Journal articles: 'Focusing wave'

1

Murray, D. R., and P. Öhberg. "Matter wave focusing." Journal of Physics B: Atomic, Molecular and Optical Physics 38, no. 8 (March 30, 2005): 1227–34. http://dx.doi.org/10.1088/0953-4075/38/8/012.

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Xu, Guochun, Hongbin Hao, Qingwei Ma, and Qinqin Gui. "An Experimental Study of Focusing Wave Generation with Improved Wave Amplitude Spectra." Water 11, no. 12 (November 28, 2019): 2521. http://dx.doi.org/10.3390/w11122521.

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We experimentally investigate the generating results of space-time focusing waves based on two new wave spectra, i.e., the quasi constant wave amplitude spectrum (QCWA) and the quasi constant wave steepness spectrum (QCWS), in which amplitude and steepness for each wave component can be adjusted with fixed wave energy. The wavemaker signal consists of a theoretical wavemaker motion signal and two different auxiliary functions at two ends of the signal. By testing a series of focusing waves in a physical wave tank, we found that with given wave energy, the QCWA spectrum can produce a focusing wave with larger crest elevation and farther focusing location from the wavemaker flap, as compared with the QCWS spectrum. However, both spectra lead to larger focusing wave crests when the wave frequency bandwidth was narrowed down and a positive correlation between the generated relative wave crest elevation and the input wave elevation parameter. The two spectra produce different focusing wave positions for the same wave frequency range. We also found that the focusing time strongly relates to the energy of the highest-frequency wave component of the wave spectrum.

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Smit, Pieter Bart, T. T. Janssen, and T. H. C. Herbers. "TOPOGRAPHY-INDUCED FOCUSING OF RANDOM WAVES." Coastal Engineering Proceedings 1, no. 33 (December 15, 2012): 6. http://dx.doi.org/10.9753/icce.v33.waves.6.

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Refraction of narrow-band surface waves in coastal areas can result in wave-focal zones where due to interference, wave statistics vary rapidly and on similar length scales as those of individual waves. However such interference patterns, or wave coherence, are not accounted for in conventional stochastic wave models that are based on the energy balance equation or radiative transfer equation. In this work we present a quasi-coherent theory, which is an extension of the radiative transfer equation and quasi-homogeneous theory. We show that this new stochastic modelling approach can resolve rapid variations in wave statistics that occur in the vicinity of a wave caustic. The results compare favourably to those obtained from ensemble averages calculated with a deterministic phase resolving model (SWASH) and, in a focal zone, constitute a significant improvement over those obtained with a conventional stochastic wave model based on an energy balance equation (SWAN).

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Vogel, K., F. Gleisberg, N. L. Harshman, P. Kazemi, R. Mack, L. Plimak, and W. P. Schleich. "Optimally focusing wave packets." Chemical Physics 375, no. 2-3 (October 2010): 133–43. http://dx.doi.org/10.1016/j.chemphys.2010.07.002.

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Chen, Jinbing, and Dmitry E. Pelinovsky. "Rogue periodic waves of the focusing nonlinear Schrödinger equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2210 (February 2018): 20170814. http://dx.doi.org/10.1098/rspa.2017.0814.

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Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov–Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine’s breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

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Zhang, Zhen Fu, Xin Wu Zeng, Qing Yu Cai, and Kai Feng Han. "Numerical Simulation on Underwater Shock Wave Focusing." Applied Mechanics and Materials 105-107 (September 2011): 121–26. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.121.

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Shock wave focusing by an ellipsoidal reflector can produce higher pressure in the focal region. The focusing process of shock wave was studied by theory analyses and numerical results. Base on the experimental observation the shock wave source is equivalent to the explosion of an underwater explosive. A finite element model was set up to investigate the shock wave focusing behaviors. Both the pressure-time history and the peak pressure along the axial position were presented. The shock wave focusing process was shown. The interactions of waves in the focal region are shown. A modified EOS of water was applied, which can be used to analyze the negative pressure observed; the numerical results based on the modified EOS agree well with the experimental data.

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Merkoune, D., J. Touboul, N. Abcha, D. Mouazé, and A. Ezersky. "Focusing wave group on a current of finite depth." Natural Hazards and Earth System Sciences 13, no. 11 (November 19, 2013): 2941–49. http://dx.doi.org/10.5194/nhess-13-2941-2013.

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Abstract. Formation of freak waves resulting from the wave packets propagating in finite water depth on the background of a current is studied experimentally and numerically. In the experiment, the freak waves appear as a result of dispersion focusing of wave train excited by wave maker with modulated frequency. The space evolution of the frequency modulated train is studied in numerical simulations. We showed that in the water of finite depth, a distance of focusing increases and amplitude in the focal point decreases in comparison with infinite water depth. Experimental results are in good agreement with numerical simulations if wave breaking of surface waves does not occur.

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Zhou, Binzhen, Kanglixi Ding, Jiahao Wang, Lei Wang, Peng Jin, and Tianning Tang. "Experimental study on the interactions between wave groups in double-wave-group focusing." Physics of Fluids 35, no. 3 (March 2023): 037118. http://dx.doi.org/10.1063/5.0142042.

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Nonlinear interactions in wave-group focusing are regarded as one of the main mechanisms in the generation of destructive extreme waves. In real seas, the wideband bimodal state is a typical configuration, containing interactions within a single wave group and between different wave groups. The former has been well uncovered under the assumption of narrow bandwidth, but the latter is poorly understood. In this paper, physical experiments are conducted to reveal the physics of double-wave-group focusing considering various energy distributions. Superposed wavemaker signals generated by the iteration method are applied to produce a double-wave-group focusing with the interactions being decomposed. Results of the wavelet-based bicoherence spectrum show that double-wave-group focusing is distinguished from the linear superposition of two single-wave-group focusing mainly in the nonlinear interactions induced by the second-order sum harmonics. Under the assumption of equivalent energy, interactions of the second-order sum harmonics between the lower frequency group and higher frequency group cannot be ignored in swell-dominated states, and lesser linear interactions and stronger nonlinear interactions are observed while the spectral distribution of the double-wave-group is more asymmetrical. This work is anticipated to contribute to the understanding of the generation mechanism of extreme waves driven by strong nonlinearity.

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Liu, Mao, Haijie Yu, and Ben Wang. "Tuning and controlling antiplane shear wave propagation in elastic membranes." AIP Advances 12, no. 8 (August 1, 2022): 085319. http://dx.doi.org/10.1063/5.0103469.

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In this paper, a rotary-focusing device for the antiplane shear wave is constructed to control and guide elastic wave energy transmission in elastic membranes. The designed device can cloak the antiplane shear waves outside the device and has a rotary-focusing effect on the shear waves energy inside the device in a membrane. The multilayered isotropic material properties of the rotary-focusing device are derived based on the transformation and rotary medium method, and a rotation parameter to guide the propagating trajectories of the antiplane shear waves is introduced. The efficiency of the rotary-focusing device for the antiplane shear waves is verified. The stability of shear wave fields in a membrane with the rotary-focusing device is analyzed to study the performance of rotary-focusing. Numerical examples show that the constructed rotary-focusing device for antiplane shear waves can effectively rotate and focus the antiplane shear wave energy into the device for a wide range of exciting frequencies, which can enhance the antiplane shear energy. Therefore, this study can provide theoretical support for potential applications in the fields of energy harvesting and vibration control.

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10

Vines, R. E., Shin-ichiro Tamura, and J. P. Wolfe. "Surface Acoustic Wave Focusing and Induced Rayleigh Waves." Physical Review Letters 74, no. 14 (April 3, 1995): 2729–32. http://dx.doi.org/10.1103/physrevlett.74.2729.

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Vines, R. E., Shin-ichiro Tamura, and J. P. Wolfe. "Surface Acoustic Wave Focusing and Induced Rayleigh Waves." Physical Review Letters 75, no. 9 (August 28, 1995): 1873. http://dx.doi.org/10.1103/physrevlett.75.1873.

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12

CHAMPEAUX, S., T. PASSOT, and P. L. SULEM. "Alfvén-wave filamentation." Journal of Plasma Physics 58, no. 4 (December 1997): 665–90. http://dx.doi.org/10.1017/s0022377897006119.

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Transverse focusing or filamentation of weakly nonlinear Alfvén waves propagating in a dispersive medium is studied using an amplitude-equation formalism. Special attention is devoted to the small-β regime, where kinetic effects are weak and Alfvén-wave trains are unstable to convective filamentation. It is shown that, according to their initial duration, focusing wave packets can collapse in a finite distance or, conversely, the focusing can be arrested by the development of magnetosonic waves, which in both cases may lead to the formation of sharp acoustic fronts. This effect, which dominates the usual longitudinal steepening, provides an efficient mechanism to heat the plasma without requiring large-amplitude waves. It can significantly contribute to the acceleration of the solar wind.

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13

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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WATANABE, Yasunori, and Takashi OGUMA. "WAVE PACKET FOCUSING UNIFORM CURRENT." Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering) 77, no. 2 (2021): I_31—I_36. http://dx.doi.org/10.2208/kaigan.77.2_i_31.

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15

Aktosun, Tuncay, and James H. Rose. "Wave focusing on the line." Journal of Mathematical Physics 43, no. 7 (July 2002): 3717–45. http://dx.doi.org/10.1063/1.1483894.

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16

Wang, Weizhi, Arun Kamath, Csaba Pakozdi, and Hans Bihs. "Investigation of Focusing Wave Properties in a Numerical Wave Tank with a Fully Nonlinear Potential Flow Model." Journal of Marine Science and Engineering 7, no. 10 (October 21, 2019): 375. http://dx.doi.org/10.3390/jmse7100375.

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Nonlinear wave interactions and superpositions among the different wave components and wave groups in a random sea sometimes produce rogue waves with extremely large wave heights that appear unexpectedly. A good understanding of the generation and evolution of such extreme wave events is of great importance for the analysis of wave forces on marine structures. A fully nonlinear potential flow (FNPF) model is proposed in the presented paper to investigate the different factors that influence the wave focusing location, focusing time and focusing wave height in a numerical wave tank. Those factors include wave steepness, spectrum bandwidth, wave generation method, focused wave spectrum, and wave spreading functions. The proposed model solves the Laplace equation together with the boundary conditions on a σ -coordinate grid using high-order discretisation schemes on a fully parallel computational framework. The model is validated against the focused wave experiments and thereafter used to obtain insights into the effects of the different factors. It is found that the wave steepness contributes to changing the location and time of focus significantly. Spectrum bandwidth and directional spreading affect the focusing wave height and profile, for example, a wider bandwidth and a wider directional spread lead to a lower focusing wave height. A Neumann boundary condition represents the nonlinearity of the wave groups better than a relaxation method for wave generation.

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Ermanyuk, E. V., N. D. Shmakova, and J. B. Flór. "Internal wave focusing by a horizontally oscillating torus." Journal of Fluid Mechanics 813 (January 26, 2017): 695–715. http://dx.doi.org/10.1017/jfm.2016.871.

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This paper presents an experimental study on internal waves emitted by a horizontally oscillating torus in a linearly stratified fluid. Two internal wave cones are generated with the kinetic energy focused at the apices of the cones above and below the torus where the wave amplitude is maximal. Their motion is measured via tracking of distortions of horizontal fluorescein dye planes created prior to the experiments and illuminated by a vertical laser sheet. The distortion of the dye planes gives a direct access to the Lagrangian displacement of local wave amplitudes and slopes, and in particular, allows us to calculate a local Richardson number. In addition particle image velocimetry measurements are used. Maximum wave slopes are found in the focal region and close to the surface of the torus. As the amplitude of oscillations of the torus increases, wave profiles in the regions of maximum wave slopes evolve nonlinearly toward local overturning. A theoretical approximation based on the theory of Hurley & Keady (J. Fluid Mech., vol. 351, 1997, pp. 119–138) is presented and shows, for small amplitudes of oscillation, a very reasonable agreement with the experimental data. For the focal region the internal wave amplitude is found to be overestimated by the theory. The wave breaking in the focal region is investigated as a function of the Keulegan–Carpenter number, $Ke=A/a$, with $A$ the oscillation amplitude and $a$ the short radius of the torus. A linear wave regime is found for $Ke<0.4$, nonlinear effects start at $Ke\approx 0.6$ and breaking for $Ke>0.8$. For large forcing, the measured wave amplitude normalized with the oscillation amplitude decreases almost everywhere in the wave field, but increases locally in the focal region due to nonlinear effects. Due to geometric focusing the amplitude of the wave increases with $\sqrt{\unicode[STIX]{x1D716}}$, with $\unicode[STIX]{x1D716}=b/a$ and $b$ is the mean radius of the torus. The relevance of wave focusing due to ocean topography is discussed.

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BÜHLER, OLIVER, and CAROLINE J. MULLER. "Instability and focusing of internal tides in the deep ocean." Journal of Fluid Mechanics 588 (September 24, 2007): 1–28. http://dx.doi.org/10.1017/s0022112007007410.

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The interaction of tidal currents with sea-floor topography results in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation due to nonlinear wave breaking and concomitant three-dimensional turbulence could play an important role in the mixing of the abyssal ocean, and hence in controlling the large-scale ocean circulation.As part of on-going work aimed at providing a theory for the vertical distribution of wave breaking over sea-floor topography, in this paper we investigate the instability of internal tides in a very simple linear model that helps us to relate the formation of unstable regions to simple features in the sea-floor topography. For two-dimensional tides over one-dimensional topography we find that the formation of overturning instabilities is closely linked to the singularities in the topography shape and that it is possible to have stable waves at the sea floor and unstable waves in the ocean interior above.For three-dimensional tides over two-dimensional topography there is in addition an effect of geometric focusing of wave energy into localized regions of high wave amplitude, and we investigate this focusing effect in simple examples. Overall, we find that the distribution of unstable wave breaking regions can be highly non-uniform even for very simple idealized topography shapes.

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Li, Chi-Yu, Ruey-Syan Shih, and Wen-Kai Weng. "Investigation of Ocean-Wave-Focusing Characteristics Induced by a Submerged Crescent-Shaped Plate for Long-Crested Waves." Water 12, no. 2 (February 12, 2020): 509. http://dx.doi.org/10.3390/w12020509.

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The need for renewable energy has gained importance with growing concerns about climate change. Wave energy has attracted considerable attention owing to its sustainability potential. Reflection, refraction, diffraction, and shoaling of waves occur when waves propagate through a submerged structure. These mechanics, when properly utilized, can be employed to focus waves to a specific location and also to increase wave heights, by which wave energy is usually represented, for planning and designing wave farms. Wave focusing induced by a submerged crescent-shaped plate for different wave conditions, incident wave directions, and submerged depths mainly considering the potential applications of absorber wave-energy converters within the wave farm was investigated experimentally and numerically. All experimental regular wave conditions were controlled to be nonbreaking, and the numerical results were obtained by a 3D model, implemented through the boundary element method based on Airy wave theory. The results show that wave focusing appears behind the plate along the direction of the incident waves, and the locations of focused waves tend to be farther away from the plate for shorter-period waves. The maximum measured wave height can be 3.44 times higher than the incident wave height.

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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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DONATO, A. N., D. H. PEREGRINE, and J. R. STOCKER. "The focusing of surface waves by internal waves." Journal of Fluid Mechanics 384 (April 10, 1999): 27–58. http://dx.doi.org/10.1017/s0022112098003917.

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The surface current generated by internal waves in the ocean affects surface gravity waves. The propagation of short surface waves is studied using both simple ray theory for linear waves and a fully nonlinear numerical potential solver. Attention is directed to the case of short waves with initially uniform wavenumber, as may be generated by a strong gust of wind. In general, some of the waves are focused by the surface current and in these regions the waves steepen and may break. Comparisons are made between ray theory and the more accurate solutions. For ray theory, the occurrence of focusing is examined in some detail and exact analytic solutions are found for rays on currents with linear and quadratic spatial variation – only the latter giving focusing for our initial conditions. With regard to interpretation of remote sensing of the sea surface, we find that enhanced wave steepness is not necessarily associated with a particular phase of the internal wave, and simplistic interpretations may sometimes be misleading.

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Georgieva, M., A. Shivarova, and I. Urdev†. "Self-focusing of surface waves in a cylindrical plasma waveguide." Journal of Plasma Physics 52, no. 3 (December 1994): 391–407. http://dx.doi.org/10.1017/s0022377800027215.

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Self-consistent nonlinear changes of plasma parameters and characteristics of electromagnetic guided waves are studied with regard to the effect of self- focusing and waveguided channel formation in a cylindrical plasma waveguide. Besides the nonlinearity due to the ponderomotive force action usually involved, ionization nonlinearity specified for different regimes of particle loss mechanisms is considered. An azimuthally symmetric electromagnetic surface wave is the guided mode that forms and sustains the wave channel.The nonlinear dispersion law and the nonlinear changes in the wave field distribution and power flow are obtained, describing the effect of the self-focusing of the waves under conditions of weak nonlinearity.

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Jeon, Wooyoung, Sunho Park, Gyu-Mok Jeon, and Jong-Chun Park. "Computational Study on Rogue Wave and Its Application to a Floating Body." Applied Sciences 12, no. 6 (March 10, 2022): 2853. http://dx.doi.org/10.3390/app12062853.

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A rogue wave is a huge wave that is generated by wave energy focusing. Rogue waves can cause critical damage to ships and offshore platforms due to their great wave energy and unpredictability. In this paper, to generate a rogue wave, a bull’s-eye wave, which is a focusing of multi-directional waves, was simulated in a numerical wave tank. A multi-directional wave generating boundary was developed using OpenFOAM, which is an open-source computational fluid dynamics (CFD) library. The wave height and profile of the generated rogue wave were compared to those of the regular wave. In addition, the pressure and velocity contours of water particles and velocity vectors at the free surface of the rogue wave were studied, along with the kinematic and dynamic effects of the rogue wave on a floating body.

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Liu, Dianyong, Yuxiang Ma, Guohai Dong, and Marc Perlin. "Detuning and wave breaking during nonlinear surface wave focusing." Ocean Engineering 113 (February 2016): 215–23. http://dx.doi.org/10.1016/j.oceaneng.2015.12.048.

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Zhang, Haiming, Aifeng Tao, Junhao Tu, Junwei Su, and Shuya Xie. "The Focusing Waves Induced by Bragg Resonance with V-Shaped Undulating Bottom." Journal of Marine Science and Engineering 9, no. 7 (June 27, 2021): 708. http://dx.doi.org/10.3390/jmse9070708.

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Intensive wave reflection occurs when the wavelengths of the incident waves and bottom undulations are in a 2:1 ratio. Existing studies have included the Bragg resonance phenomenon of waves passing over a continuous undulating bottom parallel to and oblique to the shoreline. More generally, the Bragg resonance mechanism is used as a means of coastal protection, rather than wave power generation. To focus the wave energy in a specific area, here, we propose sinusoidal sandbars of a horizontal V-shaped pattern, which is formed by two continuous undulating bottoms inclined at an angle to each other and the center axis of the angle is perpendicular to the shoreline. Based on the high-order spectral (HOS) numerical model, both the characteristics of Bragg resonance induced by the regular waves and random waves are investigated. In the scenario of regular waves, it shows that the wave-focusing effect is related to the angle of the V-shaped undulating bottom, and the optimal angle of inclination for the V-shaped undulating bottom is 162.24°. On that basis, considering the interactions between the random waves and the V-shaped undulating bottom of 162.24°, the Bragg resonance characteristics of random waves are studied. The BFI factor combining wave steepness and spectrum width can evaluate the focusing intensity of the Bragg resonance of the random waves. For BFI, in the range of 0.15–1.0, the values of Hsmax/Hs0 linearly increase with the increase of BFI.

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IBRAHIM, SLIM. "GEOMETRIC-OPTICS FOR NONLINEAR CONCENTRATING WAVES IN FOCUSING AND NON-FOCUSING TWO GEOMETRIES." Communications in Contemporary Mathematics 06, no. 01 (February 2004): 1–23. http://dx.doi.org/10.1142/s0219199704001239.

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With the methods used in [1] and [4], we prove that in the absence of focus, nonlinear geometrical optics of the critical wave equation with variable coefficients, is reduced to linear geometrical optics combined with wave operators for the critical wave equation with coefficients fixed on concentrating points. On the odd-dimensional spheres, we prove that passing through a focus is generated by a modified scattering operator.

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Sadin, D. V., B. V. Belyaev, and V. A. Davidchuk. "EFFECT OF RELAXATION PROCESSES ON THE SHOCK WAVE FOCUSING IN A GAS SUSPENSION CLOUD." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 66 (2020): 121–31. http://dx.doi.org/10.17223/19988621/66/10.

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In this paper, the interaction of a plane shock wave in air with a cylindrical region of a gas suspension and the effect of relaxation processes for various particle sizes on the refraction and focusing of the shock wave are studied. In the course of numerical modeling, the Euler approach is used to describe non-equilibrium motion of the gas and dispersed phases. A second order accuracy method in space and time is used. Verification of the method through test problems by comparing with exact solutions and calculations of other authors confirms a capability of detecting shock wave refraction effects and wave focusing with the appearance of peak profiles in a distribution of parameters. With an increase in particle sizes, the relaxation zones behind the shock wave and secondary waves, which propagate through a gas suspension cloud, have a significant impact on the shock wave refraction, focusing of transverse shock waves, and interface instability evolution. A focus point is shifted towards suspension cloud boundaries, while for sufficiently large particles, it moves beyond the boundaries (external focus mode). Thus, the reflection pressure of transverse waves and intensity of the instability at the interface reduce.

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Mukherjee, Joydeep, and A. Roy Chowdhury. "Self-focusing of Nonlinear Waves in a Relativistic Plasma with Positive and Negative Ions." Australian Journal of Physics 47, no. 6 (1994): 773. http://dx.doi.org/10.1071/ph940773.

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We have analysed the phenomenon of self-focusing of nonlinear waves in a relativistic plasma consisting of both positive and negative ions, which are assumed to be hot. We also consider the effect of the inertia of the relativistic electron by treating it dynamically. A modified form of reductive perturbation is used to deduce a nonlinear Schr�dinger equation describing the purely spatial variation of the nonlinear wave. Self-focusing of the wave can be ascertained by analysing the transversal stability of the solitary wave. It is shown that the zones of stability of the wave may become wider due to the mutual influence of various factors present in the plasma, thus favouring the process of self-focusing.

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Infeld, E. "Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas." Journal of Plasma Physics 33, no. 2 (April 1985): 171–82. http://dx.doi.org/10.1017/s0022377800002415.

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The Zakharov-Kuznetsov equation describing Korteweg–de Vries waves and solitons in a strong, uniform magnetic field is rederived taking space stretching to be isotropic. This equation is then used to investigate nonlinear waves and solitons for long-wave instabilities. A solid angle of instability develops around the plane perpendicular to the magnetic field. For weakly nonlinear waves this angle is very narrow: widening as the amplitude of the nonlinear wave is increased. The soliton wave is unstable for all directions other than parallel to the field. Previous results of other authors, limited to solitons and perpendicular propagation are recovered. Calculations are illustrated by polar diagrams for the perturbations. Some broader implications are pointed out.

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SHRIRA, VICTOR I., and WILLIAM A. TOWNSEND. "Inertia-gravity waves beyond the inertial latitude. Part 1. Inviscid singular focusing." Journal of Fluid Mechanics 664 (October 15, 2010): 478–509. http://dx.doi.org/10.1017/s0022112010003812.

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The paper is concerned with analytical study of inertia-gravity waves in rotating density-stratified ideal fluid confined in a spherical shell. It primarily aims at clarifying the possible role of these motions in deep ocean mixing. Recently, it was found that on the ‘non-traditional’ β-plane inertia-gravity internal waves can propagate polewards beyond their inertial latitude, where the wave frequency equals the local Coriolis parameter, by turning into subinertial modes trapped in the narrowing waveguides around the local minima of buoyancy frequency N. The behaviour of characteristics was established: wave horizontal and vertical scales decrease as the wave advances polewards and tend to zero at a latitude corresponding to an attractor of characteristics. However, the basic questions about wave evolution, its quantitative description and the possibility of its reflection from the critical latitude remain open. The present work addresses these issues by studying the linear inviscid evolution of finite bandwidth wavepackets on the ‘non-traditional’ β-plane past the inertial latitude for generic oceanic stratification. Beyond the inertial latitude, the wave field is confined in narrowing waveguides of three distinct generic types around different local minima of the buoyancy frequency. In the oceanic context, the widest is adjacent to the flat bottom, the thinnest is the upper mixed layer, and the middle one is located between the seasonal and main thermocline. We find explicit asymptotic solutions describing the wave field in the WKB approximation. As a byproduct, the conservation of wave action principle is explicitly formulated for all types of internal waves on the ‘non-traditional’ β-plane. The wave velocities and vertical shear tend to infinity and become singular at the attractor latitude or its vicinity for both monochromatic and finite bandwidth packets. We call this phenomenon singular focusing. These WKB solutions are shown to remain valid up to singularity for the bottom and mid-ocean waveguides. The main conclusion is that even in the inviscid setting the wave evolution towards smaller and smaller horizontal and vertical scales is irreversible: there is no reflection. For situations typical of deep ocean, a simultaneous increase in wave amplitude and decrease of vertical scale causes a sharp increase of vertical shear, which may lead to wave breaking and increased mixing.

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Li Yong-Feng, Zhang Jie-Qiu, Qu Shao-Bo, Wang Jia-Fu, Wu Xiang, Xu Zhuo, and Zhang An-Xue. "Circularly polarized wave reflection focusing metasurfaces." Acta Physica Sinica 64, no. 12 (2015): 124102. http://dx.doi.org/10.7498/aps.64.124102.

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Murashige, Sunao, and Takeshi Kinoshita. "Fundamental Studies on Ocean Wave Focusing." Journal of the Society of Naval Architects of Japan 1990, no. 168 (1990): 183–92. http://dx.doi.org/10.2534/jjasnaoe1968.1990.168_183.

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Apazidis, N., S. Sembian, and M. Liverts. "Supersonic jet by blast wave focusing." Physics of Fluids 33, no. 12 (December 2021): 126101. http://dx.doi.org/10.1063/5.0068309.

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Kim, Gunho, Carlos M. Portela, Paolo Celli, Antonio Palermo, and Chiara Daraio. "Poroelastic microlattices for underwater wave focusing." Extreme Mechanics Letters 49 (November 2021): 101499. http://dx.doi.org/10.1016/j.eml.2021.101499.

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Wang, Zhenyu, Z. X. Li, Ruifang Wang, Bo Liu, Hao Meng, Yunshan Cao, and Peng Yan. "Spin-wave focusing induced skyrmion generation." Applied Physics Letters 117, no. 22 (November 30, 2020): 222406. http://dx.doi.org/10.1063/5.0029401.

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36

Lubow, Stephen H. "A wave focusing model for starbursts." Astrophysical Journal 328 (May 1988): L3. http://dx.doi.org/10.1086/185148.

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37

Watanabe, Yasunori, Yosuke Tsuda, and Ayumi Saruwatari. "Wave packet focusing in shallow water." Coastal Engineering Journal 62, no. 2 (April 2, 2020): 336–49. http://dx.doi.org/10.1080/21664250.2020.1756033.

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38

Berg, Richard E. "Heat‐wave focusing by concave relectors." Physics Teacher 28, no. 1 (January 1990): 56–57. http://dx.doi.org/10.1119/1.2342934.

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39

Ramm, A. G., and S. Gutman. "Computational method for acoustic wave focusing." International Journal of Computing Science and Mathematics 1, no. 1 (2007): 1. http://dx.doi.org/10.1504/ijcsm.2007.013760.

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40

Smirnov, N. N., O. G. Penyazkov, K. L. Sevrouk, V. F. Nikitin, L. I. Stamov, and V. V. Tyurenkova. "Detonation onset following shock wave focusing." Acta Astronautica 135 (June 2017): 114–30. http://dx.doi.org/10.1016/j.actaastro.2016.09.014.

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41

Ishikawa, Katsuji. "Automatic focusing apparatus using ultrasonic wave." Journal of the Acoustical Society of America 78, no. 1 (July 1985): 284. http://dx.doi.org/10.1121/1.392513.

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42

Hosseini, S. H. R., O. Onodera, and K. Takayama. "Focusing of Converging Cylindrical Shock Wave." REVIEW OF HIGH PRESSURE SCIENCE AND TECHNOLOGY 7 (1998): 927–29. http://dx.doi.org/10.4131/jshpreview.7.927.

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43

Gowda, Vinay R., Mohammadreza F. Imani, Timothy Sleasman, and David R. Smith. "Efficient Holographic Focusing Metasurface." Electronics 10, no. 15 (July 30, 2021): 1837. http://dx.doi.org/10.3390/electronics10151837.

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We present the design and experimental demonstration of an efficient holographic metasurface aperture that focuses microwaves in the Fresnel zone. The proposed circular structure consists of two stacked plates with their periphery terminated in a conductive layer. Microwaves are injected into the bottom plate, which forms the feed layer, and are coupled to the top holographic metasurface layer via an annular ring. This coupling results in an inward traveling cylindrical wave in the top layer, which serves as the reference wave for a hologram. The radiating elements consist of a slot pair with their orientations designed to couple efficiently with the cylindrical reference wave while maintaining a linearly polarized focused beam. A general condition on the slot pairs radiated power is proposed to ensure low sidelobe level (SLL) and is validated with full-wave simulation. An aperture that is 20 cm in diameter, operates at 20 GHz in the K-band frequency, and forms a diffraction-limited focal spot at a distance of 10 cm is experimentally demonstrated. The proposed near-field focusing metasurface has high antenna efficiency and can find application as a compact source for Fresnel-zone wireless power transfer and remote sensing schemes.

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Zhuang, Ze-Peng, Rui Chen, Zhi-Bin Fan, Xiao-Ning Pang, and Jian-Wen Dong. "High focusing efficiency in subdiffraction focusing metalens." Nanophotonics 8, no. 7 (June 22, 2019): 1279–89. http://dx.doi.org/10.1515/nanoph-2019-0115.

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AbstractVector beams with phase modulation in a high numerical aperture system are able to break through the diffraction limit. However, the implementation of such a device requires a combination of several discrete bulky optical elements, increasing its complexity and possibility of the optical loss. Dielectric metalens, an ultrathin and planar nanostructure, has a potential to replace bulky optical elements, but its optimization with full-wave simulations is time-consuming. In this paper, an accurate and efficient theoretical model of planar metalens is developed. Based on this model, a twofold optimization scheme is proposed for optimizing the phase profile of metalenses so as to achieve subdiffraction focusing with high focusing efficiency. Then, a metalens that enables to simultaneously generate radially polarized beam (RPB) and modulate its phase under the incidence of x-polarized light with the wavelength of 532 nm is designed. Full-wave simulations show that the designed metalens of NA = 0.95 can achieve subdiffraction focusing (FWHM = 0.429λ) with high transmission efficiency (77.6%) and focusing efficiency (17.2%). Additionally, superoscillation phenomenon is found, leading to a compromise between the subdiffraction spot and high efficiency. The proposed method may provide an accurate and efficient way to achieve sub-wavelength imaging with the expected performances, which shows a potential application in super-resolution imaging.

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Menachof, David A., and Anthony Damian. "Mergers and alliances in the liner shipping industry: an historical perspective." Journal of Transportation Management 10, no. 2 (September 1, 1998): 44–56. http://dx.doi.org/10.22237/jotm/901929900.

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This article chronicles the history of mergers and alliances in the liner shipping industry during the past century before focusing on the latest wave of mergers to hit the industry Each merger wave in the liner shipping industry generally coincided with merger waves from the general industrial world. The incentive for each wave of mergers seemed to be different, with the most recent wave focusing on synergy between the merging companies. The reduction of competing firms through mergers has implications for the shipper and these are also examined.

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Smirnov, Nickolay, and Valeriy Nikitin. "Three-dimensional simulation of combustion, detonation and deflagration to detonation transition processes." MATEC Web of Conferences 209 (2018): 00003. http://dx.doi.org/10.1051/matecconf/201820900003.

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The paper presents results of numerical and experimental investigation of mixture ignition and detonation onset in shock wave reflected from inside a wedge. Contrary to existing opinion of shock wave focusing being the mechanism for detonation onset in reflection from a wedge or cone, it was demonstrated that along with the main scenario there exists a transient one, under which focusing causes ignition and successive flame acceleration bringing to detonation onset far behind the reflected shock wave. Several different flow scenarios manifest in reflection of shock waves all being dependent on incident shock wave intensity: reflecting of shock wave with lagging behind combustion zone, formation of detonation wave in reflection and focusing, and intermediate transient regimes. Comparison of numerical and experimental results made it possible to validate the developed 3-D transient mathematical model of chemically reacting gas mixture flows incorporating hydrogen – air mixtures.

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Fuscaldo, Walter, Santi C. Pavone, Davide Comite, Guido Valerio, Matteo Albani, Mauro Ettorre, and Alessandro Galli. "Design criteria of X-wave launchers for millimeter-wave applications." International Journal of Microwave and Wireless Technologies 11, no. 9 (May 27, 2019): 939–47. http://dx.doi.org/10.1017/s175907871900062x.

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AbstractBessel-beam launchers are promising and established technologies for focusing applications at microwaves. Their use in time-domain leads to the definition of a new class of devices, namely, the X-wave launchers. In this work, we discuss the focusing features of such devices with a specific interest at millimeter waves. The spatial resolutions of such systems are described under a rigorous mathematical framework to derive novel operating conditions for designing X-wave launchers. These criteria might be particularly appealing for specific millimeter-wave applications. In particular, it is shown that an electrically large aperture is not strictly required, as it seemed from previous works. However, the use of an electrically small aperture would demand a considerably wideband capability. The various discussions presented here provide useful information for the design of X-wave launchers. This aspect is finally shown with reference to the practical design of two different X-wave launchers.

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Beckebanze, F., C. Brouzet, I. N. Sibgatullin, and L. R. M. Maas. "Damping of quasi-two-dimensional internal wave attractors by rigid-wall friction." Journal of Fluid Mechanics 841 (February 26, 2018): 614–35. http://dx.doi.org/10.1017/jfm.2018.107.

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The reflection of internal gravity waves at sloping boundaries leads to focusing or defocusing. In closed domains, focusing typically dominates and projects the wave energy onto ‘wave attractors’. For small-amplitude internal waves, the projection of energy onto higher wavenumbers by geometric focusing can be balanced by viscous dissipation at high wavenumbers. Contrary to what was previously suggested, viscous dissipation in interior shear layers may not be sufficient to explain the experiments on wave attractors in the classical quasi-two-dimensional trapezoidal laboratory set-ups. Applying standard boundary layer theory, we provide an elaborate description of the viscous dissipation in the interior shear layer, as well as at the rigid boundaries. Our analysis shows that even if the thin lateral Stokes boundary layers consist of no more than 1 % of the wall-to-wall distance, dissipation by lateral walls dominates at intermediate wave numbers. Our extended model for the spectrum of three-dimensional wave attractors in equilibrium closes the gap between observations and theory by Hazewinkel et al. (J. Fluid Mech., vol. 598, 2008, pp. 373–382).

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MAAS, LEO R. M. "Wave focusing and ensuing mean flow due to symmetry breaking in rotating fluids." Journal of Fluid Mechanics 437 (June 22, 2001): 13–28. http://dx.doi.org/10.1017/s0022112001004074.

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Rotating fluids support waves. These inertial waves propagate obliquely through the fluid, with an angle that is fixed with respect to the rotation axis. Upon reflection, their wavelength is unchanged only when the wall obeys the local reflectional symmetry, that is, when it is either parallel or perpendicular to the rotation axis. For internal gravity waves in a density-stratified fluid, sloping boundaries thus break the symmetry of ray paths, in a two-dimensional container, predicting their focusing upon attractors: particular paths onto which the wave rays, and hence the energy, converge, and to which the wave energy returns after a small number of refections. Laboratory observations, presented here, show that, despite the intrinsic three-dimensionality of inertial waves, attractors still occur. The intensified wave energy on the attractor encourages centrifugal instabilities, leading to a mean flow. Evidence of this comes from dye spreading, observed to develop most rapidly over the location where the attractor reflects from the sloping wall, being the place where focusing and instabilities occur. This mean flow, resulting from the mixing of angular momentum, accompanying the intensification of the wave field at that location, has geophysical implications, because the ocean, atmosphere and Earth's liquid outer core can be regarded as asymmetrically contained. The relevance of wave focusing in a rotating, spherical shell, the modifications due to the addition of radial stratification, and its implications for observed equatorial current patterns and inertial oscillations are discussed. The well-known universality of oceanic, gravito-inertial wave spectra might reflect complementary, divergent (chaotic) wave-ray behaviour, which occurs in containers obeying the reflectional symmetry, but in which symmetry is broken in the horizontal plane. Periodic orbits still exist, but now repell.

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Pelinovsky, E., E. Shurgalina, and N. Chaikovskaya. "The scenario of a single freak wave appearance in deep water – dispersive focusing mechanism framework." Natural Hazards and Earth System Sciences 11, no. 1 (January 11, 2011): 127–34. http://dx.doi.org/10.5194/nhess-11-127-2011.

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Abstract. One of the possible mechanisms of the emergence of freak waves in deep water, based on the dispersive focusing of unidirectional wave packets is analysed. This mechanism is associated with the frequency dispersion of water waves and manifested in the interference of many spectral components, moving with different velocities. Formation of a single freak wave in a random wind wave field is considered in the frame of linear theory. The characteristic lifetime of an abnormal wave in the framework of this mechanism for typical conditions is approximately two minutes, thus, a rapid effect is difficult to predict and prepare for. A rogue wave quickly changes its shape from a high ridge to a deep depression.

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Journal articles on the topic 'Focusing wave'

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