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Journal articles on the topic 'Wave interactions'
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1
WEBB, G. M., A. R. ZAKHARIAN, M. BRIO, and G. P. ZANK. "Nonlinear and three-wave resonant interactions in magnetohydrodynamics." Journal of Plasma Physics 63, no. 5 (June 2000): 393–445. http://dx.doi.org/10.1017/s0022377800008370.
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Hamiltonian and variational formulations of equations describing weakly nonlinear magnetohydrodynamic (MHD) wave interactions in one Cartesian space dimension are discussed. For wave propagation in uniform media, the wave interactions of interest consist of (a) three-wave resonant interactions in which high-frequency waves may evolve on long space and time scales if the wave phases satisfy the resonance conditions; (b) Burgers self-wave steepening for the magnetoacoustic waves, and (c) mean wave field effects, in which a particular wave interacts with the mean wave field of the other waves. The equations describe four types of resonant triads: slow–fast magnetoacoustic wave interaction, Alfvén–entropy wave interaction, Alfvén–magnetoacoustic wave interaction, and magnetoacoustic–entropy wave interaction. The formalism is restricted to coherent wave interactions. The equations are used to investigate the Alfvén-wave decay instability in which a large-amplitude forward propagating Alfvén wave decays owing to three-wave resonant interaction with a backward-propagating Alfvén wave and a forward-propagating slow magnetoacoustic wave. Exact solutions of the equations for Alfvén–entropy wave interactions are also discussed.
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Momynov, S. B., E. S. Mukhametkarimov, I. R. Gabitov, and A. E. Davletov. "Nonlinear wave interactions in modern photonics." Physical Sciences and Technology 2, no. 1 (2015): 30–36. http://dx.doi.org/10.26577/2409-6121-2015-2-1-30-36.
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Lin, Ray Q., and Will Perrie. "Nonlinear wave-wave interactions and wedge waves." Chinese Journal of Oceanology and Limnology 23, no. 2 (June 2005): 129–43. http://dx.doi.org/10.1007/bf02894229.
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Matsuba, Yoshinao, Takenori Shimozono, and Yoshimitsu Tajima. "OBSERVATION OF NEARSHORE WAVE-WAVE INTERACTION USING UAV." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 12. http://dx.doi.org/10.9753/icce.v36.waves.12.
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Infragravity waves, generated by nearshore wave-wave interaction, potentially increase the coastal hazard. Lack of detailed observation of nearshore wave fields however makes it difficult to fully understand the behavior of infragravity waves under wave-wave interactions. These days, UAVs (Unmanned Aerial Vehicles) have enabled us to easily capture the top-view images of the dynamic nearshore behavior with sufficiently high spatial and temporal resolutions. In this study, we conducted UAV-based observations of cross-shore variations of wave spectral characteristics to clarify the nearshore wave-wave interactions.
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Lin, Lihwa, Zeki Demirbilek, Jinhai Zheng, and Hajime Mase. "RAPID CALCULATION OF NONLINEAR WAVE-WAVE INTERACTIONS." Coastal Engineering Proceedings 1, no. 32 (January 27, 2011): 36. http://dx.doi.org/10.9753/icce.v32.waves.36.
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This paper presents an efficient numerical algorithm for the nonlinear wave-wave interactions that can be important in the evolution of coastal waves. Indeed, ocean waves truly interact with each others. However, because ocean waves can also interact with the atmosphere such as under variable wind and pressure fields, and waves will deform from deep to shallow water, it is generally difficult to differentiate the actual amount of the nonlinear energy transfer among spectral waves mixed with the atmospheric input and wave breaking. The classical derivation of the nonlinear wave energy transfer has involved tedious numerical calculation that appears impractical to the engineering application. The present study proposed a theoretically based formulation to efficiently calculate nonlinear wave-wave interactions in the spectral wave transformation equation. It is approved to perform well in both idealized and real application examples. This rapid calculation algorithm indicates the nonlinear energy transfer is more significant in the intermediate depth than in deep and shallow water conditions.
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WEBB, G. M., A. ZAKHARIAN, M. BRIO, and G. P. ZANK. "Wave interactions in magnetohydrodynamics, and cosmic-ray-modified shocks." Journal of Plasma Physics 61, no. 2 (February 1999): 295–346. http://dx.doi.org/10.1017/s0022377898007399.
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Multiple-scales perturbation methods are used to study wave interactions in magnetohydrodynamics (MHD), in one Cartesian space dimension, with application to cosmic-ray-modified shocks. In particular, the problem of the propagation and interaction of short wavelength MHD waves, in a large-scale background flow, modified by cosmic rays is studied. The wave interaction equations consist of seven coupled evolution equations for the backward and forward Alfvén waves, the backward and forward fast and slow magnetoacoustic waves and the entropy wave. In the linear wave regime, the waves are coupled by wave mixing due to gradients in the background flow, cosmic-ray squeezing instability effects, and damping due to the diffusing cosmic rays. In the most general case, the evolution equations also contain nonlinear wave interaction terms due to Burgers self wave steepening for the magnetoacoustic modes, resonant three wave interactions, and mean wave field interaction terms. The form of the wave interaction equations in the ideal MHD case is also discussed. Numerical simulations of the fully nonlinear cosmic ray MHD model equations are compared with spectral code solutions of the linear wave interaction equations for the case of perpendicular, cosmic-ray-modified shocks. The solutions are used to illustrate how the different wave modes can be generated by wave mixing, and the modification of the cosmic ray squeezing instability due to wave interactions. It is shown that the Alfvén waves are coupled to the magnetoacoustic and entropy waves due to linear wave mixing, only in background flows with non-zero field aligned electric current and/or vorticity (i.e. if B·∇×B≠0 and/or B·∇×u≠0, where B and u are the magnetic field induction and fluid velocity respectively).
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ZHU, QIANG, YUMING LIU, and DICK K. P. YUE. "Resonant interactions between Kelvin ship waves and ambient waves." Journal of Fluid Mechanics 597 (February 1, 2008): 171–97. http://dx.doi.org/10.1017/s002211200700969x.
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We consider the nonlinear interactions between the steady Kelvin waves behind an advancing ship and an (unsteady) ambient wave. It is shown that, for moderately steep ship waves and/or ambient waves, third-order (quartet) resonant interaction among the two wave systems could occur, leading to the generation of a new propagating wave along a specific ray in the Kelvin wake. The wave vector of the generated wave as well as the angle of the resonance ray are determined by the resonance condition and are functions of the ship forward speed and the wave vector of the ambient wave. To understand the resonance mechanism and the characteristics of the generated wave, we perform theoretical analyses of this problem using two related approaches. To obtain a relatively simple model in the form of a nonlinear Schrödinger (NLS) equation for the evolution of the resonant wave, we first consider a multiple-scale approach assuming locally discrete Kelvin wave components, with constant wave vectors but varying amplitudes along the resonance ray. This NLS model captures the key resonance mechanism but does not account for the detuning effect associated with the wave vector variation of Kevin waves in the neighbourhood of the resonance ray. To obtain the full quantitative features and evolution characteristics, we also consider a more complete model based on Zakharov's integral equation applied in the context of a continuous wave vector spectrum. The resulting evolution equation can be reduced to an NLS form with, however, cross-ray variable coefficients, on imposing a narrow-band assumption valid in the neighbourhood of the resonance ray. As expected, the two models compare well when wave vector detuning is small, in the near wake close to the ray. To verify the analyses, direct high-resolution simulations of the nonlinear wave interaction problem are obtained using a high-order spectral method. The simulations capture the salient features of the resonance in the near wake of the ship, with good agreements with theory for the location of the resonance and the growth rate of the generated wave.
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Casaday, B., and J. Crockett. "Investigation of High-Frequency Internal Wave Interactions with an Enveloped Inertia Wave." International Journal of Geophysics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/863792.
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Using ray theory, we explore the effect an envelope function has on high-frequency, small-scale internal wave propagation through a low-frequency, large-scale inertia wave. Two principal interactions, internal waves propagating through an infinite inertia wavetrain and through an enveloped inertia wave, are investigated. For the first interaction, the total frequency of the high-frequency wave is conserved but is not for the latter. This deviance is measured and results of waves propagating in the same direction show the interaction with an inertia wave envelope results in a higher probability of reaching that Jones' critical level and a reduced probability of turning points, which is a better approximation of outcomes experienced by expected real atmospheric interactions. In addition, an increase in wave action density and wave steepness is observed, relative to an interaction with an infinite wavetrain, possibly leading to enhanced wave breaking.
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Smith, Warren R. "Wave–structure interactions for the distensible tube wave energy converter." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2192 (August 2016): 20160160. http://dx.doi.org/10.1098/rspa.2016.0160.
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A comprehensive linear mathematical model is constructed to address the open problem of the radiated wave for the distensible tube wave energy converter. This device, full of sea water and located just below the surface of the sea, undergoes a complex interaction with the waves running along its length. The result is a bulge wave in the tube which, providing certain criteria are met, grows in amplitude and captures the wave energy through the power take-off mechanism. Successful optimization of the device means capturing the energy from a much larger width of the sea waves (capture width). To achieve this, the complex interaction between the incident gravity waves, radiated waves and bulge waves is investigated. The new results establish the dependence of the capture width on absorption of the incident wave, energy loss owing to work done on the tube, imperfect tuning and the radiated wave. The new results reveal also that the wave–structure interactions govern the amplitude, phase, attenuation and wavenumber of the transient bulge wave. These predictions compare well with experimental observations.
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Elsayed, Mohamed A. K. "Nonlinear Wave-Wave Interactions." Journal of Coastal Research 243 (May 2008): 798–803. http://dx.doi.org/10.2112/05-0445.1.
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JAVAM, A., J. IMBERGER, and S. W. ARMFIELD. "Numerical study of internal wave–wave interactions in a stratified fluid." Journal of Fluid Mechanics 415 (July 25, 2000): 65–87. http://dx.doi.org/10.1017/s0022112000008594.
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A finite volume method is used to study the generation, propagation and interaction of internal waves in a linearly stratified fluid. The internal waves were generated using single and multiple momentum sources. The full unsteady equations of motion were solved using a SIMPLE scheme on a non-staggered grid. An open boundary, based on the Sommerfield radiation condition, allowed waves to propagate through the computational boundaries with minimum reflection and distortion. For the case of a single momentum source, the effects of viscosity and nonlinearity on the generation and propagation of internal waves were investigated.Internal wave–wave interactions between two wave rays were studied using two momentum sources. The rays generated travelled out from the sources and intersected in interaction regions where nonlinear interactions caused the waves to break. When two rays had identical properties but opposite horizontal phase velocities (symmetric interaction), the interactions were not described by a triad interaction mechanism. Instead, energy was transferred to smaller wavelengths and, a few periods later, to standing evanescent modes in multiples of the primary frequency (greater than the ambient buoyancy frequencies) in the interaction region. The accumulation of the energy caused by these trapped modes within the interaction region resulted in the overturning of the density field. When the two rays had different properties (apart from the multiples of the forcing frequencies) the divisions of the forcing frequencies as well as the combination of the different frequencies were observed within the interaction region.The model was validated by comparing the results with those from experimental studies. Further, the energy balance was conserved and the dissipation of energy was shown to be related to the degree of nonlinear interaction.
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Ghosh, B., and K. P. Das. "Nonlinear interactions of two compressional hydromagnetic waves." Journal of Plasma Physics 39, no. 2 (April 1988): 215–28. http://dx.doi.org/10.1017/s002237780001299x.
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Nonlinear interactions of two azimuthally symmetric compressional hydromagnetic waves propagating in a cylindrical waveguide filled with cold magnetized plasma are investigated. Two cases are considered: the nonlinear interaction of two identical oppositely propagating compressional waves and the nonlinear interaction of two compressional waves propagating with equal group velocities. In the first case the second-order perturbation fields generated through self- and mutual interactions of the waves are calculated and their effect on the otherwise-formed simple linear standing-wave pattern is studied. The possibility of observing a resonant nonlinear interaction is shown. In the second case, in order to describe the nonlinear evolution of the wave amplitudes, two coupled nonlinear Schrödinger (NLS) equations are presented. When excited individually, both the waves are seen to be modulationally stable; but when excited simultaneously, a strong nonlinear wave-wave coupling comes into play, which makes the waves modulationally unstable. The corresponding growth rate of the instability is also calculated.
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Eden, Carsten, Manita Chouksey, and Dirk Olbers. "Mixed Rossby–Gravity Wave–Wave Interactions." Journal of Physical Oceanography 49, no. 1 (January 2019): 291–308. http://dx.doi.org/10.1175/jpo-d-18-0074.1.
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AbstractMixed triad wave–wave interactions between Rossby and gravity waves are analytically derived using the kinetic equation for models of different complexity. Two examples are considered: initially vanishing linear gravity wave energy in the presence of a fully developed Rossby wave field and the reversed case of initially vanishing linear Rossby wave energy in the presence of a realistic gravity wave field. The kinetic equation in both cases is numerically evaluated, for which energy is conserved within numerical precision. The results are validated by a corresponding ensemble of numerical model simulations supporting the validity of the weak-interaction assumption necessary to derive the kinetic equation. Since they are generated by nonresonant interactions only, the energy transfers toward the respective linear wave mode with vanishing energy are small in both cases. The total generation of energy of the linear gravity wave mode in the first case scales to leading order as the square of the Rossby number in agreement with independent estimates from laboratory experiments, although a part of the linear gravity wave mode is slaved to the Rossby wave mode without wavelike temporal behavior.
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Gonzalez-Santamaria, Raul, Qingping Zou, Shunqi Pan, and Roberto Padilla-Hernandez. "MODELLING WAVE-TIDE INTERACTIONS AT A WAVE FARM." Coastal Engineering Proceedings 1, no. 32 (January 27, 2011): 34. http://dx.doi.org/10.9753/icce.v32.waves.34.
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The Wave Hub project will create the world’s largest wave farm off the coast of Cornwall, Southwest England. This study is to investigate wave and tide interactions, in particular their effects on bottom friction and sediment transport at the wave-farm coast. This is an ambitious project research which includes the use of a very complex numerical modelling system. The main question to answer is how waves, tidal currents and winds affect the bottom friction at the Wave Hub site and the near-shore zone, as well as their impact on the sediment transport. Results show that tidal elevation and tidal currents have a significant effect on the wave height predictions, tidal forcing and wind waves have a significant effect on the bed shear-stress, relevant to sediment transport, waves via radiation stresses have an important effect on the long-shore and cross-shore velocity components, particularly during the spring tides, waves can impact on bottom boundary layer and the mixing in the water column. Interactions between waves and tides at the Wave Hub site is important when modelling coastal morphology influenced by wave energy devices, this open-source modelling system tool will help the study of physical impacts on the Wave Hub farm area.
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Lee, Woo-Dong, Norimi Mizutani, and Dong-Soo Hur. "2-D Characteristics of Wave Deformation Due to Wave-Current Interactions with Density Currents in an Estuary." Water 12, no. 1 (January 9, 2020): 183. http://dx.doi.org/10.3390/w12010183.
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In this study, numerical simulations were conducted in order to understand the role of wave-current interactions in wave deformation. The wave-current interaction mechanisms, wave reflection and energy loss due to currents, the effect of incident conditions on wave-current interactions, the advection-diffusion characteristics of saltwater, and the effect of density currents on wave-current interactions were discussed. In addition, the effect of saltwater–freshwater density on wave-current interactions was investigated under a hypopycnal flow field via numerical model testing. Turbulence was stronger under the influence of wave-current interactions than under the influence of waves alone, as wave-current interactions reduced wave energy, which led to decreases in wave height. This phenomenon was more prominent under shorter wave periods and higher current velocities. These results increase our understanding of hydrodynamic phenomena in estuaries in which saltwater–freshwater and wave-current pairs coexist.
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Zhao, W., P. H. Taylor, H. A. Wolgamot, and R. Eatock Taylor. "Amplification of random wave run-up on the front face of a box driven by tertiary wave interactions." Journal of Fluid Mechanics 869 (May 2, 2019): 706–25. http://dx.doi.org/10.1017/jfm.2019.229.
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Wave run-up phenomena driven by nonlinear wave interactions with a fixed rectangular box are investigated. Experiments are carried out in different types of uni-directional waves with normal incidence. Significant wave run-ups featuring tertiary interaction effects, similar to those reported by Molin et al. (J. Fluid Mech., vol. 528, 2005, pp. 323–354) for a fixed vertical plate, are observed in regular wave tests. Transient wave group tests are conducted for comparison, to facilitate the analysis of the tertiary interactions in irregular waves. The most striking observation is that the wave surface elevations at the centre of the front face of the fixed box can reach $4\times$ the incident waves even in irregular waves, much larger than the ${\sim}2\times$ predicted from linear theory and observed for the transient groups. The extra amplification builds up slowly and is localized on the weather side of the box. It is believed to result from tertiary interactions between the incident and reflected wave fields upstream, which induce a local lensing effect and thus wave focusing on the weather side. These interactions, though a nonlinear process, occur at the first harmonic quantities rather than high harmonics. Supporting evidence is extracted from random wave runs using NewWave analysis, where surface amplifications and phase lag – both key characteristics of tertiary wave interactions – are identified. The identification of these tertiary interactions in irregular waves is new, and may be of practical importance.
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Li, Zhisong, Kirti Ghia, Ye Li, Zhun Fan, and Lian Shen. "Unsteady Reynolds-averaged Navier–Stokes investigation of free surface wave impact on tidal turbine wake." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2246 (February 2021): 20200703. http://dx.doi.org/10.1098/rspa.2020.0703.
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Tidal current is a promising renewable energy source. Previous studies have investigated the influence of surface waves on tidal turbines in many aspects. However, the turbine wake development in a surface wave environment, which is crucial for power extraction in a turbine array, remains elusive. In this study, we focus on the wake evolution behind a single turbine and its interaction with surface waves. A numerical solver is developed to study the effects of surface waves on an industrial-size turbine. A case without surface wave and two cases with waves and different rotor depths are investigated. We obtain three-dimensional flow field descriptions near the free surface, around the rotor, and in the near- and far-wake. In a comparative analysis, the time-averaged and instantaneous flow fields are examined for various flow characteristics, including momentum restoration, power output, free surface elevation and vorticity dynamics. A model reduction technique is employed to identify the coherent flow structures and investigate the spatial and temporal characteristics of the wave–wake interactions. The results indicate the effect of surface waves in augmenting wake restoration and reveal the interactions between the surface waves and the wake structure, through a series of dynamic processes and the Kelvin–Helmholtz instability.
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Vashchenko, V. I., and I. V. Zavislyak. "Three-wave interactions in magnetostatic waves." Radiophysics and Quantum Electronics 32, no. 1 (January 1989): 34–40. http://dx.doi.org/10.1007/bf01039045.
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KOMINIS, Y., and K. HIZANIDIS. "SOLITARY WAVE INTERACTIONS WITH CONTINUOUS WAVES." International Journal of Bifurcation and Chaos 16, no. 06 (June 2006): 1753–64. http://dx.doi.org/10.1142/s0218127406015659.
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Solitary wave propagation under interaction with continuous waves is studied in the context of the Nonlinear Schrödinger Equation. An analytical approach, based on the conserved quantities of the wave evolution, is used to study transverse velocity variations for the case of nonzero transverse wavenumber difference between the solitary and continuous waves. The method is applicable for any number of transverse dimensions and any kind of nonlinearity. Moreover, the presence of a coherent continuous background is shown to be responsible for the creation of solitary rings and spirals, under interaction with solitary structures with nonzero topological charge. Numerical simulations for specific cases were used to confirm the analytical results.
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Shih, Ruey Syan. "Numerical Study of the Characteristics of Wave-Wave Interactions in Multiphase Wave Field Near Coastal Area." Advanced Materials Research 255-260 (May 2011): 2313–17. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.2313.
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Numerical investigations of multiphase irregular wave field are presented by using the BEM, which incorporates the interaction between incoming wave and reflected wave in the coastal area. This study discusses the case of multi-component wave generation using the 2D-NWT, which incorporates the wave-wave interactions between various conditions of incoming waves and high frequency reflected waves, including the variation of wave field and particle trajectory. The surf beats in the surf zone is mainly the cause of the cross-shore motion, and the generations of high frequency harmonics waves, these phenomena will be study accordingly in this preliminary study for the modeling of oscillations cause by surf beat and back swash, the generation of high frequency multi-phase reflected wave are carried out to investigate the deformation of wave profile, wave field and particle path-line.
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Osborne, A. R. "Shallow water cnoidal wave interactions." Nonlinear Processes in Geophysics 1, no. 4 (December 31, 1994): 241–51. http://dx.doi.org/10.5194/npg-1-241-1994.
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Abstract. The nonlinear dynamics of cnoidal waves, within the context of the general N-cnoidal wave solutions of the periodic Korteweg-de Vries (KdV) and Kadomtsev-Petvishvilli (KP) equations, are considered. These equations are important for describing the propagation of small-but-finite amplitude waves in shallow water; the solutions to KdV are unidirectional while those of KP are directionally spread. Herein solutions are constructed from the 0-function representation of their appropriate inverse scattering transform formulations. To this end a general theorem is employed in the construction process: All solutions to the KdV and KP equations can be written as the linear superposition of cnoidal waves plus their nonlinear interactions. The approach presented here is viewed as significant because it allows the exact construction of N degree-of-freedom cnoidal wave trains under rather general conditions.
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Luo, Qinghuan, and D. B. Melrose. "Induced Three-wave Interactions in Eclipsing Pulsars." Publications of the Astronomical Society of Australia 12, no. 1 (April 1995): 71–75. http://dx.doi.org/10.1017/s1323358000020063.
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AbstractThree-wave interactions involving two high-frequency waves (in the same mode) and a low-frequency wave are discussed and applied to pulsar eclipses. When the magnetic field is taken into account, the low-frequency waves can be the ω-mode (the low-frequency branch of the ordinary mode) or the z-mode (the low-frequency branch of the extraordinary mode). It is shown that in the cold plasma approximation, effective growth of the low-frequency waves due to an anisotropic photon beam can occur only for z-mode waves near the resonance frequency. In the application to pulsar eclipses, the cold plasma approximation may not be adequate and we suggest that when thermal effects are included, three-wave interaction involving low-frequency cyclotron waves (e.g. Bernstein modes) is a plausible candidate for pulsar eclipses
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Yuan, C., R. Grimshaw, E. Johnson, and Z. Wang. "Topographic effect on oblique internal wave–wave interactions." Journal of Fluid Mechanics 856 (September 28, 2018): 36–60. http://dx.doi.org/10.1017/jfm.2018.678.
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Based on a variable-coefficient Kadomtsev–Petviashvili (KP) equation, the topographic effect on the wave interactions between two oblique internal solitary waves is investigated. In the absence of rotation and background shear, the model set-up featuring idealised shoaling topography and continuous stratification is motivated by the large expanse of continental shelf in the South China Sea. When the bottom is flat, the evolution of an initial wave consisting of two branches of internal solitary waves can be categorised into six patterns depending on the respective amplitudes and the oblique angles measured counterclockwise from the transverse axis. Using theoretical multi-soliton solutions of the constant-coefficient KP equation, we select three observed patterns and examine each of them in detail both analytically and numerically. The effect of shoaling topography leads to a complicated structure of the leading waves and the emergence of two types of trailing wave trains. Further, the case when the along-crest width is short compared with the transverse domain of interest is examined and it is found that although the topographic effect can still modulate the wave field, the spreading effect in the transverse direction is dominant.
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Bruhn, B. "Ionization waves: Hopf–Hopf bifurcations and nonlinear wave-wave interactions." Physics of Plasmas 11, no. 9 (September 2004): 4446–55. http://dx.doi.org/10.1063/1.1782551.
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WEBB, G. M., E. Kh KAGHASHVILI, and G. P. ZANK. "Magnetohydrodynamic wave mixing in shear flows: Hamiltonian equations and wave action." Journal of Plasma Physics 73, no. 1 (February 2007): 15–68. http://dx.doi.org/10.1017/s0022377806004399.
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Abstract.Magnetohydrodynamic wave interactions in a linear shear flow are investigated using the Lagrangian fluid displacement ξ and entropy perturbation Δ S, in which a spatial Fourier solution is obtained in the frame of the background shear flow (Kelvin's method). The equations reduce to three coupled oscillator equations, with time-dependent coefficients and with source terms proportional to the entropy perturbation. In the absence of entropy perturbations, the system admits a wave action conservation integral consisting of positive and negative energy waves. Variational and Hamiltonian forms of the equations are obtained. Examples of wave amplification phenomena and sharp resonant-type wave interactions are obtained. Implications for the interaction of magnetohydrodynamic waves in the shear flow between fast, polar coronal-hole solar wind and slow, streamer belt solar wind are discussed.
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Grimshaw, R. "Resonant wave interactions near a critical level in a stratified shear flow." Journal of Fluid Mechanics 269 (June 25, 1994): 1–22. http://dx.doi.org/10.1017/s0022112094001461.
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Resonant interactions between internal gravity waves propagating in a stratified shear flow are considered for the case when the background density and shear flow vary slowly with respect to the waves. In Grimshaw (1988) triad resonances were considered, and interaction equations derived for the case when the resonance conditions are met only on certain space-time surfaces, being resonance sites. Here this analysis is extended to include higher-order resonances, with the aim of studying resonant wave interactions near a critical level. It is shown that a secondary resonant interaction between two incoming waves, in which two harmonic components of one incoming wave interact with a single harmonic component of another incoming wave, produces a reflected wave. This result is shown to agree with the study of Brown & Stewartson (1980, 1982a, b) who obtained this same result by a different approach.
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Ram, Abhay K., Kyriakos Hizanidis, and Richard J. Temkin. "Current drive by high intensity, pulsed, electron cyclotron wave packets." EPJ Web of Conferences 203 (2019): 01009. http://dx.doi.org/10.1051/epjconf/201920301009.
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The nonlinear interaction of electrons with a high intensity, spatially localized, Gaussian, electro-magnetic wave packet, or beam, in the electron cyclotron range of frequencies is described by the relativistic Lorentz equation. There are two distinct sets of electrons that result from wave-particle interactions. One set of electrons is reflected by the ponderomotive force due to the spatial variation of the wave packet. The second set of electrons are energetic enough to traverse across the wave packet. Both sets of electrons can exchange energy and momentum with the wave packet. The trapping of electrons in plane waves, which are constituents of the Gaussian beam, leads to dynamics that is distinctly different from quasilinear modeling of wave-particle interactions. This paper illustrates the changes that occur in the electron motion as a result of the nonlinear interaction. The dynamical differences between electrons interacting with a wave packet composed of ordinary electromagnetic waves and electrons interacting with a wave packet composed of extraordinary waves are exemplified.
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Janssen, Peter A. E. M. "Nonlinear Four-Wave Interactions and Freak Waves." Journal of Physical Oceanography 33, no. 4 (April 2003): 863–84. http://dx.doi.org/10.1175/1520-0485(2003)33<863:nfiafw>2.0.co;2.
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Brodin, G., and L. Stenflo. "Nonlinear wave interactions of kinetic sound waves." Annales Geophysicae 33, no. 8 (August 14, 2015): 1007–10. http://dx.doi.org/10.5194/angeo-33-1007-2015.
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Abstract. We reconsider the nonlinear resonant interaction between three electrostatic waves in a magnetized plasma. The general coupling coefficients derived from kinetic theory are reduced here to the low-frequency limit. The main contribution to the coupling coefficient we find in this way agrees with the coefficient recently presented in Annales Geophysicae. But we also deduce another contribution which sometimes can be important, and which qualitatively agrees with that of an even more recent paper. We have thus demonstrated how results derived from fluid theory can be improved and generalized by means of kinetic theory. Possible extensions of our results are outlined.
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Simaciu, Ion, Gheorghe Dumitrescu, Zoltan Borsos, and Mariana Brădac. "Interactions in an Acoustic World: Dumb Hole." Advances in High Energy Physics 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/7265362.
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The present paper aims to complete an earlier paper where the acoustic world was introduced. This is accomplished by analyzing the interactions which occur between the inhomogeneities of the acoustic medium, which are induced by the acoustic vibrations travelling in the medium. When a wave packet travels in a medium, the medium becomes inhomogeneous. The spherical wave packet behaves like an acoustic spherical lens for the acoustic plane waves. According to the principle of causality, there is an interaction between the wave and plane wave packet. In specific conditions, the wave packet behaves as an acoustic black hole.
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Smith, Jerome A. "Wave–Current Interactions in Finite Depth." Journal of Physical Oceanography 36, no. 7 (July 1, 2006): 1403–19. http://dx.doi.org/10.1175/jpo2911.1.
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Abstract The energy, momentum, and mass-flux exchanges between surface waves and underlying Eulerian mean flows are considered, and terms in addition to the classical wave “radiation stress” are identified. The formulation is made in terms of the vertically integrated flow. The various terms are identified with other analyses and interpreted in terms of physical mechanisms, permitting reasonable estimates of the associated depth dependencies. One term is identified with the integrated “CL vortex force” implemented, for example, in simulations of Langmuir circulation. However, as illustrated with a simple example of steady refraction across a shear zone, other terms of the same order can significantly alter the results. The classic example of long waves forced by short-wave groups is also revisited. In this case, an apparent singularity arising in shallow water is countered by finite-amplitude dispersion corrections, these being formally of the same order as the forced long-wave response, and becoming significant or dominant as shallow water is approached.
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Salim, M. N., M. N. M. Khairy, and T. Hayashi. "Effect of Oval Defect on Propagation of Fundamental Lamb Wave." Applied Mechanics and Materials 833 (April 2016): 49–58. http://dx.doi.org/10.4028/www.scientific.net/amm.833.49.
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Complicated Lamb wave propagation in structures can cause a misinterpretation in defect location and sizing during nondestructive inspections. A visualization of Lamb wave interactions with oval defects was carried out in our study to investigate the phenomenon of fundamental Lamb wave interaction around defect by using a reduced model of plate in ABAQUS. The visualized wave propagations with oval shape of through defects in plates demonstrated different patterns of wave interactions for the symmetric and anti-symmetric modes. The results also visualized the mode conversions around defects which converted from the incident waves. The visualized changes on the wave structures due to wave interaction with defects is important to increase our understanding on the guided wave propagation and reduce misinterpretation in nondestructive inspection when using the wave modes during inspection on large structures.
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Yoon, Sung B., and Philip L. F. Liu. "WAVE AND CURRENT INTERACTIONS IN SHALLOW WATER." Coastal Engineering Proceedings 1, no. 20 (January 29, 1986): 125. http://dx.doi.org/10.9753/icce.v20.125.
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Interactions between waves and currents are common and important phenomena in the coastal zone. Coastal currents, such as longshore currents, rip currents, and river flows, can significantly change wave heights and directions of wave propagation. Consequently, the design for shoreline protection measures must be adjusted accordingly. Various theories for wave-current interactions exist and have been reviewed by Peregrine and Jonsson (1983). Most of these theories are developed for large-scale currents where the length-scale for the current variation is much greater than the typical wavelength. These theories cannot be applied to the coastal currents which are small-scale currents. In this paper, the interactions between currents and nonlinear shallow water waves are investigated. Boussinesq equations are used to derive evolution equations for spectral wave components. The current intensity is assumed to be larger than the leading wave orbital velocity and smaller than the group velocity. The length-scale of the current is much shorter than those assumed in the existing large-scale theories. To facilitate numerical computations, the parabolic approximation is applied and a simplified model is developed. A numerical example is given for the refraction and diffraction of cnoidal waves over a rip current on a sloping topography. Both normal and oblique incident cases are examined.
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Krafft, C., and A. Volokitin. "Resonant three-wave interaction in the presence of suprathermal electron fluxes." Annales Geophysicae 22, no. 6 (June 14, 2004): 2171–79. http://dx.doi.org/10.5194/angeo-22-2171-2004.
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Abstract. A theoretical and numerical model is presented which describes the nonlinear interaction of lower hybrid waves with a non-equilibrium electron distribution function in a magnetized plasma. The paper presents some relevant examples of numerical simulations which show the nonlinear evolution of a set of three waves interacting at various resonance velocities with a flux of electrons presenting some anisotropy in the parallel velocity distribution (suprathermal tail); in particular, the case when the interactions between the waves are neglected (for sufficiently small waves' amplitudes) is compared to the case when the three waves follow a resonant decay process. A competition between excitation (due to the fan instability with tail electrons or to the bump-in-tail instability at the Landau resonances) and damping processes (involving bulk electrons at the Landau resonances) takes place for each wave, depending on the strength of the wave-wave coupling, on the linear growth rates of the waves and on the modifications of the particles' distribution resulting from the linear and nonlinear wave-particle interactions. It is shown that the energy carried by the suprathermal electron tail is more effectively transfered to lower energy electrons in the presence of wave-wave interactions.
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Ge, Z., and P. C. Liu. "Long-term wave growth and its linear and nonlinear interactions with wind fluctuations." Annales Geophysicae 26, no. 4 (May 13, 2008): 747–58. http://dx.doi.org/10.5194/angeo-26-747-2008.
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Abstract. Following Ge and Liu (2007), the simultaneously recorded time series of wave elevation and wind velocity are examined for long-term (on Lavrenov's τ4-scale or 3 to 6 h) linear and nonlinear interactions between the wind fluctuations and the wave field. Over such long times the detected interaction patterns should reveal general characteristics for the wave growth process. The time series are divided into three episodes, each approximately 1.33 h long, to represent three sequential stages of wave growth. The classic Fourier-domain spectral and bispectral analyses are used to identify the linear and quadratic interactions between the waves and the wind fluctuations as well as between different components of the wave field. The results show clearly that as the wave field grows the linear interaction becomes enhanced and covers wider range of frequencies. Two different wave-induced components of the wind fluctuations are identified. These components, one at around 0.4 Hz and the other at around 0.15 to 0.2 Hz, are generated and supported by both linear and quadratic wind-wave interactions probably through the distortions of the waves to the wind field. The fact that the higher-frequency wave-induced component always stays with the equilibrium range of the wave spectrum around 0.4 Hz and the lower-frequency one tends to move with the downshifting of the primary peak of the wave spectrum defines the partition of the primary peak and the equilibrium range of the wave spectrum, a characteristic that could not be revealed by short-time wavelet-based analyses in Ge and Liu (2007). Furthermore, these two wave-induced peaks of the wind spectrum appear to have different patterns of feedback to the wave field. The quadratic wave-wave interactions also are assessed using the auto-bispectrum and are found to be especially active during the first and the third episodes. Such directly detected wind-wave interactions, both linear and nonlinear, may complement the existing theoretical and numerical models, and can be used for future model development and validation.
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Gao, Xinliang, Jicheng Sun, Quanming Lu, Lunjin Chen, and Shui Wang. "Generation of Lower Harmonic Magnetosonic Waves Through Nonlinear Wave‐Wave Interactions." Geophysical Research Letters 45, no. 16 (August 24, 2018): 8029–34. http://dx.doi.org/10.1029/2018gl079090.
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Katoh, Y., M. Kitahara, H. Kojima, Y. Omura, S. Kasahara, M. Hirahara, Y. Miyoshi, et al. "Significance of Wave-Particle Interaction Analyzer for direct measurements of nonlinear wave-particle interactions." Annales Geophysicae 31, no. 3 (March 19, 2013): 503–12. http://dx.doi.org/10.5194/angeo-31-503-2013.
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Abstract. In the upcoming JAXA/ERG satellite mission, Wave Particle Interaction Analyzer (WPIA) will be installed as an onboard software function. We study the statistical significance of the WPIA for measurement of the energy transfer process between energetic electrons and whistler-mode chorus emissions in the Earth's inner magnetosphere. The WPIA measures a relative phase angle between the wave vector E and velocity vector v of each electron and computes their inner product W, where W is the time variation of the kinetic energy of energetic electrons interacting with plasma waves. We evaluate the feasibility by applying the WPIA analysis to the simulation results of whistler-mode chorus generation. We compute W using both a wave electric field vector observed at a fixed point in the simulation system and a velocity vector of each energetic electron passing through this point. By summing up Wi of an individual particle i to give Wint, we obtain significant values of Wint as expected from the evolution of chorus emissions in the simulation result. We can discuss the efficiency of the energy exchange through wave-particle interactions by selecting the range of the kinetic energy and pitch angle of the electrons used in the computation of Wint. The statistical significance of the obtained Wint is evaluated by calculating the standard deviation σW of Wint. In the results of the analysis, positive or negative Wint is obtained at the different regions of velocity phase space, while at the specific regions the obtained Wint values are significantly greater than σW, indicating efficient wave-particle interactions. The present study demonstrates the feasibility of using the WPIA, which will be on board the upcoming ERG satellite, for direct measurement of wave-particle interactions.
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Williams, R. L., C. E. Clayton, C. Joshi, T. Katsouleas, and W. B. Mori. "Studies of relativistic wave–particle interactions in plasma-based collective accelerators." Laser and Particle Beams 8, no. 3 (September 1990): 427–49. http://dx.doi.org/10.1017/s0263034600008673.
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The interaction of externally injected charged particles (electrons) with plasma waves moving with a phase velocity that is very close to the speed of light is examined. Such plasma waves form the basis of at least three collective accelerator schemes: the plasma beat wave accelerator (PBWA), the plasma wake-field accelerator (PWFA), and the laser wake-field accelerator (LWFA). First, the electron trapping threshold, energy gain and acceleration length are examined using a 1-D model. This model elucidates how the final energies of the injected test electrons depend upon their injection and extraction phases and phase slippage. Phase energy diagrams are shown to be extremely useful in visualizing wave-particle interactions in 1-D. Second, we examine, using a two-dimensional model, the effects of radial electric fields on focusing or defocusing the injected particles depending upon their radial positions and phases in the relativistically moving potential well. Finally, we extend the model to 3-D so that the effect of injected particles' emittance on the acceleration process may be determined. This simple 3-D model will be extremely useful in predicting the electron energy spectra of several current experiments designed to demonstrate ultrahigh gradient acceleration of externally injected test particles by relativistic plasma waves.
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Campbell, Bryce K., and Yuming Liu. "Nonlinear resonant interactions of interfacial waves in horizontal stratified channel flows." Journal of Fluid Mechanics 717 (February 1, 2013): 612–42. http://dx.doi.org/10.1017/jfm.2012.598.
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AbstractWe consider the problem of nonlinear resonant interactions of interfacial waves with the presence of a linear interfacial instability in an inviscid two-fluid stratified flow through a horizontal channel. The resonant triad consists of a (linearly) unstable wave and two stable waves, one of which has a wavelength that can be much longer than that of the unstable component. Of special interest is the development of the long wave by energy transfer from the base flow due to the coupled effect of nonlinear resonance and interfacial instability. By use of the method of multiple scales, we derive the interaction equations which govern the time evolution of the amplitudes of the interacting waves including the effect of interfacial instability. The solution of the evolution equations shows that depending on the flow conditions, the (stable) long wave can achieve a bi-exponential growth rate through the resonant interaction with the unstable wave. Moreover, the unstable wave can grow unboundedly even when the nonlinear self-interaction effect is included, as do the stable waves in the associated resonant triad. For the verification of the theoretical analysis and the practical application involving a broadbanded spectrum of waves, we develop an effective direct simulation method, based on a high-order pseudo-spectral approach, which accounts for nonlinear interactions of interfacial waves up to an arbitrary high order. The direct numerical simulations compare well with the theoretical analysis for all of the characteristic flows considered, and agree qualitatively with the experimental observation of slug development near the entrance of two-phase flow into a pipe.
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Moreira, R. M., and D. H. Peregrine. "Nonlinear interactions between deep-water waves and currents." Journal of Fluid Mechanics 691 (December 6, 2011): 1–25. http://dx.doi.org/10.1017/jfm.2011.436.
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AbstractThe effects of nonlinearity on a train of linear water waves in deep water interacting with underlying currents are investigated numerically via a boundary-integral method. The current is assumed to be two-dimensional and stationary, being induced by a distribution of singularities located beneath the free surface, which impose sharp and gentle surface velocity gradients. For ‘slowly’ varying currents, the fully nonlinear results confirm that opposing currents induce wave steepening and breaking within the region where a high convergence of rays occurs. For ‘rapidly’ varying currents, wave blocking and breaking are more prominent. In this case reflection was observed when sufficiently strong adverse currents are imposed, confirming that at least part of the wave energy that builds up within the caustic can be released in the form of partial reflection and wave breaking. For bichromatic waves, the fully nonlinear results show that partial wave blocking occurs at the individual wave components in the wave groups and that waves become almost monochromatic upstream of the blocking region.
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Feng, X. "Linear and Nonlinear Wave-Current Interactions over Constant Water Depth." Journal of Clean Energy Technologies 6, no. 2 (March 2018): 143–49. http://dx.doi.org/10.18178/jocet.2018.6.2.450.
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Mo, Dongxue, Jian Li, and Yijun Hou. "Assessing the Impact of Wave–Current Interactions on Storm Surges and Waves during Cold Air Outbreaks in the Northern East China Sea." Journal of Marine Science and Engineering 9, no. 8 (July 30, 2021): 824. http://dx.doi.org/10.3390/jmse9080824.
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Storm surges and disastrous waves induced by cold air outbreaks, a type of severe weather system, often impact the coastal economic development. Using the Climate Forecast System Reanalysis wind product and the Coupled Ocean–Atmosphere–Wave–Sediment Transport model, we developed a coupled numerical model and applied it to examine the interaction between surface gravity waves and ocean currents during cold air outbreaks in two case studies in the northern East China Sea. The results revealed that wave–current interactions improved the simulation accuracy, especially the water level, as verified by tidal station measurements. We conducted sensitivity experiments to explore the spatiotemporal variation of the impact of wave–current interactions on storm surges and waves in the northern East China Sea, away from the coastline. The wave-induced surge (up to 0.4 m) and the wave-induced current (up to 0.5 m/s) were found to be related to the difference between wave direction and current direction. The significant wave height difference (up to 0.5 m) was sensitive to the storm surge nearshore and sensitive to the current field offshore, while the mean wave direction change (up to 40°) was more sensitive to the current field than to the storm surge. Additionally, the wave–current interaction regulated the momentum balance and wave action balance, respectively. By comparison, the momentum residuals of pressure gradient, Coriolis force, Coriolis–Stokes force, and bottom stress, which were pronounced in different areas, were modulated more significantly by the wave effect than other terms. The dominant mechanisms of wave–current interactions on waves included the current-induced modification of energy generation caused by wind input, the current-induced modification of energy dissipation caused by whitecapping, and the current-induced wave advection.
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Yeoman, T. K., and D. M. Wright. "ULF waves with drift resonance and drift-bounce resonance energy sources as observed in artificially-induced HF radar backscatter." Annales Geophysicae 19, no. 2 (February 28, 2001): 159–70. http://dx.doi.org/10.5194/angeo-19-159-2001.
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Abstract. HF radar backscatter which has been artificially-induced by a high power RF facility such as the EISCAT heater at Tromsø has been demonstrated to provide ionospheric electric field data of unprecedented temporal resolution and accuracy. Here such data are used to investigate ULF wave processes observed by the CUTLASS HF radars. Within a short period of time during a single four hour experiment three distinct wave types are observed with differing periods, and latitudinal and longitudinal phase evolution. Combining information from the three waves allows them to be divided into those with a large-scale nature, driven externally to the magnetosphere, and those with small azimuthal scale lengths, driven by wave-particle interactions. Furthermore, the nature of the wave-particle interactions for two distinct small-scale waves is revealed, with one wave interpreted as being driven by a drift resonance process and the other by a drift-bounce resonance interaction. Both of these mechanisms with m ≈ -35 and proton energies of 35–45 keV appear to be viable wave energy sources in the postnoon sector.Key words. Ionosphere (active experiments; wave-particle interactions) – Magnetospheric physics (MHD waves and in-stabilities).
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Onorato, Miguel, Lara Vozella, Davide Proment, and Yuri V. Lvov. "Route to thermalization in the α-Fermi–Pasta–Ulam system." Proceedings of the National Academy of Sciences 112, no. 14 (March 24, 2015): 4208–13. http://dx.doi.org/10.1073/pnas.1404397112.
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We study the original α-Fermi–Pasta–Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α-FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ϵ8, where ϵ is the small parameter in the system. The wave–wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed.
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Melito, Lorenzo, Matteo Postacchini, Alex Sheremet, Joseph Calantoni, Gianluca Zitti, Giovanna Darvini, and Maurizio Brocchini. "Wave-Current Interactions and Infragravity Wave Propagation at a Microtidal Inlet." Proceedings 2, no. 11 (August 2, 2018): 628. http://dx.doi.org/10.3390/proceedings2110628.
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Recent studies have shown that wave blocking occurs at river mouths with strong currents typically preventing relatively short period sea and swell waves from propagating up the river. However, observations demonstrate that lower frequency waves, so-called infragravity waves, do pass through and propagate up the river, particularly during storm events. We present observations from the Misa River estuary of infragravity wave propagation up the river during storm conditions. A model of the complex nonlinear interactions that drive infragravity waves is presented. The results are discussed in the context of an observed river mouth bar formed in the lower reach of the Misa River.
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Verao Fernandez, Gael, Vasiliki Stratigaki, Panagiotis Vasarmidis, Philip Balitsky, and Peter Troch. "Wake Effect Assessment in Long- and Short-Crested Seas of Heaving-Point Absorber and Oscillating Wave Surge WEC Arrays." Water 11, no. 6 (May 29, 2019): 1126. http://dx.doi.org/10.3390/w11061126.
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In the recent years, the potential impact of wave energy converter (WEC) arrays on the surrounding wave field has been studied using both phase-averaging and phase-resolving wave propagation models. Obtaining understanding of this impact is important because it may affect other users in the sea or on the coastline. However, in these models a parametrization of the WEC power absorption is often adopted. This may lead to an overestimation or underestimation of the overall WEC array power absorption, and thus to an unrealistic estimation of the potential WEC array impact. WEC array power absorption is a result of energy extraction from the incoming waves, and thus wave height decrease is generally observed downwave at large distances (the so-called “wake” or “far-field” effects). Moreover, the power absorption depends on the mutual interactions between the WECs of an array (the so-called “near field” effects). To deal with the limitations posed by wave propagation models, coupled models of recent years, which are nesting wave-structure interaction solvers into wave propagation models, have been used. Wave-structure interaction solvers can generally provide detailed hydrodynamic information around the WECs and a more realistic representation of wave power absorption. Coupled models have shown a lower WEC array impact in terms of wake effects compared to wave propagation models. However, all studies to date in which coupled models are employed have been performed using idealized long-crested waves. Ocean waves propagate with a certain directional spreading that affects the redistribution of wave energy in the lee of WEC arrays, and thus gaining insight wake effect for irregular short-crested sea states is crucial. In our research, a new methodology is introduced for the assessment of WEC array wake effects for realistic sea states. A coupled model is developed between the wave-structure interaction solver NEMOH and the wave propagation model MILDwave. A parametric study is performed showing a comparison between WEC array wake effects for regular, long-crested irregular, and short-crested irregular waves. For this investigation, a nine heaving-point absorber array is used for which the wave height reduction is found to be up to 8% lower at 1.0 km downwave the WEC array when changing from long-crested to short-crested irregular waves. Also, an oscillating wave surge WEC array is simulated and the overestimation of the wake effects in this case is up to 5%. These differences in wake effects between different wave types indicates the need to consider short-crested irregular waves to avoid overestimating the WEC array potential impacts. The MILDwave-NEMOH coupled model has proven to be a reliable numerical tool, with an efficient computational effort for simulating the wake effects of two different WEC arrays under the action of a range of different sea states.
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KUO, ALLEN C., and LORENZO M. POLVANI. "Wave–vortex interaction in rotating shallow water. Part 1. One space dimension." Journal of Fluid Mechanics 394 (September 10, 1999): 1–27. http://dx.doi.org/10.1017/s0022112099005534.
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Using a physical space (i.e. non-modal) approach, we investigate interactions between fast inertio-gravity (IG) waves and slow balanced flows in a shallow rotating fluid. Specifically, we consider a train of IG waves impinging on a steady, exactly balanced vortex. For simplicity, the one-dimensional problem is studied first; the limitations of one-dimensionality are offset by the ability to define balance in an exact way. An asymptotic analysis of the problem in the small-amplitude limit is performed to demonstrate the existence of interactions. It is shown that these interactions are not confined to the modification of the wave field by the vortex but, more importantly, that the waves are able to alter in a non-trivial way the potential vorticity associated with that vortex. Interestingly, in this one-dimensional problem, once the waves have traversed the vortex region and have propagated away, the vortex exactly recovers its initial shape and thus bears no signature of the interaction. Furthermore, we prove this last result in the case of arbitrary vortex and wave amplitudes. Numerical integrations of the full one-dimensional shallow-water equations in strongly nonlinear regimes are also performed: they confirm that time-dependent interactions exist and increase with wave amplitude, while at the final state the vortex bears no sign of the interaction. In addition, they reveal that cyclonic vortices interact more strongly with the wave field than anticyclonic ones.
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Ferdousi, M., T. Babaie-Janvier, and P. A. Robinson. "Nonlinear wave-wave interactions in the brain." Journal of Theoretical Biology 500 (September 2020): 110308. http://dx.doi.org/10.1016/j.jtbi.2020.110308.
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Zhang, Jun, Robert E. Randall, and C. Anthony Spell. "Component Wave Interactions and Irregular Wave Kinematics." Journal of Waterway, Port, Coastal, and Ocean Engineering 118, no. 4 (July 1992): 401–16. http://dx.doi.org/10.1061/(asce)0733-950x(1992)118:4(401).
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Guralnik, Z., J. Bourdelais, X. Zabalgogeazcoa, and W. E. Farrell. "Wave–wave interactions and deep ocean acoustics." Journal of the Acoustical Society of America 134, no. 4 (October 2013): 3161–73. http://dx.doi.org/10.1121/1.4818782.
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