates is derived. This is followed by a review of the current knowledge on analytical theories and numerical treatments of nonlinear diffraction of water waves by offshore cylindrical structures. A brief discussion is made on water waves incident on a circular harbor with a narrow gap. Special emphasis is given to the resonance phenomenon associated with this problem. A new theoretical analysis is also presented to estimate the wave forces on large conical structures. Second-order (nonlinear) effects are included in the calculation of the wave forces on the conical structures. A list of important references is also given.
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Gonzalez-Rodriguez, David, and Ole Secher Madsen. "PREDICTION OF NET BEDLOAD TRANSPORT RATES OBTAINED IN OSCILLATING WATER TUNNELS AND APPLICABILITY TO REAL SURF ZONE WAVES." Coastal Engineering Proceedings 1, no. 32 (January 19, 2011): 21. http://dx.doi.org/10.9753/icce.v32.sediment.21.
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Experimental studies of sediment transport rates due to nearshore waves are often conducted in oscillating water tunnels (OWTs). In an OWT, the oscillatory motion produced by the piston propagates almost instantaneously along the entire tunnel. Consequently, unlike the wave motion in the sea or in a wave flume, flow in an OWT is uniform along the tunnel, and second-order wave propagation effects (such as Longuet-Higgins's streaming) are absent. The effect of these hydrodynamic differences between OWT and sea waves on sediment transport rates has generally been neglected. In this paper we present a simple, practical formulation to evaluate bed shear stresses and bedload transport rates due to asymmetric and skewed waves plus a current in an OWT, based on fitting the exact results of a rigorous, analytical model of the OWT wave-current boundary layer. By then accounting for real wave effects we find that wave propagation significantly affects the predicted period-averaged net sediment transport rates. Such real wave effects can therefore not be neglected when comparing nearshore transport models with OWT data.
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Thais, L., and J. Magnaudet. "Turbulent structure beneath surface gravity waves sheared by the wind." Journal of Fluid Mechanics 328 (December 10, 1996): 313–44. http://dx.doi.org/10.1017/s0022112096008749.
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New experiments have been carried out in a large laboratory channel to explore the structure of turbulent motion in the water layer beneath surface gravity waves. These experiments involve pure wind waves as well as wind-ruffled mechanically generated waves. A submersible two-component LDV system has been used to obtain the three components of the instantaneous velocity field along the vertical direction at a single fetch of 26 m. The displacement of the free surface has been determined simultaneously at the same downstream location by means of wave gauges. For both types of waves, suitable separation techniques have been used to split the total fluctuating motion into an orbital contribution (i.e. a motion induced by the displacement of the surface) and a turbulent contribution. Based on these experimental results, the present paper focuses on the structure of the water turbulence. The most prominent feature revealed by the two sets of experiments is the enhancement of both the turbulent kinetic energy and its dissipation rate with respect to values found near solid walls. Spectral analysis provides clear indications that wave–turbulence interactions greatly affect energy transfers over a significant frequency range by imposing a constant timescale related to the wave-induced strain. For mechanical waves we discuss several turbulent statistics and their modulation with respect to the wave phase, showing that the turbulence we observed was deeply affected at both large and small scales by the wave motion. An analysis of the phase variability of the bursting suggests that there is a direct interaction between the waves and the underlying turbulence, mainly at the wave crests. Turbulence budgets show that production essentially takes place in the wavy region of the flow, i.e. above the wave troughs. These results are finally used to address the nature of the basic mechanisms governing wave–turbulence interactions.
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Niu, Xiaojing, and Xiping Yu. "A NUMERICAL MODEL FOR WAVE PROPAGATION OVER MUDDY SLOPE." Coastal Engineering Proceedings 1, no. 32 (January 29, 2011): 27. http://dx.doi.org/10.9753/icce.v32.waves.27.
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A numerical model for the interaction between waves and muddy seabed is developed, in which the motion of the movable mud and the motion of water are solved simultaneously. The governing equations for both water and the mud are the continuity equation and the equations of motion for incompressible fluids. Water is treated as a Newtonian fluid, while a visco-elastic-plastic model is used to describe the rheology of the mud. Both the interface between water and the mud and the free water surface are traced by the VOF (Volume of Fluid) method. The numerical method is based on the well-known SMAC method. The numerical model is applied to simulate wave propagation over a muddy slope, and the numerical results are in reasonable agreement with the experimental data. The present model is proved better performance than the traditional analytic model in case that topography change is not negligible.
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Kirke, Alexis, Samuel Freeman, and Eduardo Reck Miranda. "Wireless Interactive Sonification of Large Water Waves to Demonstrate the Facilities of a Large-Scale Research Wave Tank." Computer Music Journal 39, no. 3 (September 2015): 59–70. http://dx.doi.org/10.1162/comj_a_00315.
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Interactive sonification can provide a platform for demonstration and education as well as for monitoring and investigation. We present a system designed to demonstrate the facilities of the UK's most advanced large-scale research wave tank. The interactive sonification of water waves in the “ocean basin” wave tank at Plymouth University consisted of a number of elements: generation of ocean waves, acquisition and sonification of ocean-wave measurement data, and gesture-controlled pitch and amplitude of sonifications. The generated water waves were linked in real time to sonic features via depth monitors and motion tracking of a floating buoy. Types of water-wave patterns, varying in shape and size, were selected and triggered using wireless motion detectors attached to the demonstrator's arms. The system was implemented on a network of five computers utilizing Max/MSP alongside specialist marine research software, and was demonstrated live in a public performance for the formal opening of the Marine Institute building.
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Pizzo, Nick E. "Surfing surface gravity waves." Journal of Fluid Mechanics 823 (June 16, 2017): 316–28. http://dx.doi.org/10.1017/jfm.2017.314.
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A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497–503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.
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Qi, Yusheng, Guangyu Wu, Yuming Liu, Moo-Hyun Kim, and Dick K. P. Yue. "Nonlinear phase-resolved reconstruction of irregular water waves." Journal of Fluid Mechanics 838 (January 25, 2018): 544–72. http://dx.doi.org/10.1017/jfm.2017.904.
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We develop and validate a high-order reconstruction (HOR) method for the phase-resolved reconstruction of a nonlinear wave field given a set of wave measurements. HOR optimizes the amplitude and phase of $L$ free wave components of the wave field, accounting for nonlinear wave interactions up to order $M$ in the evolution, to obtain a wave field that minimizes the reconstruction error between the reconstructed wave field and the given measurements. For a given reconstruction tolerance, $L$ and $M$ are provided in the HOR scheme itself. To demonstrate the validity and efficacy of HOR, we perform extensive tests of general two- and three-dimensional wave fields specified by theoretical Stokes waves, nonlinear simulations and physical wave fields in tank experiments which we conduct. The necessary $L$, for general broad-banded wave fields, is shown to be substantially less than the free and locked modes needed for the nonlinear evolution. We find that, even for relatively small wave steepness, the inclusion of high-order effects in HOR is important for prediction of wave kinematics not in the measurements. For all the cases we consider, HOR converges to the underlying wave field within a nonlinear spatial-temporal predictable zone ${\mathcal{P}}_{NL}$ which depends on the measurements and wave nonlinearity. For infinitesimal waves, ${\mathcal{P}}_{NL}$ matches the linear predictable zone ${\mathcal{P}}_{L}$, verifying the analytic solution presented in Qi et al. (Wave Motion, vol. 77, 2018, pp. 195–213). With increasing wave nonlinearity, we find that ${\mathcal{P}}_{NL}$ contains and is generally greater than ${\mathcal{P}}_{L}$. Thus ${\mathcal{P}}_{L}$ provides a (conservative) estimate of ${\mathcal{P}}_{NL}$ when the underlying wave field is not known.
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Takezawa, Mitsuo, Masaru Mizuguchi, Shintaro Hotta, and Susumu Kubota. "WAVE RUN-UP ON A NATURAL BEACH." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 10. http://dx.doi.org/10.9753/icce.v21.10.
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The swash oscillation, waves and water particle velocity in the surf zone were measured by using 16 mm memo-motion cameras and electromagnetic current meters. It was inferred that incident waves form two-dimensional standing waves with the anti-node in the swash slope. Separation of the incident waves and reflected waves was attempted with good results using small amplitude long wave theory. Reflection coefficient of individual waves ranged between 0.3 and 1.0. The joint distribution of wave heights and periods in the swash oscillation exhibited different distribution from that in and outside the surf zone. This indicates that simple application of wave to wave transformation model fails in the swash zone.
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Adytia, Didit. "Momentum Conservative Scheme for Simulating Wave Runup and Underwater Landslide." Indonesian Journal on Computing (Indo-JC) 4, no. 1 (March 22, 2019): 29. http://dx.doi.org/10.21108/indojc.2019.4.1.250.
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This paper focuses on the numerical modelling and simulation of tsunami waves triggered by an underwater landslide. The equation of motion for water waves is represented by the Nonlinear Shallow Water Equations (NSWE). Meanwhile, the motion of underwater landslide is modeled by incorporating a term for bottom motion into the NSWE. The model is solved numerically by using a finite volume method with a momentum conservative staggered grid scheme that is proposed by Stelling & Duinmeijer 2003 [12]. Here, we modify the scheme for the implementation of bottom motion. The accuracy of the implementation for representing wave runup and rundown is shown by performing the runup of harmonic wave as proposed by Carrier & Greenspan 1958 [2], and also solitary wave runup of Synolakis, 1986 [14], for both breaking and non-breaking cases. For the underwater landslide, result of the simulation is compared with simulation using the Boundary Integral Equation Model (BIEM) that is performed by Lynett and Liu, 2002 [9].
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LONGUET-HIGGINS, MICHAEL S. "Viscous dissipation in steep capillary–gravity waves." Journal of Fluid Mechanics 344 (August 10, 1997): 271–89. http://dx.doi.org/10.1017/s0022112097006046.
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Some simple but exact general expressions are derived for the viscous stresses required at the surface of irrotational capillary–gravity waves of periodic or solitary type on deep water in order to maintain them in steady motion. These expressions are applied to nonlinear capillary waves, and to capillary–gravity waves of solitary type on deep water. In the case of pure capillary waves some algebraic expressions are found for the work done by the surface stresses, from which it is possible to infer the viscous rate of decay of free, nonlinear capillary waves.Similar calculations are carried out for capillary–gravity waves of solitary type on deep water. It is shown that the limiting rate of decay of a solitary wave at low amplitudes is just twice that for linear, periodic waves. This is due to the spreading out of the wave envelope at low wave steepnesses. At large wave steepnesses the dissipation increases by an order of magnitude, owing to the sharply increased curvature in the wave troughs. The calculated rates of decay are in agreement with recent observations.
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Sun, Shi Yan, Hai Long Chen, and Gang Xu. "Water Entry of A Wedge Into Waves in Three Degrees Offreedom." Polish Maritime Research 26, no. 1 (March 1, 2019): 117–24. http://dx.doi.org/10.2478/pomr-2019-0013.
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Abstract The hydrodynamic problem of a two-dimensional wedge entering into a nonlinear wave in three degrees of freedom is investigated based on the incompressible velocity potential theory. The problem is solved through the boundary element method in the time domain. To avoid numerical difficulties due to an extremely small contact area at the initial stage, a stretched coordinate system is used based on the ratio of the Cartesian system in the physical space to the distance travelled by the wedge in the vertical direction. The mutual dependence of body motion and wave loading is decoupled by using the auxiliary function method. Detailed results about body accelerations, velocities and displacements at different Froude numbers or different waves are provided, and the mutual effect between body motion and wave loading is analysed in depth.
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Yang, Zhiwen, Jinzhao Li, Huaqing Zhang, Chunguang Yuan, and Hua Yang. "Experimental Study on 2D Motion Characteristics of Submerged Floating Tunnel in Waves." Journal of Marine Science and Engineering 8, no. 2 (February 15, 2020): 123. http://dx.doi.org/10.3390/jmse8020123.
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Submerged floating tunnel (SFT) is a new type of transportation infrastructure for crossing sea straits in relatively deeper water. Compared with the fixed tunnel, the main challenge in designing a SFT is the stability maintaining in a complex hydrodynamic environment, especially for the wave-induced dynamic load. In this study, a series of systematic experiments were conducted to investigate the 2D motion characteristics (i.e., heave, sway and roll) of the SFT exposed to regular waves. The movement of the SFT model is measured by the image processing method which is a noncontact measurement. The experimental observation of SFT motion during the process of wave and SFT interaction is described in detail, and the influence of several governing parameters is thoroughly analyzed, including the wave height and period, submergence depth, buoyancy to weight ratio (BWR), and the mooring line angle. The results show that the motion amplitudes of SFT increase with the wave height increasing. The effect of wave period is related to the natural period of the structure. The sway, heave and roll of the SFT submerged beneath the water surface are much smaller than that of the SFT on the water surface. With the increase of BWR, the motion of SFT decreases. The motion amplitude increases with mooring line angle increasing. Finally, empirical equations are proposed to estimate the motion characteristics of the SFT.
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Smeltzer, Benjamin K., Eirik Æsøy, and Simen Å. Ellingsen. "Observation of surface wave patterns modified by sub-surface shear currents." Journal of Fluid Mechanics 873 (June 25, 2019): 508–30. http://dx.doi.org/10.1017/jfm.2019.424.
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We report experimental observations of two canonical surface wave patterns – ship waves and ring waves – skewed by sub-surface shear, thus confirming effects predicted by recent theory. Observed ring waves on a still surface with sub-surface shear current are strikingly asymmetric, an effect of strongly anisotropic wave dispersion. Ship waves for motion across a sub-surface current on a still surface exhibit striking asymmetry about the ship’s line of motion, and large differences in transverse wavelength for upstream versus downstream motion are demonstrated, all of which is in good agreement with theoretical predictions. Neither of these phenomena can occur on a depth-uniform current. A quantitative comparison of measured versus predicted average phase shift for a ring wave is grossly mispredicted by no-shear theory, but in good agreement with predictions for the measured shear current. A clear difference in wave frequency within the ring wave packet is observed in the upstream versus downstream direction for all shear flows, while wave dispersive behaviour is identical to that for quiescent water for propagation normal to the shear current, as expected. Peak values of the measured two-dimensional Fourier spectrum for ship waves are shown to agree well with the predicted criterion of stationary ship waves, with the exception of some cases where results are imperfect due to the limited wavenumber resolution, transient effects and/or experimental noise. Experiments were performed on controlled shear currents created in two different ways, with a curved mesh and beneath a blocked stagnant-surface flow. Velocity profiles were measured with particle image velocimetry, and surface waves with a synthetic schlieren method. Our observations lend strong empirical support to recent predictions that wave forces on vessels and structures can be greatly affected by shear in estuarine and tidal waters.
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Paprota, Maciej. "Experimental Study on Spatial Variation of Mass Transport Induced by Surface Waves Generated in a Finite-Depth Laboratory Flume." Journal of Physical Oceanography 50, no. 12 (December 2020): 3501–11. http://dx.doi.org/10.1175/jpo-d-20-0092.1.
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AbstractThe aim of laboratory experiments conducted in a wave flume is to confirm that wave-induced mass transport varies along the way of propagation of regular mechanically generated waves in water of finite depth. This effect is attributed to the interactions between primary waves generated in the flume and associated free waves. Measurements of wave kinematics in several locations along the flume are performed to evaluate mass transport. Wave gauges and the particle image velocimetry technique are employed, respectively, to provide information on the evolution of the oscillating water surface and the wave velocity field under regular waves. Laboratory data are compared with numerical predictions of the derived nonlinear wavemaker model based on a pseudospectral approach. The experimental data exhibit good agreement with the numerical results with respect to particle trajectories and mass transport for nonlinear transitional and shallow water waves. Numerical and experimental investigations confirm that free-surface oscillatory motion and particle kinematics are affected by second-order free waves, which modify the characteristics of laboratory waves, especially in a strongly nonlinear shallow water regime. Moreover, the present study gives valuable insight into the effects of the interaction between two independent waves on wave-induced mass transport, which highlights the need of including nonlinear energy transfers between higher harmonics for the reliable estimation of wave processes in ocean circulation models.
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Wiegel, R. L. "WIND WAVES AND SWELL." Coastal Engineering Proceedings 1, no. 7 (January 29, 2011): 1. http://dx.doi.org/10.9753/icce.v7.1.
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Winds blowing over the water surface generate waves. In general the higher the wind velocity, the larger the fetch over which it blows, and the longer it blows the higher and longer will be the average waves . Waves still under the action of the winds that created them are called wind waves, or a sea. They are forced waves rather than free waves. They are variable in their direction of advance (Arthur, 1949). They are irregular in the direction of propagation. The flow is rotational due to the shear stress of the wind on the water surface and it is quite turbulent as observations of dye in the water indicates. After the waves leave the generating area their characteristics become somewhat different, principally they are smoother, losing the rough appearance due to the disappearance of the multitude of smaller waves on top of the bigger ones and the whitecaps and spray. When running free of the storm the waves are known as swell. In Fig. 1 are shown some photographs taken in the laboratory of waves still rising under the action of wind and this same wave system after it has left the windy section of the wind-wave tunnel. It can be seen thati-the freely running swell has a smoother appearance than the waves in the windy section. The motion of the swell is nearly irrotational and nonturbulent, unless the swell runs into other regions where the water is in turbulent motion. Turbulence is a property of the fluid rather than of the wave motion. After the waves have travelled a distance from the generating area they have lost some energy due to air resistance, internal friction, and by large scale turbulent scattering if they run into other storm areas, and the rest of the energy has become spread over a larger area due to the dispersive and angular spreading characteristics of water gravity waves. All of these mechanisms lead to a decrease in energy density. Thus, the waves become lower in height. In addition, due to their dispersive characteristic the component wave periods tend to segregate in such a way that the longest waves lead the main body of waves and the shortest waves form the tail of the main body of waves. Finally, the swell may travel through areas where winds are present, adding new wind waves to old swell, and perhaps directly increasing or decreasing the size of the old swell.
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Jiao, Jialong, and Songxing Huang. "CFD Simulation of Ship Seakeeping Performance and Slamming Loads in Bi-Directional Cross Wave." Journal of Marine Science and Engineering 8, no. 5 (April 29, 2020): 312. http://dx.doi.org/10.3390/jmse8050312.
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Accurate prediction of ship seakeeping performance in complex ocean environment is a fundamental requirement for ship design and actual operation in seaways. In this paper, an unsteady Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) solver with overset grid technique was applied to estimate the seakeeping performance of an S175 containership operating in bi-directional cross waves. The cross wave is reproduced by linear superposition of two orthogonal regular waves in a rectangle numerical wave tank. The ship nonlinear motion responses, bow slamming loads, and green water on deck induced by cross wave with different control parameters such as wave length and wave heading angle are systemically analyzed. The results demonstrate that both vertical and transverse motion responses, as well as slamming pressure of ship induced by cross wave, can be quite large, and they are quite different from those in regular wave. Therefore, ship navigational safety when suffering cross waves should be further concerned.
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Cavallaro, Luca, Carlo Lo Re, Giovanni Paratore, Antonino Viviano, and Enrico Foti. "RESPONSE OF POSIDONIA OCEANICA TO WAVE MOTION IN SHALLOW-WATERS - PRELIMINARY EXPERIMENTAL RESULTS." Coastal Engineering Proceedings 1, no. 32 (January 30, 2011): 49. http://dx.doi.org/10.9753/icce.v32.waves.49.
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Aim of the present work is to contribute to the knowledge about the interaction between the flow induced by wave and the aquatic vegetation. More in details the results of preliminary tests of an experimental laboratory investigation about the response of a Posidonia Oceanica meadow to wave motion in shallow waters is reported. A wide attention was posed to the behavior of a synthetic plants with plastic material. To this aim an image acquisition technique was used to analyze and compare the movement of both the artificial plant and the real one. The experiments carried out about the interaction between the artificial meadow and the waves showed a significant wave dumping, in particular in the case of plants having the same length of the water depth.
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Wang, Benlong, Xiaoyu Guo, and Chiang C. Mei. "Surface water waves over a shallow canopy." Journal of Fluid Mechanics 768 (March 11, 2015): 572–99. http://dx.doi.org/10.1017/jfm.2015.110.
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The dynamics of water waves passing over a vegetation canopy is modelled theoretically. To simplify the geometry, we examine a periodic array of vertical cylinders fixed on a slowly varying seabed. The macroscale behaviour of wave attenuation is predicted based on microscale dynamics between plants. Interstitial turbulence is modelled by Reynolds equations with a locally constant eddy viscosity determined by energy considerations. Using the asymptotic method of multiple-scale expansions, the slow evolution of waves is derived by considering the coupling with the small-scale motion in the canopy. After numerical solution of the canonical boundary-value problem in a few unit cells, predictions of macroscale effects such as wave attenuation are made and compared with laboratory experiments. The counteracting effects of shoaling and dissipation are discussed for different vegetation densities.
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Lee, Kwangseok, Jeong-won Lee, Kihwan Kim, Donghyeon Yoo, Dong Kim, Woonbong Hwang, Insang Song, and Jae-Yoon Sim. "A Spherical Hybrid Triboelectric Nanogenerator for Enhanced Water Wave Energy Harvesting." Micromachines 9, no. 11 (November 15, 2018): 598. http://dx.doi.org/10.3390/mi9110598.
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Water waves are a continuously generated renewable source of energy. However, their random motion and low frequency pose significant challenges for harvesting their energy. Herein, we propose a spherical hybrid triboelectric nanogenerator (SH-TENG) that efficiently harvests the energy of low frequency, random water waves. The SH-TENG converts the kinetic energy of the water wave into solid–solid and solid–liquid triboelectric energy simultaneously using a single electrode. The electrical output of the SH-TENG for six degrees of freedom of motion in water was investigated. Further, in order to demonstrate hybrid energy harvesting from multiple energy sources using a single electrode on the SH-TENG, the charging performance of a capacitor was evaluated. The experimental results indicate that SH-TENGs have great potential for use in self-powered environmental monitoring systems that monitor factors such as water temperature, water wave height, and pollution levels in oceans.
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SWAN, C., I. P. CUMMINS, and R. L. JAMES. "An experimental study of two-dimensional surface water waves propagating on depth-varying currents. Part 1. Regular waves." Journal of Fluid Mechanics 428 (February 10, 2001): 273–304. http://dx.doi.org/10.1017/s0022112000002457.
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This paper describes an experimental study of two-dimensional surface water waves propagating on a depth-varying current with a non-uniform vorticity distribution. The investigation is divided into two parts. The first concerns the ‘equilibrium’ conditions in which the oscillatory wave motion and the current co-exist. Measurements of the water-surface elevation, the water-particle kinematics, and the near-bed pressure fluctuations are compared to a number of wave and wave–current solutions including a nonlinear model capable of incorporating the vertical structure of the current profile. These comparisons confirm that the near-surface vorticity leads to an important modification of the dispersion equation, and thus affects the nature of the wave-induced orbital motion over the entire water depth. However, the inclusion of vorticity-dependent terms within the dispersion equation is not sufficient to define the combined wave–current flow. The present results suggest that vorticity may lead to a significant change in the water-surface profile. If a current is positively sheared, dU/dz > 0, with negative vorticity at the water surface, as would be the case in a wind-driven current, a wave propagating in the same direction as the current will experience increased crest–trough asymmetry due to the vorticity distribution. With higher and sharper wave crests there is a corresponding increase in both the maximum water-particle accelerations and the maximum horizontal water-particle velocities. These results are consistent with previous theoretical calculations involving uniform vorticity distributions (Simmen & Saffman 1985 and Teles da Silva & Peregrine 1988).The second part of the study addresses the ‘gradually varying’ problem in which there are changes in the current, the wavelength and the wave height due to the initial interaction between the wave and the current. These data show that there is a large and non-uniform change in the current profile that is dependent upon both the steepness of the waves and the vorticity distribution. Furthermore, comparisons between the measured wave height change and a number of solutions based on the conservation of wave action, confirm that the vorticity distribution plays a dominant role. In the absence of a conservation equation for wave action appropriate for nonlinear waves on a depth-varying current, an alternative approach based on the conservation of total energy flux, first proposed by Longuet-Higgins & Stewart (1960), is shown to be in good agreement with the measured data.
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Le, Cong Huan, Hong Yan Ding, Guo Hai Dong, and Pu Yang Zhang. "Experimental Research on the Influences of Wave Height on Towing of 4-Bucket Foundation Platform." Advanced Materials Research 243-249 (May 2011): 4723–27. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.4723.
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Internal air pressure and water pressure of the buckets foundation, acceleration and dragging force of the 4-bucket foundation platform were determined to analyze the influences of wave height on towing when 4-Bucket foundation platform is towing in conditions of a certain towing velocity, mooring point position and draught in different regular waves based on the model test. Comparing platform towing in following and head waves, the heave motion of the latter is more strenuous than that of the former; the stability and seakeeping of the former is better than those of the latter. Roll motion, pitch motion and heave motion appear aggravate phenomenon with the increase of wave height.
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D'Arrigo, Agatino. "HYDROGEOLOGICAL BREAKING CHARACTERISTICS OF WAVES ABOVE FRESH WATER SUBAQUEOUS SOURCES." Coastal Engineering Proceedings 1, no. 5 (January 29, 2011): 11. http://dx.doi.org/10.9753/icce.v5.11.
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After a short review of the usefulness of maritime structures, particularly vertical wall breakwaters, long term observations of hydrogeological breaking on the bottom of Italy's Seas, as caused by the subaqueous source of fresh water, are discussed. The correlation between hydrogeological breaking and wave motion perturbation produced by compressed air or by oil is presented. These considerations are related to the observations of Admiral Alessandro Cialdi on the morphological breaking of waves above sand banks, thus producing calmness in the upper water.
Therefore, it appears possible to establish a very suggestive analogy between the atomic disintegration of the transformation of potential energy of the oscillatory tide wave into kinematic energy of its components (because of breaking), in accordance with the disintegration of the circular motion.
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Li, Yan, and Simen Å. Ellingsen. "Ship waves on uniform shear current at finite depth: wave resistance and critical velocity." Journal of Fluid Mechanics 791 (February 24, 2016): 539–67. http://dx.doi.org/10.1017/jfm.2016.20.
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We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is calculated for the first time, containing in general a non-zero lateral component. While formally apparently a straightforward extension of existing deep water theory, the introduction of finite water depth is physically non-trivial, since the surface waves are now affected by a subtle interplay of the effects of the current and the sea bed. This becomes particularly pronounced when considering the phenomenon of critical velocity, the velocity at which transversely propagating waves become unable to keep up with the moving source. The phenomenon is well known for shallow water, and was recently shown to exist also in deep water in the presence of a shear current (Ellingsen, J. Fluid Mech., vol. 742, 2014, R2). We derive the exact criterion for criticality as a function of an intrinsic shear Froude number $S\sqrt{b/g}$ ($S$ is uniform vorticity, $b$ size of source), the water depth and the angle between the shear current and the ship’s motion. Formulae for both the normal and lateral wave resistance forces are derived, and we analyse their dependence on the source velocity (or Froude number $Fr$) for different amounts of shear and different directions of motion. The effect of the shear current is to increase wave resistance for upstream ship motion and decrease it for downstream motion. Also the value of $Fr$ at which $R$ is maximal is lowered for upstream and increased for downstream directions of ship motion. For oblique angles between ship motion and current there is a lateral wave resistance component which can amount to 10–20 % of the normal wave resistance for side-on shear and $S\sqrt{b/g}$ of order unity. The theory is fully laid out and far-field contributions are carefully separated off by means of Cauchy’s integral theorem, exposing potential pitfalls associated with a slightly different method (Sokhotsky–Plemelj) used in several previous works.
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Pudjaprasetya, S. R., I. Magdalena, and S. S. Tjandra. "A Nonhydrostatic Two-Layer Staggered Scheme for Transient Waves due to Anti-Symmetric Seabed Thrust." Journal of Earthquake and Tsunami 11, no. 01 (March 2017): 1740002. http://dx.doi.org/10.1142/s1793431117400024.
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The development of transient waves generated by bottom motion is studied numerically in this work. A nonhydrostatic numerical scheme, based on solving the two-dimensional Euler equations using two-layer approximation for the vertical direction, is implemented. The dispersion relation of this scheme is shown to agree with the analytical dispersion relation over a wide range of [Formula: see text], where [Formula: see text] denotes the wave number and [Formula: see text] the characteristic water depth. To ensure that a good balance between nonlinearity and dispersion is accommodated by the scheme, the propagation of a solitary wave (undisturbed in shape) was simulated. Our next focus was on the simulation of transient waves generated by bottom motion. After conducting a benchmark test against Hammack’s experimental results for downward bottom motion, an anti-symmetric bottom thrust was considered. The resulting transient waves developed different behavior depending on the water depth. Finally, to mimic the December 2004 tsunami, a seabed motion was generated over Aceh bathymetry. This simulation showed that a package of wave trains developed and propagated towards the Aceh coast, and exhibited inter alia the feature of shoreline withdrawal often observed.
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Lohmann, K., A. Swartz, and C. Lohmann. "Perception of ocean wave direction by sea turtles." Journal of Experimental Biology 198, no. 5 (May 1, 1995): 1079–85. http://dx.doi.org/10.1242/jeb.198.5.1079.
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At the beginning of their offshore migration, hatchling sea turtles enter the ocean at night and establish a course away from land by swimming directly into oceanic waves. How turtles can detect wave direction while swimming under water in darkness, however, has not been explained. Objects in a water column beneath the surface of the ocean describe a circular movement as waves pass above. In principle, swimming turtles might, therefore, detect wave direction by monitoring the sequence of accelerations they experience under water. To determine whether loggerhead (Caretta caretta L.) and green turtle (Chelonia mydas L.) hatchlings can detect wave direction in this way, we constructed a wave motion simulator to reproduce in air the circular movements that occur beneath small ocean waves. Hatchlings suspended in air and subjected to movements that simulated waves approaching from their right sides attempted to turn right, whereas movements that simulated waves from the left elicited left-turning behavior. Movements simulating waves from directly in front of the turtles elicited little turning in either direction. The results demonstrate that hatchling sea turtles can determine the propagation direction of ocean waves by monitoring the circular movements that occur as waves pass above. Although sea turtles are the first animals shown to be capable of detecting wave direction in this way, such an orientation mechanism may be widespread among other transoceanic migrants such as fish and cetaceans.
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Chen, Qin, Ling Zhu, Fengyan Shi, and Steve Brandt. "BOUSSINESQ MODELING OF COMBINED STORM SURGE AND WAVES OVER WETLANDS FORCED BY WIND." Coastal Engineering Proceedings, no. 36v (December 28, 2020): 6. http://dx.doi.org/10.9753/icce.v36v.waves.6.
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Coastal wetlands protect the shoreline and infrastructure by attenuating wind waves and reducing storm surge. It is of importance to accurately quantify the flood protection provided by vegetation. Existing numerical models for hurricane waves and storm surge are based on the phase-averaged wave action balance equation and the nonlinear shallow water equations, respectively, with the wind forcing and vegetal drag as the free surface and bottom boundary conditions. To consider the interaction of waves and surge, the phase-averaged short wave and long wave (storm surge) models can be coupled in a staggered fashion. If the time step of the wave model and storm surge model are 30 minutes and 1 s, respectively, both models would exchange information every 30 minutes. There is no iteration between the wave and surge models at each coupling interval. An alternative to this state-of-the-practice of hurricane wave and storm surge modeling is to simulate the combined wave and surge motion driven by wind and attenuated by wetland vegetation using a phase-resolving Boussinesq model. The objective of this study is threefold: 1) to demonstrate the capability of modeling wave growth by wind, wave reduction by vegetation, and the total water level (wave setup, wind setup and wave runup) using the extended FUNWAVE-TVD model; 2) to analyze the energy balance of the combined wave and surge motion; 3) to examine the momentum balance with an emphasis on the vegetal drag owing to the combined wave orbital velocity and wind-driven current velocity.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/-o_kx4hPvC8
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Miyata, Hideaki, Makoto Kanai, Noriaki Yoshiyasu, and Yohichi Furuno. "Diffraction Waves About an Advancing Wedge Model in Deep Water." Journal of Ship Research 34, no. 02 (June 1, 1990): 105–22. http://dx.doi.org/10.5957/jsr.1990.34.2.105.
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The diffraction of regular waves by advancing wedge models is studied both experimentally and numerically. The nonlinear features of diffracted waves are visualized by wave pattern pictures and the formation is analyzed by the grid-projection method. The experimental observation indicates that the diffracted waves have a number of nonlinear characteristics similar to shock waves due to the interaction of incident waves with the advancing obstacle in the flow-field caused by the advancing motion. Bow waves of both oblique type and normal detached type are observed at remarkably lower Froude numbers than in the case of a ship in steady advance motion. Their occurrence systematically depends on the Froude number and the wedge angle. The numerical simulation of this phenomenon by a finite-difference method shows approximate agreement with the experimental results.
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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 (October 1, 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 that the numerical scheme is unconditionally stable.
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Pizzo, N. E., and W. Kendall Melville. "Vortex generation by deep-water breaking waves." Journal of Fluid Mechanics 734 (October 8, 2013): 198–218. http://dx.doi.org/10.1017/jfm.2013.453.
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AbstractThe connection between wave dissipation by breaking deep-water surface gravity waves and the resulting turbulence and mixing is crucial for an improved understanding of air–sea interaction processes. Starting with the ensemble-averaged Euler equations, governing the evolution of the mean flow, we model the forcing, associated with the breaking-induced Reynolds shear stresses, as a body force describing the bulk scale effects of a breaking deep-water surface gravity wave on the water column. From this, we derive an equation describing the generation of circulation, $\Gamma $, of the ensemble-average velocity field, due to the body force. By examining the relationship between a breaking wave and an impulsively forced fluid, we propose a functional form for the body force, allowing us to build upon the classical work on vortex ring phenomena to both quantify the circulation generated by a breaking wave and describe the vortex structure of the induced motion. Using scaling arguments, we show that $\Gamma = \alpha {(hk)}^{3/ 2} {c}^{3} / g$, where ($c, h, k$) represent a characteristic speed, height and wavenumber of the breaking wave, respectively, $g$ is the acceleration due to gravity and $\alpha $ is a constant. This then allows us to find a direct relationship between the circulation and the wave energy dissipation rate per unit crest length due to breaking, ${\epsilon }_{l} $. Finally, we compare our model and the available experimental data.
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Rodin, A. A., N. A. Rodina, A. A. Kurkin, and E. N. Pelinovsky. "The influence of nonlinear interaction on the evolution of waves in a shallow basin." Известия Российской академии наук. Физика атмосферы и океана 55, no. 4 (September 17, 2019): 82–86. http://dx.doi.org/10.31857/s0002-351555482-86.
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The influence of counter interaction of nonlinear wave in the shallow water has been studied. It is shown that such an interaction leads to a change in the phase of propagation of the main wave, which is forced to propagate along the flow induced by the counter-propagating wave. Estimates of the height of the non-breaking wave at the moment of interaction are in agreement with theoretical predictions. The phase shift in the interaction of non-breaking waves is small enough, but becomes noticeable in the case of the breaking waves motion.
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Fang, M. C., and C. H. Kim. "An Analysis of Water Shipping Between Two Floating Platforms in the Beam Waves." Journal of Offshore Mechanics and Arctic Engineering 109, no. 2 (May 1, 1987): 179–85. http://dx.doi.org/10.1115/1.3257007.
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This paper presents a frequency domain method for predicting the relative wave elevation due to the hydrodynamic interaction between two floating structures in the beam waves. The strip method has been found to be a practically useful technique to analyze the hydrodynamically coupled motions of two parallel structures in waves. The two-dimensional procedure which is an integral equation method is therefore used in this paper. The present study uses the linearized resultant pressure including the interaction effect to calculate the wave elevation. Both diffraction and radiation cases are considered. The relative wave elevations at each hull are investigated and the wave elevation amplitudes along the sea surface between two structures are also analyzed. It was found that some significant waves occur at the coupled resonance of the body motion. Therefore, the water shipping must be considered as an important factor for the safety of cargo transfer problem. The results shown in the paper may be regarded as analytically reasonable from the viewpoint of energy conservation.
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Nguyen, Duoc, Niels Jacobsen, and Dano Roelvink. "Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method." Journal of Marine Science and Engineering 9, no. 1 (January 13, 2021): 76. http://dx.doi.org/10.3390/jmse9010076.
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This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.
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Vivanco, Isis, Bruce Cartwright, A. Ledesma Araujo, Leonardo Gordillo, and Juan F. Marin. "Generation of Gravity Waves by Pedal-Wavemakers." Fluids 6, no. 6 (June 13, 2021): 222. http://dx.doi.org/10.3390/fluids6060222.
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Experimental wave generation in channels is usually achieved through wavemakers (moving paddles) acting on the surface of the water. Although practical for engineering purposes, wavemakers have issues: they perform poorly in the generation of long waves and create evanescent waves in their vicinity. In this article, we introduce a framework for wave generation through the action of an underwater multipoint mechanism: the pedal-wavemaking method. Our multipoint action makes each point of the bottom move with a prescribed pedalling-like motion. We analyse the linear response of waves in a uniform channel in terms of the wavelength of the bottom action. The framework naturally solves the problem of the performance for long waves and replaces evanescent waves by a thin boundary layer at the bottom of the channel. We also show that proper synchronisation of the orbital motion on the bottom can produce waves that mimic deep water waves. This last feature has been proved to be useful to study fluid–structure interaction in simulations based on smoothed particle hydrodynamics.
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NIKORA, VLADIMIR I., ALEXANDER N. SUKHODOLOV, and PAWEL M. ROWINSKI. "Statistical sand wave dynamics in one-directional water flows." Journal of Fluid Mechanics 351 (November 25, 1997): 17–39. http://dx.doi.org/10.1017/s0022112097006708.
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Moving sand waves and the overlying tubulent flow were measured on the Wilga River in Poland, and the Tirnava Mica and Buzau Rivers in Romania. Bottom elevations and flow velocities were measured at six points simultaneously by multi-channel measuring systems. From these data, the linear and two-dimensional sections of the three-dimensional correlation and structure functions and various projections of sand wave three-dimensional spectra were investigated.It was found that the longitudinal wavenumber spectra of the sand waves in the region of large wavenumbers followed Hino's −3 law (S(Kx) ∝K−3x) quite satisfactorily, confirming the theoretical predictions of Hino (1968) and Jain & Kennedy (1974). However, in contrast to Hino (1968), the sand wave frequency spectrum in the high-frequency region was approximated by a power function with the exponent −2, while in the lower-frequency region this exponent is close to −3.A dispersion relation for sand waves has been investigated from analysis of structure functions, frequency spectra and the cross-correlation functions method. For wavelengths less than 0.15–0.25 of the flow depth, their propagation velocity C is inversely proportional to the wavelength λ. When the wavelengths of spectral components are as large as 3–4 times the flow depth, no dispersion occurs. These results proved to be in good qualitative agreement with the theoretical dispersion relation derived from the potential-flow-based analytical models (Kennedy 1969; Jain & Kennedy 1974). We also present another, physically-based, explanation of this phenomenon, introducing two types of sand movement in the form of sand waves. The first type (I) is for the region of large wavenumbers (small wavelengths) and the second one (II) is for the region of small wavenumbers (large wavelengths). The small sand waves move due to the motion of individual sand particles (type I, C∝λ−1) while larger sand waves propagate as a result of the motion of smaller waves on their upstream slopes (type II, C∝λ0). Like the sand particles in the first type, these smaller waves redistribute sand from upstream slopes to downstream ones. Both types result in sand wave movement downstream but with a different propagation velocity.The main characteristics of turbulence, as well as the quantitative values characterizing the modulation of turbulence by sand waves, are also presented.
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Musumeci, Rosaria Ester, Laura Maria Stancanelli, and Enrico Foti. "EXPERIMENTAL INVESTIGATIONS ON FULL DEPTH BUOYANCY FLOWS IN THE PRESENCEOF SURFACE WAVES." Coastal Engineering Proceedings, no. 35 (June 23, 2017): 16. http://dx.doi.org/10.9753/icce.v35.management.16.
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The propagation of density currents in the presence of waves is experimentally investigated by considering a lock exchange schematization. In particular, we perform experiments considering the classical lock release, where the only driving force is buoyancy, as well as lock-exchange experiments with superimposed periodic surface waves, where the driving forces are both buoyancy and the wave-induced orbital motion. The application of an image processing technique is used for the detection of the main features of the front propagation (i.e depth, height, velocity etc.). All experiments are in full-depth conditions. The propagation of the waves is in intermediate water depth conditions. The presence of surface waves induces an orbital motion along the water column able to modify the dynamics of the density current propagation. Results show that the oscillation of the front advancement, as well as the oscillation of the gravity current depth observed in the presence of waves, are directly correlated with the wave period.
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Banaja, M. A., and H. O. Bakodah. "Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/274579.
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The equal width (EW) equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW) equation is obtained by using the method of lines (MOL) based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing theL2andL∞error norms. The results are found in good agreement with exact solution.
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Craig, Walter, Philippe Guyenne, David P. Nicholls, and Catherine Sulem. "Hamiltonian long–wave expansions for water waves over a rough bottom." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2055 (March 8, 2005): 839–73. http://dx.doi.org/10.1098/rspa.2004.1367.
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This paper is a study of the problem of nonlinear wave motion of the free surface of a body of fluid with a periodically varying bottom. The object is to describe the character of wave propagation in a long–wave asymptotic regime, extending the results of R. Rosales & G. Papanicolaou (1983 Stud. Appl. Math. 68 , 89–102) on periodic bottoms for two–dimensional flows.We take the point of view of perturbation of a Hamiltonian system dependent on a small scaling parameter, with the starting point being Zakharov's Hamiltonian (V. E. Zakharov 1968 J. Appl. Mech. Tech. Phys. 9, 1990–1994) for the Euler equations for water waves. We consider bottom topography which is periodic in horizontal variables on a short length–scale, with the amplitude of variation being of the same order as the fluid depth. The bottom may also exhibit slow variations at the same length–scale as, or longer than, the order of the wavelength of the surface waves. We do not take up the question of random bottom variations, a topic which is considered in Rosales & Papanicolaou (1983). In the two–dimensional case of waves in a channel, we give an alternate derivation of the effective Korteweg–de Vries (KdV) equation that is obtained in Rosales & Papanicolaou (1983). In addition, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves, in cases in which the bottom possesses both short and long–scale variations. In certain cases we also obtain unidirectional equations that are similar to the KdV equation. In three dimensions we obtain effective three–dimensional long–wave equations in a Boussinesq scaling regime, and again in certain cases an effective Kadomtsev–Petviashvili (KP) system in the appropriate unidirectional limit. The computations for these results are performed in the framework of an asymptotic analysis of multiple–scale operators. In the present case this involves the Dirichlet–Neumann operator for the fluid domain which takes into account the variations in bottom topography as well as the deformations of the free surface from equilibrium.
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Congy, T., G. A. El, and M. A. Hoefer. "Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves." Journal of Fluid Mechanics 875 (July 26, 2019): 1145–74. http://dx.doi.org/10.1017/jfm.2019.534.
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A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (Phys. Rev. Lett., vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.
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Shipway, B. J., and D. V. Evans. "Wave Trapping by Axisymmetric Concentric Cylinders." Journal of Offshore Mechanics and Arctic Engineering 125, no. 1 (February 1, 2003): 59–64. http://dx.doi.org/10.1115/1.1537727.
Full textAbstract:
It is both a pleasure and privilege to present a paper on the uniqueness of linearized water waves at this mini-symposium in honor of Professor John Wehausen whose classic review article Surface Waves (with E. V. Laitone) has done so much to influence workers in the field in the forty-two years since its publication. The question of the uniqueness of solutions to the linearized water wave equations was settled once and for all in a paper in the Journal of Fluid Mechanics by M. McIver. She constructed a solution for the motion between a pair of fixed rigid surface-piercing cylinders in two dimensions which decayed at large distances from the cylinders. Soon after she was joined by P. McIver in producing an axisymmetric example in the form of a fixed rigid surface-piercing toroid of a special shape which supported an oscillatory motion in its interior fluid region whilst the motion in the exterior region decayed to zero. This wave trapping effect or non-uniqueness occurred for a particular relation between the wave frequency and the toroid geometry. In the present paper we show that such a phenomenon can occur for simple geometries also. In particular we show that wave trapping can occur in the annular region between two partially immersed vertical concentric circular cylindrical shells for particular values of radii and frequencies.