Статті в журналах: "Wave mechanics"

1

Shang-Wu, Qian, and Xu Lai-Zi. "Wave Mechanics or Wave Statistical Mechanics." Communications in Theoretical Physics 48, no. 2 (August 2007): 243–44. http://dx.doi.org/10.1088/0253-6102/48/2/008.

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2

Williamson, C. H. K., and A. Prasad. "Acoustic forcing of oblique wave resonance in the far wake." Journal of Fluid Mechanics 256 (November 1993): 315–41. http://dx.doi.org/10.1017/s0022112093002800.

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In this paper, we investigate to what extent the far-wake ‘signature’ of the near-wake vortex dynamics of a nominally two-dimensional bluff body is affected by the character of the free-stream noise. We confirm the existence of an oblique wave resonance (at frequency, fK–fT), which is caused by nonlinear ‘quadratic’ interactions between primary oblique shedding waves (fK) and secondary two-dimensional waves (fT), which are amplified from free-stream disturbances. In this work, oblique wave resonance is induced by acoustic forcing of two-dimensional waves. The use of acoustic forcing reveals a set of higher-order oblique wave resonances corresponding to frequencies (fK–nfT), where n is an integer. We find from visualization that, even when the secondary two-dimensional waves have the same frequency as the oblique waves, it is the oblique waves that are preferentially amplified. Oblique wave angles up to 74° have been observed. The response of the wake to a large range of forcing frequencies shows a broad region of peak response, centred around F = (fT/fK) = 0.55, and is in reasonable agreement with predictions from linear stability analysis. A similar broad response is found for each of the higher-order oblique wave modes. Simple equations for the oblique waves yield approximate conditions for maximum wake response, with a frequency for peak response given by Fmax = 1/2n = 1/2, 1/4, 1/6,…, and an oblique wave angle given by θmax = 2θK, where θK is the angle of oblique vortex shedding. An increase in forcing amplitude has the effect of bringing the nonlinear wave interactions, leading to oblique wave resonance, further upstream. Paradoxically, the effect of an increase in amplitude (A) of the two-dimensional wave forcing is to further amplify the oblique waves in preference to the two-dimensional waves and, under some conditions, to inhibit the appearance of prominent two-dimensional waves where they would otherwise appear. With a variation in forcing amplitude, the amplitude of oblique wave response is found to be closely proportional to A½. In summary, this investigation confirms the surprising result that it is only through the existence of noise in the free stream that the far wake is ‘connected’ to the near wake.

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3

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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4

Lima, Nathan, and Ricardo Karam. "Schrödinger’s equation from Snell’s law." European Journal of Physics 43, no. 3 (March 21, 2022): 035402. http://dx.doi.org/10.1088/1361-6404/ac5635.

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Abstract A new derivation of Schrödinger’s equation is presented, based on Schrödinger’s original discussions on refraction and the optical-mechanical analogy, but adopting a much simpler formalism: Newtonian mechanics and some basic elements of classical wave theory (such as Snell’s law). We compare how particles and waves refract and show that the ‘law of particle refraction’ and the ‘law of wave refraction’ may become consistent if one assumes that a particle can be represented by a wave group. In this case, the differential equation whose solutions represent the waves forming such wave group is the Schrödinger equation. Due to the simplicity of the adopted mathematical formalism, we argue that this derivation can be used in quantum mechanics courses at introductory level to give students an idea of Schrödinger’s original path to his wave equation.

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5

Widrow, Lawrence M. "Galactic wave mechanics." Nature Physics 10, no. 7 (June 22, 2014): 477–78. http://dx.doi.org/10.1038/nphys3020.

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6

Nimtz, Guenter, and Paul Bruney. "On the Universal Scattering Time of Neutrons." Zeitschrift für Naturforschung A 73, no. 10 (October 25, 2018): 919–21. http://dx.doi.org/10.1515/zna-2018-0331.

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AbstractTunnelling and barrier interaction times of neutrons were previously measured. Here we show that the neutron interaction time with barriers corresponds to the universal tunnelling time of wave mechanics which was formerly observed with elastic, electromagnetic and electron waves. The universal tunnelling time seems to hold for neutrons also. Such an adequate general wave mechanical behaviour was conjectured by Brillouin. Remarkably, wave mechanical effects, and even virtual particles, hold from the microcosm to the macrocosm.

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7

Tavakoli, Sasan, Poorya Shaghaghi, Simone Mancini, Fabio De Luca, and Abbas Dashtimanesh. "Wake waves of a planing boat: An experimental model." Physics of Fluids 34, no. 3 (March 2022): 037104. http://dx.doi.org/10.1063/5.0084074.

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The wake waves generated by the steady movement of a planing hull are analyzed by means of towing tank tests. Two sets of waves, including divergent and transverse waves, are identified and then analyzed. The wave period of the divergent waves is seen to decrease by the increase in speed of the vessel. These waves are seen to damp temporally. The mechanisms that lead to damping of the divergent wave were found to depend on the wave orbital Reynolds number in semi-planing regime, though that of in-planing regime is a function of the Reynolds number of the boat. The wake angle is seen to decrease with the increase in Froude number, the rate of which becomes relatively large in-planing regime. Transverse waves are captured through measurements, and it is shown that while their period is longer than those of the divergent waves, they are not noticeably damped. Throughout the spectral analysis, it is demonstrated that divergent waves reach a higher level of nonlinearity by the increase in Froude number and, hence, the wave energy is distributed over a boarder range of frequency. The height of the transverse wave is observed to become lower by the increase in speed, but as the towing speed increases, the probability density function curves of surface elevation deviate more and more from the Gaussian distribution.

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8

Ma, Yong-Xin, Bo Tian, Qi-Xing Qu, He-Yuan Tian, and Shao-Hua Liu. "Bilinear Bäcklund transformation, breather- and travelling-wave solutions for a (2+1)-dimensional extended Kadomtsev–Petviashvili II equation in fluid mechanics." Modern Physics Letters B 35, no. 19 (June 1, 2021): 2150315. http://dx.doi.org/10.1142/s0217984921503152.

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Fluid-mechanics studies are applied in mechanical engineering, biomedical engineering, oceanography, meteorology and astrophysics. In this paper, we investigate a (2+1)-dimensional extended Kadomtsev–Petviashvili II equation in fluid mechanics. Based on the Hirota bilinear method, we give a bilinear Bäcklund transformation. Via the extended homoclinic test technique, we construct the breather-wave solutions under certain constraints. We obtain the velocities of the breather waves, which depend on the coefficients in that equation. Besides, we derive the lump solutions with the periods of the breather-wave solutions tending to the infinity. Based on the polynomial-expansion method, travelling-wave solutions are constructed. We observe that the shapes of a breather wave and a lump remain unchanged during the propagation. We graphically discuss the effects of those coefficients on the breather wave and lump.

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9

Larson, D. J. "Understanding quantum mechanics." Physics Essays 37, no. 2 (June 3, 2024): 133–38. http://dx.doi.org/10.4006/0836-1398-37.2.133.

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Quantum mechanics presently has many unanswered questions, paradoxes, and even outright logical contradictions. To make progress in understanding quantum mechanics, we begin by proposing that relativity be set aside in favor of an absolute aetherial theory. Once that step is taken, we can understand quantum collapse as a description of real wave-packets collapsing in a faster-than-light way. By assuming that a partially observable reality exists, we can then extend our analysis of wave-packets into the subquantum, and the Heisenberg uncertainty principle then follows from the Fourier uncertainty principle coupled with the de Broglie relation. Further progress in understanding quantum mechanics is possible by modifying the de Broglie and Planck relations. Those modifications lead to matter-waves moving at the speed of light rather than superluminally as presently theorized, and they allow the results of matter-wave two-slit experiments to be understood from any reference frame. A modified time-dependent Schrödinger Equation results from our modifications, but the spatial time-independent Schrödinger equation is retained.

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10

Hayashi, Takahiro, Koichiro Kawashima, Zongqi Sun, and Joseph L. Rose. "Guided Wave Propagation Mechanics Across a Pipe Elbow." Journal of Pressure Vessel Technology 127, no. 3 (January 24, 2005): 322–27. http://dx.doi.org/10.1115/1.1990210.

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Wave propagation across a pipe elbow region is complex. Subsequent reflected and transmitted waves are largely deformed due to mode conversions at the elbow. This prevents us to date from applying guided waves to the nondestructive evaluation of meandering pipeworks. Since theoretical development of guided wave propagation in a pipe is difficult, numerical modeling techniques are useful. We have introduced a semianalytical finite element method, a special modeling technique for guided wave propagation, because ordinary finite element methods require extremely long computational times and memory for such a long-range guided wave calculation. In this study, the semianalytical finite element method for curved pipes is developed. A curved cylindrical coordinate system is used for the curved pipe region, where a curved center axis of the pipe elbow region is an axis (z′ axis) of the coordinate system, instead of the straight axis (z axis) of the cylindrical coordinate system. Guided waves in the z′ direction are described as a superposition of orthogonal functions. The calculation region is divided only in the thickness and circumferential directions. Using this calculation technique, echoes from the back wall beyond up to four elbows are discussed.

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11

Delphenich, D. H. "The optical-mechanical analogy for wave mechanics: a new hope." Journal of Physics: Conference Series 2197, no. 1 (March 1, 2022): 012005. http://dx.doi.org/10.1088/1742-6596/2197/1/012005.

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Abstract The continuum-mechanical formulation of wave mechanics suggests that there is an intermediate stage of theoretical generality between wave mechanics and point mechanics, namely, continuum mechanics. When that argument is applied to the corresponding transition from wave optics to geometrical optics, the corresponding intermediate stage is essentially the geometrical theory of diffraction, i.e., the theory of diffracted geodesics.

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12

Williamson, C. H. K., and A. Prasad. "A new mechanism for oblique wave resonance in the ‘natural’ far wake." Journal of Fluid Mechanics 256 (November 1993): 269–313. http://dx.doi.org/10.1017/s0022112093002794.

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There has been some debate recently on whether the far-wake structure downstream of a cylinder is dependent on, or ‘connected’ with, the precise details of the near-wake structure. Indeed, it has previously been suggested that the far-wake scale and frequency are unconnected with those of the near wake. In the present paper, we demonstrate that both the far-wake scale and frequency are dependent on the near wake. Surprisingly, the characteristic that actually forges a ‘connection’ between the near and far wakes is the sensitivity to free-stream disturbances. It is these disturbances that are also responsible for the regular three-dimensional patterns that may be visualized. Observations of a regular ‘honeycomb’-like three-dimensional pattern in the far wake is found to be caused by an interaction between oblique shedding waves from upstream and large-scale two-dimensional waves, amplified from the free-stream disturbances. The symmetry and spanwise wavelength of Cimbala, Nagib & Roshko's (1988) three-dimensional pattern are precisely consistent with such wave interactions. In the presence of parallel shedding, the lack of a honeycomb pattern shows that such a three-dimensional pattern is clearly dependent on upstream oblique vortex shedding.With the deductions above as a starting point, we describe a new mechanism for the resonance of oblique waves, as follows. In the case of two-dimensional waves, corresponding to a very small spectral peak in the free stream (fT) interacting (quadratically) with the oblique shedding waves frequency (fK), it appears that the most amplified or resonant frequency in the far wake is a combination frequency fFW = (fK–fT), which corresponds physically with ‘oblique resonance waves’ at a large oblique angle. The large scatter in (fFW/fK) from previous studies is principally caused by the broad response of the far wake to a range of free-stream spectral peaks (fT). We present clear visualization of the oblique wave phenomenon, coupled with velocity measurements which demonstrate that the secondary oblique wave energy can far exceed the secondary two-dimensional wave energy by up to two orders of magnitude. Further experiments show that, in the absence of an influential free-stream spectral peak, the far wake does not resonate, but instead has a low-amplitude broad spectral response. The present phenomena are due to nonlinear instabilities in the far wake, and are not related to vortex pairing. There would appear to be distinct differences between this oblique wave resonance and the subharmonic resonances that have been previously studied in channel flow, boundary layers, mixing layers and airfoil wakes.

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13

Feng, Pang Xiao. "The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation." JOURNAL OF ADVANCES IN PHYSICS 5, no. 3 (October 16, 2014): 871–981. http://dx.doi.org/10.24297/jap.v5i3.1927.

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We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary waveâ€™s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear SchrÃ¶dinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

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14

Engelbrecht, J. "Wave equations in mechanics." Estonian Journal of Engineering 19, no. 4 (2013): 273. http://dx.doi.org/10.3176/eng.2013.4.02.

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15

McCrea, William. "Origin of wave mechanics." Contemporary Physics 31, no. 1 (January 1990): 43–48. http://dx.doi.org/10.1080/00107519008222000.

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16

Wódkiewicz, K., and M. O. Scully. "Weinberg’s nonlinear wave mechanics." Physical Review A 42, no. 9 (November 1, 1990): 5111–16. http://dx.doi.org/10.1103/physreva.42.5111.

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17

Li, Hong-Xing. "Unified theory of classic mechanics and quantum mechanics." Modern Physics Letters A 35, no. 38 (October 1, 2020): 2030022. http://dx.doi.org/10.1142/s0217732320300220.

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In this paper, I review one of the most important and interesting parts of my new book “Fuzzy Systems to Quantum Mechanics” (see Ref. 1). Several conclusions in this part are worth introducing here. First of all, the motion of a mass point in classic mechanics has also waviness and the wave function of the motion of a mass point is composed of wave functions of countably infinite microscopic particles. Secondly, based on the waviness of the motion of a mass point we surely know the new conclusion described as the wave-mass-point dualism in classic mechanics. And thirdly, by using the closed relation between the wave-mass-point dualism in classic mechanics and the wave-particle dualism in quantum mechanics, unified theory of classic mechanics and quantum mechanics is naturally formed.

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18

Canero, Armando TomÃ¡s. "Sound as a transverse wave." JOURNAL OF ADVANCES IN PHYSICS 13, no. 1 (February 28, 2017): 4522–34. http://dx.doi.org/10.24297/jap.v13i1.5670.

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This paper presents sound propagation based on a transverse wave model which does not collide with the interpretation of physical events based on the longitudinal wave model, but responds to the correspondence principle and allows interpreting a significant number of scientific experiments that do not follow the longitudinal wave model. Among the problems that are solved are: the interpretation of the location of nodes and antinodes in a Kundt tube of classical mechanics, the traslation of phonons in the vacuum interparticle of quantum mechanics and gravitational waves in relativistic mechanics.

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19

Liang, Hui, and Xiaobo Chen. "Viscous effects on the fundamental solution to ship waves." Journal of Fluid Mechanics 879 (October 1, 2019): 744–74. http://dx.doi.org/10.1017/jfm.2019.698.

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The fundamental solution to steady ship waves accounting for viscous effects (the viscous-ship-wave Green function) is investigated within the framework of the weakly damped free-surface flow theory. An explicit expression of the viscous-ship-wave Green function is firstly derived, and an accurate and efficient technique is described to evaluate the Green function via decomposing the free-surface term into the local-flow component and wave component. To delve into the physical features of the viscous-ship-wave Green function, the asymptotic approximations in the far field due to Kelvin, Havelock and Peters are presented for the flow-field point located inside, at and outside the Kelvin wedge. In addition, uniform approximations to the wave component based on the Chester–Friedman–Ursell (CFU) approximation and the Kelvin–Havelock–Peters (KHP) approximation are carried out. Both numerical evaluation and asymptotic approximations show that the singular behaviour is eliminated and the divergent waves associated with large wavenumbers leading to rapid oscillations are severely damped when viscous effects are accounted for. In addition, viscous effects also alter the apparent wake angle associated with the wave pattern created by a high-speed translating source, and the apparent wake angle is dependent on both $\mathscr{U}^{-1}$ and $\mathscr{U}^{-2}$, where $\mathscr{U}$ is the translating speed of the source.

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20

DORIA IRIARTE, JOSE JAVIER, and IÑIGO DORIA ELEJOSTE. "A NEW THEORY ON OCEAN WAVE MECHANICS AND ITS APLICATION IN ENERGY POWER GENERATION." DYNA 96, no. 3 (May 1, 2021): 276–80. http://dx.doi.org/10.6036/9931.

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We provide here a theoretical solution to the calculation of wave power generation possibilities, showing that the energy and other parameters of each wave are a function exclusively of its height. The numerical result obtained is compatible with the most used formulations. All authors cited, offer oversimplified formulas for complicated wave power and energy calculations in contrast with our very simple, coherent and innovative formulas, treating each wave individually and assuming the same sinusoidal profile, without wind and ocean currents. The sand waves, or ripple marks, generation is described. This proposed wave generation and propagation process lead us to use turbines directly driven by waves, device capable of extracting energy from both waves and rivers or tides with this new type of turbines. The exposed theory has been supported by tests in the laboratory, at sea, and in breakers Key Words: Ocean wave mechanics. Wave energy. Energy generation

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21

Hayashi, Takahiro, Koichiro Kawashima, Zongqi Sun, and Joseph L. Rose. "Guided Wave Focusing Mechanics in Pipe." Journal of Pressure Vessel Technology 127, no. 3 (January 24, 2005): 317–21. http://dx.doi.org/10.1115/1.1990209.

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Guided waves can be used in pipe inspection over long distances. Presented in this paper is a beam focusing technique to improve the S∕N ratio of the reflection from a tiny defect. Focusing is accomplished by using nonaxisymmetric waveforms and subsequent time delayed superposition at a specific point in a pipe. A semianalytical finite element method is used to present wave structure in the pipe. Focusing potential is also studied with various modes and frequencies.

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22

ZHU, Q., Y. LIU, A. A. TJAVARAS, M. S. TRIANTAFYLLOU, and D. K. P. YUE. "Mechanics of nonlinear short-wave generation by a moored near-surface buoy." Journal of Fluid Mechanics 381 (February 25, 1999): 305–35. http://dx.doi.org/10.1017/s0022112098003826.

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We consider the nonlinear interaction problem of surface waves with a tethered near-surface buoy. Our objective is to investigate mechanisms for nonlinear short surface wave generation in this complete coupled wave–buoy–cable dynamical system. We develop an effective numerical simulation capability coupling an efficient and high-resolution high-order spectral method for the nonlinear wave–buoy interaction problem with a robust implicit finite-difference method for the cable–buoy dynamics. The numerical scheme accounts for nonlinear wave–wave and wave–body interactions up to an arbitrary high order in the wave steepness and is able to treat extreme motions of the cable including conditions of negative cable tension. Systematic simulations show that beyond a small threshold value of the incident wave amplitude, the buoy performs chaotic motions, characterized by the snapping of the cable. The root cause of the chaotic response is the interplay between the snapping of the cable and the generation of surface waves, which provides a source of strong (radiation) damping. As a result of this interaction, the chaotic buoy motion switches between two competing modes of snapping response: one with larger average peak amplitude and lower characteristic frequency, and the other with smaller amplitude and higher frequency. The generated high-harmonic/short surface waves are greatly amplified once the chaotic motion sets in. Analyses of the radiated wave spectra show significant energy at higher frequencies which is orders of magnitude larger than can be expected from nonlinear generation under regular motion.

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23

KELLER, OLE. "OPTICAL NEAR-FIELD INTERACTION ON THE BASIS OF PHOTON WAVE MECHANICS." Journal of Nonlinear Optical Physics & Materials 12, no. 04 (December 2003): 393–417. http://dx.doi.org/10.1142/s0218863503001547.

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Near-field optical aspects of classical electrodynamics are brought into focus by dividing the electromagnetic field into its transverse and longitudinal vector-field parts. A transverse electromagnetic propagator formalism thereafter is used to study the field-matter interaction in the transverse current density domain, the birth domain of the photon. Subsequently, a brief summary of photon wave mechanics, the first-quantized theory of the photon, is given, paying particular attention to the dynamics in the near-field zone of matter (atom, molecule, mesoscopic particle). In the wake of a discussion of the relativistic transformation properties of the covariant photon field matrix the photon energy wave function is introduced. In a central section, photon wave mechanics and near-field optics are brought in contact, and the photon embryo state, the polychromatic photon concept, and the quantum mechanical theory for the transverse one-photon current density discussed.

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24

Tang, Shanran, Yiqin Yang, and Liangsheng Zhu. "Directing Shallow-Water Waves Using Fixed Varying Bathymetry Designed by Recurrent Neural Networks." Water 15, no. 13 (June 29, 2023): 2414. http://dx.doi.org/10.3390/w15132414.

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Directing shallow-water waves and their energy is highly desired in many ocean engineering applications. Coastal infrastructures can be protected by reflecting shallow-water waves to deep water. Wave energy harvesting efficiency can be improved by focusing shallow-water waves on wave energy converters. Changing water depth can effectively affect wave celerity and therefore the propagation of shallow-water waves. However, determining spatially varying bathymetry that can direct shallow-water waves to a designed location is not trivial. In this paper, we propose a novel machine learning method to design and optimize spatially varying bathymetry for directing shallow-water waves, in which the bathymetry is assumed fixed in time without considering morphodynamics. Shallow-water wave theory was applied to establish the mapping between water wave mechanics and recurrent neural networks (RNNs). Two wave-equivalent RNNs were developed to model shallow-water waves over fixed varying bathymetry. The resulting RNNs were trained to optimize bathymetry for wave energy focusing. We demonstrate that the bathymetry optimized by the wave-equivalent RNNs can effectively reflect and refract wave energy to various designed locations. We also foresee the potential that new engineering tools can be similarly developed based on the mathematical equivalence between wave mechanics and recurrent neural networks.

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25

Rozenman, Georgi Gary, Shenhe Fu, Ady Arie, and Lev Shemer. "Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves." Fluids 4, no. 2 (May 27, 2019): 96. http://dx.doi.org/10.3390/fluids4020096.

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We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

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26

Boccotti, P., G. Barbaro, and L. Mannino. "A field experiment on the mechanics of irregular gravity waves." Journal of Fluid Mechanics 252 (July 1993): 173–86. http://dx.doi.org/10.1017/s0022112093003714.

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In random wind-generated wave motion on the sea surface, extreme wave events have been shown theoretically to occur within groups with a well-defined configuration and time history that can be specified in terms of the space-time autocovariances of the surface displacement. The predictions of the theory have been tested in a field experiment in the Straits of Messina in which an array of nine wave gauges and nine pressure transducers supported by vertical piles provided space-time information on waves generated over a fetch of approximately 10 km. It was confirmed that the general configuration of the extreme wave groups measured was consistent with the theoretical predictions in terms of the measured space-time autocovariance. During the development stage of a group, as the height of the central (outstanding) wave grows to a maximum, the width of the wave front reduces to a minimum. As an individual wave passes through the group, its wavelength decreases as the wave height increases towards the apex, after which the wavelength increases again as the wave moves towards the front of the group and abates.

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27

Sun, Zongqi, Li Zhang, and Joseph L. Rose. "Flexural Torsional Guided Wave Mechanics and Focusing in Pipe." Journal of Pressure Vessel Technology 127, no. 4 (February 14, 2005): 471–78. http://dx.doi.org/10.1115/1.2065587.

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Theoretical work on flexural torsional guided waves in pipe is presented along with angular profile experimental justification. Combined with previous work on flexural longitudinal modes and axisymmetric longitudinal and torsional modes, this work now forms a framework of nonaxisymmetric guided wave mechanics in pipe. Pipe inspection experiments are also carried out by flexural torsional wave focusing to demonstrate the advantages of the focusing technique.

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28

Firpo, M. C., F. Leyvraz, and G. Attuel. "Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction." Physics of Plasmas 13, no. 12 (December 2006): 122302. http://dx.doi.org/10.1063/1.2397039.

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29

Broutman, D., and R. Grimshaw. "The energetics of the interaction between short small-amplitude internal waves and inertial waves." Journal of Fluid Mechanics 196 (November 1988): 93–106. http://dx.doi.org/10.1017/s0022112088002629.

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The interaction between a wave packet of small-amplitude short internal waves, and a finite-amplitude inertial wave field is described to second order in the short-wave amplitude. The discussion is based on the principle of wave action conservation and the equations for the wave-induced Lagrangian mean flow. It is demonstrated that as the short internal waves propagate through the inertial wave field they generate a wave-induced train of trailing inertial waves. The contribution of this wave-induced mean flow to the total energy balance is described. The results obtained here complement the finding of Broutman & Young (1986) that the short internal waves undergo a net change in energy after their encounter with the inertial wave field.

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30

Barrett, Jeffrey A. "Typicality in Pure Wave Mechanics." Fluctuation and Noise Letters 15, no. 03 (September 2016): 1640009. http://dx.doi.org/10.1142/s0219477516400095.

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Hugh Everett III's pure wave mechanics is a deterministic physical theory with no probabilities. He nevertheless sought to show how his theory might be understood as making the same statistical predictions as the standard collapse formulation of quantum mechanics. We will consider Everett's argument for pure wave mechanics, how it depends on the notion of branch typicality, and the relationship between the predictions of pure wave mechanics and the standard quantum probabilities.

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31

Broyles, A. A. "Wave mechanics of particle detectors." Physical Review A 48, no. 2 (August 1, 1993): 1055–65. http://dx.doi.org/10.1103/physreva.48.1055.

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32

Mayer, Alexander Franklin. "Wave energy in quantum mechanics." Journal of Physics: Conference Series 70 (May 1, 2007): 012013. http://dx.doi.org/10.1088/1742-6596/70/1/012013.

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33

Stewart, A. M. "Wave mechanics without gauge fixing." Journal of Molecular Structure: THEOCHEM 626, no. 1-3 (May 2003): 47–51. http://dx.doi.org/10.1016/s0166-1280(02)00718-2.

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34

Wall, F. T. "Discrete wave mechanics: An introduction." Proceedings of the National Academy of Sciences 83, no. 15 (August 1, 1986): 5360–63. http://dx.doi.org/10.1073/pnas.83.15.5360.

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35

Wall, F. T. "Discrete wave mechanics: Multidimensional systems." Proceedings of the National Academy of Sciences 84, no. 10 (May 1, 1987): 3091–94. http://dx.doi.org/10.1073/pnas.84.10.3091.

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36

Demirbilek, Zeki. "Wave Mechanics for Ocean Engineering." Journal of Waterway, Port, Coastal, and Ocean Engineering 127, no. 4 (August 2001): 252. http://dx.doi.org/10.1061/(asce)0733-950x(2001)127:4(252).

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37

Benn, I. M., and R. W. Tucker. "Wave mechanics and inertial guidance." Physical Review D 39, no. 6 (March 15, 1989): 1594–601. http://dx.doi.org/10.1103/physrevd.39.1594.

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38

Treder, Hans-Jürgen, and Wilfried Schröder. "Magnetohydrodynamics corresponding with wave mechanics." Foundations of Physics 27, no. 6 (June 1997): 875–79. http://dx.doi.org/10.1007/bf02550346.

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39

Wang, Lipo, and R. F. O'Connell. "Quantum mechanics without wave functions." Foundations of Physics 18, no. 10 (October 1988): 1023–33. http://dx.doi.org/10.1007/bf01909937.

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40

Mehra, Jagdish. "Erwin Schrödinger and the rise of wave mechanics. II. The creation of wave mechanics." Foundations of Physics 17, no. 12 (December 1987): 1141–88. http://dx.doi.org/10.1007/bf01889592.

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41

Pedley, T. J., and S. J. Hill. "Large-amplitude undulatory fish swimming: fluid mechanics coupled to internal mechanics." Journal of Experimental Biology 202, no. 23 (December 1, 1999): 3431–38. http://dx.doi.org/10.1242/jeb.202.23.3431.

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The load against which the swimming muscles contract, during the undulatory swimming of a fish, is composed principally of hydrodynamic pressure forces and body inertia. In the past this has been analysed, through an equation for bending moments, for small-amplitude swimming, using Lighthill's elongated-body theory and a ‘vortex-ring panel method’, respectively, to compute the hydrodynamic forces. Those models are outlined in this review, and a summary is given of recent work on large-amplitude swimming that has (a) extended the bending moment equation to large amplitude, which involves the introduction of a new (though probably usually small) term, and (b) developed a large-amplitude vortex-ring panel method. The latter requires computation of the wake, which rolls up into concentrated vortex rings and filaments, and has a significant effect on the pressure on the body. Application is principally made to the saithe (Pollachius virens). The calculations confirm that the wave of muscle activation travels down the fish much more rapidly than the wave of bending.

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42

Wilhelm, H. E. "Gallilei covariant quantum mechanics in electromagnetic fields." International Journal of Mathematics and Mathematical Sciences 8, no. 3 (1985): 589–97. http://dx.doi.org/10.1155/s0161171285000643.

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A formulation of the quantum mechanics of charged particles in time-dependent electromagnetic fields is presented, in which both the Schroedinger equation and wave equations for the electromagnetic potentials are Galilei covariant, it is shown that the Galilean relativity principle leads to the introduction of the electromagnetic substratum in which the matter and electromagnetic waves propagate. The electromagnetic substratum effects are quantitatively significant for quantum mechanics in reference frames, in which the substratum velocitywis in magnitude comparable with the velocity of lightc. The electromagnetic substratum velocitywoccurs explicitly in the wave equations for the electromagnetic potentials but not in the Schroedinger equation.

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43

Aleebrahim, Mohammad Ali, and Mirmosadegh Jamali. "Experimental investigation of instability of fluid mud layer under surface wave motion." Physics of Fluids 34, no. 3 (March 2022): 036602. http://dx.doi.org/10.1063/5.0083404.

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Motivated by environmental impacts of surface-wave induced mixing of fluid mud with clear water in nearshore areas, this paper presents quantitative measurements of excitation of interfacial waves over a bed mud layer by a surface wave in a wave flume. After an initial fluidization process, a quasi-standing interfacial wave comprised of four interfacial waves was observed at the interface as a result of a resonant wave interaction with the surface wave. The interfacial waves were subharmonic to the surface wave and traveled at the maximum possible angle from it. The growth rate and kinematic properties of the interfacial waves were measured, and good agreement with theoretical predictions of a two-layer interaction model was obtained. It was found that excitation of these waves was highly dependent on the surface wave height and fluid mud viscosity. Furthermore, thickening of the lutocline layer as a result of resuspension of fluid mud highly influenced the wavelengths as well as the damping rate of the interfacial waves.

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44

Wu, Jiang-Kang, and Philip L. F. Liu. "Harbour excitations by incident wave groups." Journal of Fluid Mechanics 217 (August 1990): 595–613. http://dx.doi.org/10.1017/s0022112090000866.

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By using the multiple-scales perturbation method, analytical solutions are obtained for the second-order low-frequency oscillations inside a rectangular harbour excited by incident wave groups. The water depth is a constant. The width of the harbour entrance is of the same order of magnitude as the wavelength of incident carrier (short) waves, but small in comparison with the wavelength of the wave envelope. Because of the modulations in the wave envelope, a second-order long wave is locked in with the wave envelope and propagates with the speed of the group velocity. Outside the harbour, locked long waves also exist in the reflected wave groups, but not in the radiated wave groups. Inside the harbour, the analytical expressions for the locked long waves are obtained. Owing to the discontinuity of the locked long waves across the harbour mouth, second-order free long waves are generated. The free long waves propagate with a speed of (gh)½ inside and outside the harbour. The free long waves inside the harbour may be resonated in a low-frequency range which is relevant to the harbour resonance.

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45

Olisa, Samuel Chukwuemeka, Muhammad A. Khan, and Andrew Starr. "Elastic Wave Mechanics in Damaged Metallic Plates." Symmetry 15, no. 11 (October 27, 2023): 1989. http://dx.doi.org/10.3390/sym15111989.

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Human health monitoring (HHM) is essential for continued daily task execution, as is structural health monitoring (SHM) for structures to ensure the continual performance of their designed tasks with optimal efficiency. The existence of damage in a structure affects its optimal use through stiffness deterioration. Damage of different forms could occur in a structure but have the singular objective of material degradation, leading to its underuse for a task. Guided wave ultrasonics has shown strength in detecting sundry damage in structures, but most of the damage monitored and detected is unfilled with substances. However, some damage could trap and accumulate substances that could hasten material degradation through corrosion activities under favorable conditions, especially in the oil and gas industry. This study used the ultrasonic-guided waves’ pitch–catch inspection technique to identify damage filled with different materials. The assessment was based on the RMSD of the dominant Lamb wave mode’s average maximum amplitude and the response signals’ transmission coefficient (TC). A five-cycle tone burst of excitation signals of different frequencies was created to generate propagating Lamb waves in the structure. The fundamental antisymmetric mode was found to be more sensitive than the fundamental symmetric mode when detecting damage filled with various substances. At 80 kHz, the deviation of the current response signals from the baseline response signals due to different filled substances in the damage was distinct and decreased with increased fluid viscosity. Given that structures in the oil and gas sector are particularly susceptible to substance-induced damage, the outcomes of this study are paramount.

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46

Sniehyrov, Ihor A., Inna А. Plakhtiienko, Viktoriia O. Kurhanska, and Yurii V. Smiianov. "THE MAIN LEITMOTIFS OF CHINESE MEDICINE IN THE CONTEXT OF THE DEVELOPMENT OF MODERN SCIENCE." Wiadomości Lekarskie 73, no. 5 (2020): 1000–1003. http://dx.doi.org/10.36740/wlek202005130.

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The aim: To demonstrate the limitations of pharmacological (chemical) therapy and the atomistic paradigm of science (in particular medicine) on the methodological basis of modern interdisciplinary directions (the theory of dissipative structures, chaos, autopoiesis), quantum mechanics, as well as the basic patterns of oriental medicine. Materials and methods: The principles used in the article include self-organization, emergence, quantum mechanics (the Heisenberg uncertainty principle), the principle of consistency; principles of using coherent millimeter waves of low power, etc. Theoretical methods of analysis and synthesis, idealization, abstraction, induction and deduction are also used. Сonclusions: The concept of “integrable system” is equivalent to the concept of “integral quantum-mechanical system”; Integral quantum-mechanical systems (nuclei, atoms, molecules, living objects) in the ground state are described by periodic wave functions of the type exp (jwt); The traditional paradigm, for the most part, eliminates the qualitative difference between living and dead matter; Any living system functioning as a whole is simultaneously a macroscopic quantum-mechanical object and a millimeter-wave laser.

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47

Watson, Kenneth M., and Steven B. Buchsbaum. "Interaction of capillary waves with longer waves. Part 1. General theory and specific applications to waves in one dimension." Journal of Fluid Mechanics 321 (August 25, 1996): 87–120. http://dx.doi.org/10.1017/s0022112096007653.

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A Hamiltonian formulation is used to investigate irrotational capillary wave dynamics. Dissipation is accounted for by putting the wave system in contact with a ‘heat bath’. The generation of short waves by longer waves is studied. It is found that millimetre-wavelength waves tend to be created on the forward face of a steep longer wave, while centimetre waves tend to form near the crest. Generation of capillary waves by wind waves is investigated. The results are compared with predictions of the Hasselmann transport equation. It is found that off-resonance interactions lead to significant corrections to the transport theory. The relative importance of three-wave and four-wave interactions is studied, as well as the role of triad resonances. For the capillary phenomena studied here, the four-wave terms in most cases lead to quantitative, but not qualitative, corrections to the three-wave only calculations. However, restricting interactions to the neighbourhood of triad resonances can give quite erroneous results. Use of a canonical transformation to pseudo-wave variables can greatly reduce numerical computation times.

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48

Smirnov, V. N., S. M. Kovalev, and A. A. Nubom. "SELF-EXCITED OSCILLATIONS IN THE DRIFTING ICE COVER OF THE ARCTIC OCEAN." DEDICATED TO THE 90TH ANNIVERSARY OF PROF. K.N. FEDOROV OCEAN PHYSICS 47, no. 3 (November 6, 2019): 122–38. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(3).11.

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During the monitoring of physical-mechanical state of the ice cover of the Arctic Ocean a wide spectrum of oscillation and wave processes was in the system ice-water studied. The investigations were carried out on the drifting stations “North Pole” with seismometers and tiltmeters. Vertical and horizontal displacements in the ice field characterize parameters of wave processes caused by compression and ridging of ice-mechanical self-excited oscillations. Mechanics of appearance and propagation of waves can be considered with an account of elastic-viscous properties of the ice cover. A phenomenological model is considered of appearance of periodic horizontal displacements on an extensive rupture in a continuous ice cover. At the fault of stresses on the rupture elastic horizontally polarized waves are emitted.

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49

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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50

Soomere, Tarmo. "Nonlinear Components of Ship Wake Waves." Applied Mechanics Reviews 60, no. 3 (May 1, 2007): 120–38. http://dx.doi.org/10.1115/1.2730847.

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Nonlinear components of wakes from large high-speed ships at times carry a substantial part of the wake energy and behave completely differently compared to the classical Kelvin wave system. This overview makes an attempt to summarize the descriptions of nonlinear parts of a ship’s wake. For completeness, also the basic properties of the Kelvin wake are sketched. The central topic is the generation of solitons by ship motion both in channels and in unbounded sea areas. The discussion is mostly limited to disturbances on the surface of nonstratified water. The optional nonlinear components of the ship wake such as the very narrow V-like wake components, packets of monochromatic waves, ship-generated depression areas, and supercritical bores are also discussed. Specific features of solitonic ship waves and their interactions have numerous applications in naval and coastal engineering, and in adjacent areas of applied mechanics. An overview of the practical use of certain properties of phase shifts, and particularly high wave humps occurring during Mach reflection and nonlinear interaction of solitons in decreasing the wave resistance at supercritical speeds and in the freak wave theory, is also presented. The final part of the paper describes the results of studies of far-field properties of nonlinear wakes and possible consequences of the increase of local hydrodynamic activity. There are 263 references cited in this review article.

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