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Journal articles on the topic 'Waves and wave analysis'
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1
Takagi, Emiko, Yasuhiko Saito, and Angelique W. M. Chan. "A Longitudinal Study of the Impact of Loneliness on Personal Mastery Among Older Adults in Singapore." Innovation in Aging 4, Supplement_1 (December 1, 2020): 318. http://dx.doi.org/10.1093/geroni/igaa057.1017.
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Abstract This study uses longitudinal data to examine the association between older adults’ sense of mastery and loneliness. We examined the data of a nationally representative sample of adults 60 years and older in Singapore (Wave1, n=4,990) from the Panel of Health and Aging among Older Singaporeans Survey. The initial participants were followed up in 2011 (Wave2, n=3,103) and in 2015 (Wave3, n=1,572). At each wave, emotional loneliness was assessed using the UCLA three-item loneliness scale and sense of mastery was measured with the five items from the Pearlin Mastery Scale. We conducted cross-lagged regression analyses where loneliness and personal mastery scores in each wave were treated as endogenous variables along with covariates including demographic characteristics, health conditions, and the overall strength of social network measured by Lubben Social Network Scale. The results showed that loneliness in wave 1 and wave 2 respectively predicted a lower level of personal sense of mastery in subsequent waves. However, the other direction, the influence of personal mastery in wave 1 and wave 2 on loneliness at subsequent waves, was not significant. Furthermore, the analysis showed that older adults’ relatively strong social network was related to a lower level of loneliness and a higher sense of mastery at Wave 3. The finding suggests that loneliness plays a critical role in influencing older adults’ personal sense of mastery and that the strength of social network is an important mediator of loneliness and personal sense of mastery amongst older adults and a potential area for intervention.
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Lou, Yuequn, Xudong Gu, Xing Cao, Mingyu Wu, Sudong Xiao, Guoqiang Wang, Binbin Ni, and Tielong Zhang. "Statistical Analysis of Lunar 1 Hz Waves Using ARTEMIS Observations." Astrophysical Journal 943, no. 1 (January 1, 2023): 17. http://dx.doi.org/10.3847/1538-4357/aca767.
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Abstract Like 1 Hz waves occurring in the upstream of various celestial bodies in the solar system, 1 Hz narrowband whistler-mode waves are often observed around the Moon. However, wave properties have not been thoroughly investigated, which makes it difficult to proclaim the generation mechanism of the waves. Using 5.5 yr wave data from ARTEMIS, we perform a detailed investigation of 1 Hz waves in the near-lunar space. The amplitude of lunar 1 Hz waves is generally 0.05–0.1 nT. In the geocentric solar ecliptic coordinates, the waves show no significant regional differentiation pattern but show an absence inside the magnetosphere. Correspondingly, in the selenocentric solar ecliptic coordinates, the waves can occur extensively at ∼1.1–12 RL, while few events are observed in the lunar wake due to a lack of interaction with the solar wind. Furthermore, the wave distributions exhibit modest day–night and dawn–dusk asymmetries but less apparent north–south asymmetry. Compared with the nightside, more intense waves with lower peak wave frequency are present on the dayside. The preferential distribution of 1 Hz waves exhibits a moderate correlation with strong magnetic anomalies. The waves propagate primarily at wave normal angles <60° with an ellipticity of [−0.8, −0.3]. For stronger wave amplitudes and lower latitudes, 1 Hz waves generally have smaller wave normal angles and become more left-hand circularly polarized. Owing to the unique interaction between the Moon and solar wind, our statistical results might provide new insights into the generation mechanism(s) of 1 Hz waves in planetary plasma environments and promote the understanding of lunar plasma dynamics.
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Nian, Ting Kai, Bo Liu, and Ping Yin. "Seafloor Slope Stability under Adverse Conditions Using Energy Approach." Applied Mechanics and Materials 405-408 (September 2013): 1445–48. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.1445.
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The effects of ocean waves on the stability of seafloor slopes are of great importance in marine environment. The stability of a seafloor slope considering wave-induced pressure is analyzed using the kinematic approach of limit analysis combined with a strength reduction technique. A seafloor slope without waves is considered first. Furthermore, waved-induced pressure is considered to act on the surface of slope as an external load to analyze the effects on the stability of slope by waves. The results show that the adverse effect of waves on slope stability increases with an increase of the wave height as well as a decrease of the water depth.
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Kashiwagi, Masashi. "Hydrodynamic Study on Added Resistance Using Unsteady Wave Analysis." Journal of Ship Research 57, no. 04 (December 1, 2013): 220–40. http://dx.doi.org/10.5957/jsr.2013.57.4.220.
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It is known that the added resistance in waves can be computed from ship-generated unsteady waves through the unsteady wave analysis method. To investigate the effects of nonlinear ship-generated unsteady waves and bluntness of the ship geometry on the added resistance, measurements of unsteady waves, wave-induced ship motions, and added resistance were carried out using two different (blunt and slender) modified Wigley models. The ship-generated unsteady waves are also produced by the linear superposition using the waves measured for the diffraction and radiation problems and the complex amplitudes of ship motions measured for the motion-free problem in waves. Then a comparison is made among the values of the added resistance by the direct measurement using a dynamometer and by the wave analysis method using the Fourier transform of measured and superposed waves. It is found that near the peak of the added resistance where ship motions become large, the degree of nonlinearity in the unsteady wave becomes prominent, especially at the forefront part of the wave. Thus, the added resistance evaluated with measured waves at larger amplitudes of incident wave becomes much smaller than the values by the direct measurement and by the wave analysis with superposed waves or measured waves at smaller amplitude of incident wave. Discussion is also made on the characteristics of the added resistance in the range of short incident waves.
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Ahn, Kyungmo, Sun-Kyung Kim, and Se-Hyun Cheon. "ON THE PROBABILITY DISTRIBUTION OF FREAK WAVES IN FINITE WATER DEPTH." Coastal Engineering Proceedings 1, no. 33 (December 15, 2012): 13. http://dx.doi.org/10.9753/icce.v33.waves.13.
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This paper presents the occurrence probability of freak waves based on the analysis of extensive wave data collected during ARSLOE project. It is suggested to use the probability distribution of extreme waves heights as a possible means of defining the freak wave criteria instead of conventional definition which is the wave height greater than the twice of the significant wave height. Analysis of wave data provided such finding as 1) threshold tolerance of 0.2 m is recommended for the discrimination of the false wave height due to noise, 2) no supportive evidence on the linear relationship between the occurrence probability of freak waves and the kurtosis of surface elevation 3) nonlinear wave-wave interactions is not thh primary cause of the generation of freak waves 4) the occurrence of freak waves does not depend on the wave period 5) probability density function of extreme waves can be used to predict the occurrence probability of freak waves. Three different distribution functions of extreme wave height by Rayleigh, Ahn, and Mori were compared for the analysis of freak waves.
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Chakrabarti, Subrata K. "Measurement and Analysis of Laboratory Generated Steep Waves." Journal of Offshore Mechanics and Arctic Engineering 125, no. 1 (February 1, 2003): 17–24. http://dx.doi.org/10.1115/1.1556403.
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In many offshore locations, storm generated steep waves are common and the survival of offshore structures in their presence is an important design condition. The design environment in depth-limited waters often includes waves of breaking and near-breaking conditions, in which currents may be present. Experiments were carried out in a wave tank with simulated steep waves with and without steady in-line current in which the wave profiles and the corresponding kinematics were simultaneously measured. The waves included both regular and random waves and often approached the breaking wave height for the water depth. These waves were analyzed by higher-order wave theory. In particular, the regular waves were simulated by the regular and irregular stream function theory. Especially steep wave profiles within the random waves were computed using the irregular stream function theory. The theory allows inclusion of steady current in its formulation for computation of wave kinematics. The correlation of the measured wave kinematics with the higher-order stream function wave theory showed that the wave theory could predict the kinematics of these steep waves (with and without the presence of current) well. However, in breaking waves, the vertical water particle velocity was not predicted well, especially near the trough. The effect of breaking and near-breaking steep waves on a fixed vertical caisson was also studied. The forces measured on the vertical caisson from the wave tank testing were analyzed to determine the effect of these waves and currents on the forces. It was found that the measured forces (and overturning moments) on the caisson model matched fairly well by the proper choice of force coefficients from the design guideline and the nonlinear stream function theory of appropriate order.
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Miles, D. R., G. Gassaway, L. Bennett, and R. Brown. "Three-component amplitude versus offset analysis." Exploration Geophysics 20, no. 2 (1989): 257. http://dx.doi.org/10.1071/eg989257.
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Three-component (3-C) amplitude versus offset (AVO) inversion is the AVO analysis of the three major energies in the seismic data, P-waves, S-waves and converted waves. For each type of energy the reflection coefficients at the boundary are a function of the contrast across the boundary in velocity, density and Poisson's ratio, and of the angle of incidence of the incoming wave. 3-C AVO analysis exploits these relationships to analyse the AVO changes in the P, S, and converted waves. 3-C AVO analysis is generally done on P, S, and converted wave data collected from a single source on 3-C geophones. Since most seismic sources generate both P and S-waves, it follows that most 3-C seismic data may be used in 3-C AVO inversion. Processing of the P-wave, S-wave and converted wave gathers is nearly the same as for single-component P-wave gathers. In split-spread shooting, the P-wave and S-wave energy on the radial component is one polarity on the forward shot and the opposite polarity on the back shot. Therefore to use both sides of the shot, the back shot must be rotated 180 degrees before it can be stacked with the forward shot. The amplitude of the returning energy is a function of all three components, not just the vertical or radial, so all three components must be stacked for P-waves, then for S-waves, and finally for converted waves. After the gathers are processed, reflectors are picked and the amplitudes are corrected for free-surface effects, spherical divergence and the shot and geophone array geometries. Next the P and S-wave interval velocities are calculated from the P and S-wave moveouts. Then the amplitude response of the P and S-wave reflections are analysed to give Poisson's ratio. The two solutions are then compared and adjusted until they match each other and the data. Three-component AVO inversion not only yields information about the lithologies and pore-fluids at a specific location; it also provides the interpreter with good correlations between the P-waves and the S-waves, and between the P and converted waves, thus greatly expanding the value of 3-C seismic data.
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Zhang, Huichen, and Markus Brühl. "GENERATION OF EXTREME TRANSIENT WAVES IN EXPERIMENTAL MODELS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 51. http://dx.doi.org/10.9753/icce.v36.waves.51.
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The transfer of natural waves and sea states into small- and large-scale model teste contributes to the proper design of offshore and coastal structure. Such shallow-water ocean surface waves are highly nonlinear and subject to wave transformation and nonlinear wave-wave interactions. However, the standard methods of wave generation according to conventional wave theories and wave analysis methods are limited to simple regular waves, simple sea states and low-order wave generation without considering the nonlinear wave-wave interactions. The research project Generation of Extreme Transient Waves in Experimental Models (ExTraWaG) aims to accurately generate target transient wave profile at a pre-defined position in the wave flume (transfer point) under shallow water conditions. For this purpose, the KdV-based nonlinear Fourier transform is introduced as a continuative wave analysis method and is applied to investigate the nonlinear spectral character of experimental wave data. Furthermore, the method is applied to generate transient nonlinear waves as specific locations in the wave flume, considering the nonlinear transformation and interactions of the propagating waves.
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Morozova, Svetlana V., Viktor N. Abannikov, Elena A. Polianskaia, and Maria A. Alimpieva. "CLIMATOLOGY OF DRY AND WET HEAT AND COLD WAVES OF DIFFERENT INTENSITY." Географический вестник = Geographical bulletin, no. 4(63) (2022): 80–89. http://dx.doi.org/10.17072/2079-7877-2022-4-80-89.
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The article discusses the results of a statistical analysis of increases and decreases in the average daily air temperature, presented as waves of heat and cold. By a wave of heat (cold) we mean a change in the average daily air temperature by three degrees or more that lasted for at least two days. If a wave of heat (cold) was interrupted by one day of cooling (warming) or isothermy, such cases were considered a single wave. All waves were divided into dry and wet. A wave was considered wet if there was precipitation on at least one day during the development of this wave. We calculated the frequency of occurrence, duration of dry and wet waves, and the number of days with precipitation for each wave. The analysis was carried out for waves of different intensities. On average, the number of warm and cold waves per year is the same. Approximately the same number of warm and cold waves occur in winter and summer. In spring, heat waves prevail over cold waves, while in autumn the trend is opposite. The average duration of a wave is 4 days. The more intense the wave, the longer its duration. The majority of waves are wet. Precipitation accompanies 85% of heat waves and 75% of cold waves. Precipitation falls on about half the days of the wave’s duration. Cold waves are quite often interrupted by one-day increases in the average daily temperature. It is during these days that precipitation is observed. Synoptic analysis has shown that such cases of one-day ‘interruption’ of cold waves are associated with active processes of cyclogenesis on cold fronts. Wave formation at the cold front stimulates precipitation.
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ZHU, QIANG, YUMING LIU, and DICK K. P. YUE. "Resonant interactions between Kelvin ship waves and ambient waves." Journal of Fluid Mechanics 597 (February 1, 2008): 171–97. http://dx.doi.org/10.1017/s002211200700969x.
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We consider the nonlinear interactions between the steady Kelvin waves behind an advancing ship and an (unsteady) ambient wave. It is shown that, for moderately steep ship waves and/or ambient waves, third-order (quartet) resonant interaction among the two wave systems could occur, leading to the generation of a new propagating wave along a specific ray in the Kelvin wake. The wave vector of the generated wave as well as the angle of the resonance ray are determined by the resonance condition and are functions of the ship forward speed and the wave vector of the ambient wave. To understand the resonance mechanism and the characteristics of the generated wave, we perform theoretical analyses of this problem using two related approaches. To obtain a relatively simple model in the form of a nonlinear Schrödinger (NLS) equation for the evolution of the resonant wave, we first consider a multiple-scale approach assuming locally discrete Kelvin wave components, with constant wave vectors but varying amplitudes along the resonance ray. This NLS model captures the key resonance mechanism but does not account for the detuning effect associated with the wave vector variation of Kevin waves in the neighbourhood of the resonance ray. To obtain the full quantitative features and evolution characteristics, we also consider a more complete model based on Zakharov's integral equation applied in the context of a continuous wave vector spectrum. The resulting evolution equation can be reduced to an NLS form with, however, cross-ray variable coefficients, on imposing a narrow-band assumption valid in the neighbourhood of the resonance ray. As expected, the two models compare well when wave vector detuning is small, in the near wake close to the ray. To verify the analyses, direct high-resolution simulations of the nonlinear wave interaction problem are obtained using a high-order spectral method. The simulations capture the salient features of the resonance in the near wake of the ship, with good agreements with theory for the location of the resonance and the growth rate of the generated wave.
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Le Roux, J. P. "Analysis of Interfering Fully Developed, Colinear Deepwater Waves." International Journal of Oceanography 2012 (February 22, 2012): 1–8. http://dx.doi.org/10.1155/2012/314064.
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The sea surface is normally irregular as a result of dissimilar waves generated in different areas. To describe such a sea state, various methods have been proposed, but there is no general consensus as to the best characterizing parameters of the interwaves. Three simple methods are proposed here to calculate a characteristic interwave period, length, and height for fully developed, colinear deepwater waves. The results of this study indicate that the interwave period and length are equal or very close to the period and length of the dominant component wave, irrespective of the periods of the subordinate waves. In cases where the dominant wave period is double or more than double the periods of the subordinate waves, the wave period, length and height are within 4% of the dominant wave parameters, so that such interfering, irregular waves have virtually the same characteristics as monochromatic waves. Secondary, individual interwaves propagate at the velocity of the component wave with the shortest period, that is, slower than the primary interwaves which have the same celerity as the dominant component wave.
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Brühl, Markus, and Hocine Oumeraci. "ANALYSIS OF SOLITON FISSION OVER A SUBMERGED STRUCTURE USING “NONLINEAR FOURIER TRANSFORM (NLFT)”." Coastal Engineering Proceedings 1, no. 32 (February 2, 2011): 59. http://dx.doi.org/10.9753/icce.v32.waves.59.
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When a single incident solitary wave passes over a submerged reef, it disintegrates into a train of solitons (soliton fission), followed by a train of oscillatory waves. One of the major problems in the analysis of the recorded time series is the uncertain identification of the number of solitons N in the transmitted wave train behind the reef due to the difficulties to distinguish between solitons and oscillatory waves, especially in the case of breaking waves. With the “nonlinear Fourier transform (NLFT)”, an application of the inverse scattering transform (IST) of the Korteweg-de Vries equation, a powerful analysis method is proposed to analyse nonlinear wave processes. Application of the NLFT to the transmitted waves of systematic numerical tests with breaking and non-breaking solitary waves behind a submerged structure (reef) with finite width br allows to separate distinctly solitons and oscillatory waves. The paper gives an overview over the first NLFT analysis results for the determination of the number of solitons N behind the reef. The influence of relative submergence depth dr/h, relative reef width br/Li and relative incident wave height Hi/dr is examined. First recommendations for the distinct identification of the number of solitons arising from the fission using NLFT will also be provided, including the limitations of the method.
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Harry, Matthew, Hong Zhang, and Gildas Colleter. "REMOTELY SENSED DATA FOR WAVE PROFILE ANALYSIS." Coastal Engineering Proceedings 1, no. 33 (December 14, 2012): 45. http://dx.doi.org/10.9753/icce.v33.waves.45.
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Laser scanning technology (LiDAR) is a form of remote sensing from which a water surface can be measured rapidly and accurately without in-situ sensors. An experimental setup for the measurement of waves in a wave flume is detailed with an analysis of various wave parameters. The experiments function as a source of reliable laboratory controlled data while the data analysis presents the range of research fields that the data can be applied to.
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Xiang-jun, Yu, Li Qing-hong, and Li Mao-lin. "Numerical Analysis of Wave Characteristic In the Freak Wave-- “New Year Wave” Formation." E3S Web of Conferences 290 (2021): 02013. http://dx.doi.org/10.1051/e3sconf/202129002013.
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Freak waves are both extremely large waves and highly transient time. Such a wave may lead to damage of ships to deaths. In this paper, to describe the connection between freak wave and wave essential factor, we use WAVEWATCH III model simulating “New Year Wave” in the North Sea to explore freak wave, with the importing of ECMWF re-analysis wind field. By this way, we successfully simulate the formation of freak wave in the random wave. Analysis shows large wave steepness and small directional spread angle are necessary conditions for freak waves to easily occur. By analyzing the wave spectrum, it is found that the wave energy is distributed in a small range, and the propagation direction is relatively concentrated.
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Park, Choon B., Richard D. Miller, and Jianghai Xia. "Multichannel analysis of surface waves." GEOPHYSICS 64, no. 3 (May 1999): 800–808. http://dx.doi.org/10.1190/1.1444590.
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The frequency‐dependent properties of Rayleigh‐type surface waves can be utilized for imaging and characterizing the shallow subsurface. Most surface‐wave analysis relies on the accurate calculation of phase velocities for the horizontally traveling fundamental‐mode Rayleigh wave acquired by stepping out a pair of receivers at intervals based on calculated ground roll wavelengths. Interference by coherent source‐generated noise inhibits the reliability of shear‐wave velocities determined through inversion of the whole wave field. Among these nonplanar, nonfundamental‐mode Rayleigh waves (noise) are body waves, scattered and nonsource‐generated surface waves, and higher‐mode surface waves. The degree to which each of these types of noise contaminates the dispersion curve and, ultimately, the inverted shear‐wave velocity profile is dependent on frequency as well as distance from the source. Multichannel recording permits effective identification and isolation of noise according to distinctive trace‐to‐trace coherency in arrival time and amplitude. An added advantage is the speed and redundancy of the measurement process. Decomposition of a multichannel record into a time variable‐frequency format, similar to an uncorrelated Vibroseis record, permits analysis and display of each frequency component in a unique and continuous format. Coherent noise contamination can then be examined and its effects appraised in both frequency and offset space. Separation of frequency components permits real‐time maximization of the S/N ratio during acquisition and subsequent processing steps. Linear separation of each ground roll frequency component allows calculation of phase velocities by simply measuring the linear slope of each frequency component. Breaks in coherent surface‐wave arrivals, observable on the decomposed record, can be compensated for during acquisition and processing. Multichannel recording permits single‐measurement surveying of a broad depth range, high levels of redundancy with a single field configuration, and the ability to adjust the offset, effectively reducing random or nonlinear noise introduced during recording. A multichannel shot gather decomposed into a swept‐frequency record allows the fast generation of an accurate dispersion curve. The accuracy of dispersion curves determined using this method is proven through field comparisons of the inverted shear‐wave velocity ([Formula: see text]) profile with a downhole [Formula: see text] profile.
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Brühl, Markus, and Rahi Shet. "TIME-FREQUENCY ANALYSIS OF 3D SHIP-WAVE FIELDS IN MARTIME WATERWAYS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 68. http://dx.doi.org/10.9753/icce.v36.waves.68.
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In the last 15 years an increased number of serious damages of protective structures such as groins and revetments have been observed in maritime waterways. The analyses of these damages have shown that the current design approaches for the rubble mound layers of such structures are not sufficient to ensure sufficient stability against ship-induced wave loads. Since these approaches are determined for wind-induced waves, they do not consider the long-period ship-wave components. Within a joint research project, the design loads of ship-induced long-period waves on rubble mound structures in maritime waterways are investigated. By means of first project results, the knowledge gaps with respect to the classification and parameterization of ship waves have been identified. The project has clearly shown the need for a 3D analysis of three-dimensional, nonlinear ship-wave fields. Therefore, another research project was initiated in order to generate the scientific knowledge for the parameterization of ship-induced 3D wave fields as required for the hydraulic design of rubble mound structures in maritime waterways with a special focus on the spatial and nonlinear properties of ship waves.
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Ouyang, Zhengyong. "Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/943167.
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We use bifurcation method of dynamical systems to study exact traveling wave solutions of a nonlinear evolution equation. We obtain exact explicit expressions of bell-shaped solitary wave solutions involving more free parameters, and some existing results are corrected and improved. Also, we get some new exact periodic wave solutions in parameter forms of the Jacobian elliptic function. Further, we find that the bell-shaped waves are limits of the periodic waves in some sense. The results imply that we can deduce bell-shaped waves from periodic waves for some nonlinear evolution equations.
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Chandrasekaran, Srinivasan, and Koshti Yuvraj. "Dynamic analysis of a tension leg platform under extreme waves." Journal of Naval Architecture and Marine Engineering 10, no. 1 (June 11, 2013): 59–68. http://dx.doi.org/10.3329/jname.v10i1.14518.
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Recent observations of the sea state that result in the undesirable events confirm the presence of extreme waves like freak waves, which is capable of causing irreparable damages to offshore installations and (or) create inoperable conditions to the crew on board. Knowledge on the extreme wave environment and the related wave-structure interaction are required for safer design of deep-water offshore structures. In the current study, typical long crested extreme waves namely: i) New Year wave at offshore Norway; and ii) Freak wave at North Sea are simulated using the combined wave model. Dynamic response of the Tension Leg Platforms (TLP) under these extreme waves is carried out for different wave approach angles. Based on the analytical studies cared out, it is seen that the TLPs are sensitive to the wave directionality when encountered by such extreme waves; ringing type response is developed in TLPs which could result in tether pull out.DOI: http://dx.doi.org/10.3329/jname.v10i1.14518
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McWilliams, James C. "Surface wave effects on submesoscale fronts and filaments." Journal of Fluid Mechanics 843 (March 22, 2018): 479–517. http://dx.doi.org/10.1017/jfm.2018.158.
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A diagnostic analysis is made for the ageostrophic secondary circulation, buoyancy flux and frontogenetic tendency (SCFT) in upper-ocean submesoscale fronts and dense filaments under the combined influences of boundary-layer turbulent mixing, surface wind stress and surface gravity waves. The analysis is based on a momentum-balance approximation that neglects ageostrophic acceleration, and the surface wave effects are represented with a wave-averaged asymptotic theory based on the time scale separation between wave and current evolution. The wave’s Stokes-drift velocity $\boldsymbol{u}_{st}$ induces SCFT effects that are dominant in strong swell with weak turbulent mixing, and they combine with Ekman and turbulent thermal wind influences in more general situations near wind–wave equilibrium. The complementary effect of the submesoscale currents on the waves is weak for longer waves near the wind–wave or swell spectrum peak, but it is strong for shorter waves.
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Bona, Jerry L., Thierry Colin, and David Lannes. "Long Wave Approximations for Water Waves." Archive for Rational Mechanics and Analysis 178, no. 3 (June 21, 2005): 373–410. http://dx.doi.org/10.1007/s00205-005-0378-1.
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Clifton, R. J. "Analysis of Failure Waves in Glasses." Applied Mechanics Reviews 46, no. 12 (December 1, 1993): 540–46. http://dx.doi.org/10.1115/1.3120315.
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Recent plate impact experiments have been interpreted as indicating the existence of “failure waves” during the compression of glass by impact at sufficiently high velocities. In experiments on soda-lime glass, Brar et al. (1991) reported the propagation of a wave across which the shearing strength dropped sharply from 2 GPa to 1 GPa, and the spall strength dropped from 3 GPa to zero. Such a drop in spall strength has also been reported by Raiser et al. (1993) in an aluminosilicate glass. Kanel et al. (1993) interpreted a small jump in the rear surface particle velocity in experiments on K19 glass as the reflection of a recompression wave from a wavefront propagating at approximately the speed reported for “failure waves”. In this paper, such “failure waves” are interpreted within the context of nonlinear wave theory. In this theory the “failure wave” corresponds to a propagating phase boundary—called a transformation shock. The theory is analogous to the theory of liquifaction shocks in fluids.
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Hou, Xiaojie. "Analysis of a Model Arising from Invasion by Precursor and Differentiated Cells." International Journal of Differential Equations 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/341473.
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We study the wave solutions for a degenerated reaction diffusion system arising from the invasion of cells. We show that there exists a family of waves for the wave speed larger than or equal a certain number and below which there are no monotonic wave solutions. We also investigate the monotonicity, uniqueness, and asymptotics of the waves.
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Tiscareno, Matthew S., and Matthew M. Hedman. "A review of Morlet wavelet analysis of radial profiles of Saturn's rings." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (July 9, 2018): 20180046. http://dx.doi.org/10.1098/rsta.2018.0046.
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Spiral waves propagating in Saturn's rings have wavelengths that vary with radial position within the disc. The best-quality observations of these waves have the form of radial profiles centred on a particular azimuth. In that context, the wavelength of a given spiral wave is seen to change substantially with position along the one-dimensional profile. In this paper, we review the use of Morlet wavelet analysis to understand these waves. When signal to noise is high and the cause of the wave is well understood, wavelet analysis has been used to solve for wave parameters that are diagnostic of local disc properties. Waves that are not readily perceptible in the spatial domain signal can be clearly identified. Furthermore, filtering in wavelet space, followed by the reverse wavelet transform, has been used to isolate the part of the signal that is of interest. When the cause of the wave is not known, comparing the phases of the complex-valued wavelet transforms from many profiles has been used to determine wave parameters that cannot be determined from any single profile. When signal to noise is low, co-adding wavelet transforms while manipulating the phase has been used to boost a wave's signal above detection limits. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.
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Bruell, Gabriele, Piotr Idzik, and Wolfgang Reichel. "Traveling waves for a quasilinear wave equation." Nonlinear Analysis 225 (December 2022): 113115. http://dx.doi.org/10.1016/j.na.2022.113115.
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Didenkulova, I., and C. Anderson. "Freak waves of different types in the coastal zone of the Baltic Sea." Natural Hazards and Earth System Sciences 10, no. 9 (September 30, 2010): 2021–29. http://dx.doi.org/10.5194/nhess-10-2021-2010.
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Abstract. We present a statistical analysis of freak waves1 measured during the 203 h of observation on sea surface elevation at a location in the coastal zone of the Baltic Sea (2.7 m depth) during June–July 2008. The dataset contains 97 freak waves occurring in both calm and stormy weather conditions. All of the freak waves are solitary waves, 63% of them having positive shape, 17.5% negative shape and 19.5% sign-variable shape. It is suggested that the freak waves can be divided into two groups. Those of the first group, which includes 92% of the freak waves, have an amplification factor (ratio of freak wave height to significant wave height) which does not vary from significant wave height and has values largely within the range of 2.0 to 2.4; while for the second group, which contain the most extreme freak waves, amplification factors depend strongly on significant wave height and can reach 3.1. Analysis based on the Generalised Pareto distribution is used to describe the waves of the first group and lends weight to the identification of the two groups. It is suggested that the probable mechanism of the generation of freak waves in the second group is dispersive focussing. The time-frequency spectra of the freak waves are studied and dispersive tracks, which can be interpreted as dispersive focussing, are demonstrated. 1 taken to be waves whose height is 2 or more times greater than the significant wave height
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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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Bettess, Peter, and Edmund Chadwick. "Wave envelope examples for progressive waves." International Journal for Numerical Methods in Engineering 38, no. 15 (August 15, 1995): 2487–508. http://dx.doi.org/10.1002/nme.1620381502.
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Smida, K., H. Lamloumi, K. Maalel, and Z. Hafsia. "CFD Analysis of Water Solitary Wave Reflection." Journal of Engineering Research [TJER] 8, no. 2 (December 1, 2011): 10. http://dx.doi.org/10.24200/tjer.vol8iss2pp10-18.
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A new numerical wave generation method is used to investigate the head-on collision of two solitary waves. The reflection at vertical wall of a solitary wave is also presented. The originality of this model, based on the Navier-Stokes equations, is the specification of an internal inlet velocity, defined as a source line within the computational domain for the generation of these non linear waves. This model was successfully implemented in the PHOENICS (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series) code. The collision of two counter-propagating solitary waves is similar to the interaction of a soliton with a vertical wall. This wave generation method allows the saving of considerable time for this collision process since the counter-propagating wave is generated directly without reflection at vertical wall. For the collision of two solitary waves, numerical results show that the run-up phenomenon can be well explained, the solution of the maximum wave run-up is almost equal to experimental measurement. The simulated wave profiles during the collision are in good agreement with experimental results. For the reflection at vertical wall, the spatial profiles of the wave at fixed instants show that this problem is equivalent to the collision process.
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Kumar, Rajneesh, and Poonam Sharma. "Analysis of plane waves in anisotropic piezothermoelastic diffusive medium." Multidiscipline Modeling in Materials and Structures 12, no. 1 (June 13, 2016): 93–109. http://dx.doi.org/10.1108/mmms-03-2015-0012.
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Purpose – The purpose of this paper is to study the propagation of harmonic plane waves in a homogeneous anisotropic piezothermoelastic diffusive medium. Design/methodology/approach – After developing the mathematical model and theoretical analysis of the problem, computational work has been performed to study the different characteristics of the plane harmonic waves. Findings – The existence of waves namely, quasi-longitudinal wave (QP), quasi-thermal wave and quasi-mass diffusion wave have been found which propagates in an anisotropic piezothermoelastic diffusive medium. The different characteristics of waves like phase velocity and attenuation quality factor are computed numerically and presented graphically to show the piezoelectric effect. Originality/value – A significant piezoelectric effects have been observed on the different characteristics of the waves in an anisotropic piezothermoelastic diffusive medium.
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Ern, M., P. Preusse, M. Krebsbach, M. G. Mlynczak, and J. M. Russell III. "Equatorial wave analysis from SABER and ECMWF temperatures." Atmospheric Chemistry and Physics Discussions 7, no. 4 (August 8, 2007): 11685–723. http://dx.doi.org/10.5194/acpd-7-11685-2007.
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Abstract. Equatorial planetary scale wave modes such as Kelvin waves or Rossby-gravity waves are excited by convective processes in the troposphere. In this paper an analysis for these and other equatorial wave modes is carried out with special focus on the stratosphere using temperature data from the SABER instrument as well as ECMWF temperatures. Space-time spectra of symmetric and antisymmetric spectral power are derived to separate the different equatorial wave types and the contribution of gravity waves is determined from the spectral background of the space-time spectra. Both gravity waves and equatorial planetary scale wave modes are main drivers of the quasi-biennial oscillation (QBO) in the stratosphere. Temperature variances attributed to the different wave types are calculated for the period from February 2002 until March 2006 and compared to previous findings. A comparison between SABER and ECMWF wave analyses shows that in the lower stratosphere SABER and ECMWF spectra and temperature variances agree remarkably well while in the upper stratosphere ECMWF tends to overestimate Kelvin wave components. Gravity wave variances are partly reproduced by ECMWF but have a significant low-bias. A case study for the time period of the SCOUT-O3 tropical aircraft measurement campaign in Darwin/Australia (in November and December 2005) is performed and we find that in the lower stratosphere also the longitude-time distribution of the Kelvin waves is correctly reproduced by ECMWF.
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Ern, M., P. Preusse, M. Krebsbach, M. G. Mlynczak, and J. M. Russell. "Equatorial wave analysis from SABER and ECMWF temperatures." Atmospheric Chemistry and Physics 8, no. 4 (February 21, 2008): 845–69. http://dx.doi.org/10.5194/acp-8-845-2008.
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Abstract. Equatorial planetary scale wave modes such as Kelvin waves or Rossby-gravity waves are excited by convective processes in the troposphere. In this paper an analysis for these and other equatorial wave modes is carried out with special focus on the stratosphere using temperature data from the SABER satellite instrument as well as ECMWF temperatures. Space-time spectra of symmetric and antisymmetric spectral power are derived to separate the different equatorial wave types and the contribution of gravity waves is determined from the spectral background of the space-time spectra. Both gravity waves and equatorial planetary scale wave modes are main drivers of the quasi-biennial oscillation (QBO) in the stratosphere. Temperature variances attributed to the different wave types are calculated for the period from February 2002 until March 2006 and compared to previous findings. A comparison between SABER and ECMWF wave analyses shows that in the lower stratosphere SABER and ECMWF spectra and temperature variances agree remarkably well while in the upper stratosphere ECMWF tends to overestimate Kelvin wave components. Gravity wave variances are partly reproduced by ECMWF but have a significant low-bias. For the examples of a QBO westerly phase (October–December 2004) and a QBO easterly phase (November/December 2005, period of the SCOUT-O3 tropical aircraft campaign in Darwin/Australia) in the lower stratosphere we find qualitatively good agreement between SABER and ECMWF in the longitude-time distribution of Kelvin, Rossby (n=1), and Rossby-gravity waves.
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Ikeda, Tatsunori, Toshifumi Matsuoka, Takeshi Tsuji, and Toru Nakayama. "Characteristics of the horizontal component of Rayleigh waves in multimode analysis of surface waves." GEOPHYSICS 80, no. 1 (January 1, 2015): EN1—EN11. http://dx.doi.org/10.1190/geo2014-0018.1.
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In surface-wave analysis, S-wave velocity estimations can be improved by the use of higher modes of the surface waves. The vertical component of P-SV waves is commonly used to estimate multimode Rayleigh waves, although Rayleigh waves are also included in horizontal components of P-SV waves. To demonstrate the advantages of using the horizontal components of multimode Rayleigh waves, we investigated the characteristics of the horizontal and vertical components of Rayleigh waves. We conducted numerical modeling and field data analyses rather than a theoretical study for both components of Rayleigh waves. As a result of a simulation study, we found that the estimated higher modes have larger relative amplitudes in the vertical and horizontal components as the source depth increases. In particular, higher-order modes were observed in the horizontal component data for an explosive source located at a greater depth. Similar phenomena were observed in the field data acquired by using a dynamite source at 15-m depth. Sensitivity analyses of dispersion curves to S-wave velocity changes revealed that dispersion curves additionally estimated from the horizontal components can potentially improve S-wave velocity estimations. These results revealed that when the explosive source was buried at a greater depth, the horizontal components can complement Rayleigh waves estimated from the vertical components. Therefore, the combined use of the horizontal component data with the vertical component data would contribute to improving S-wave velocity estimations, especially in the case of buried explosive source signal.
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Varma, Dheeraj, Manikandan Mathur, and Thierry Dauxois. "Instabilities in internal gravity waves." Mathematics in Engineering 5, no. 1 (2022): 1–34. http://dx.doi.org/10.3934/mine.2023016.
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<abstract><p>Internal gravity waves are propagating disturbances in stably stratified fluids, and can transport momentum and energy over large spatial extents. From a fundamental viewpoint, internal waves are interesting due to the nature of their dispersion relation, and their linear dynamics are reasonably well-understood. From an oceanographic viewpoint, a qualitative and quantitative understanding of significant internal wave generation in the ocean is emerging, while their dissipation mechanisms are being debated. This paper reviews the current knowledge on instabilities in internal gravity waves, primarily focusing on the growth of small-amplitude disturbances. Historically, wave-wave interactions based on weakly nonlinear expansions have driven progress in this field, to investigate spontaneous energy transfer to various temporal and spatial scales. Recent advances in numerical/experimental modeling and field observations have further revealed noticeable differences between various internal wave spatial forms in terms of their instability characteristics; this in turn has motivated theoretical calculations on appropriately chosen internal wave fields in various settings. After a brief introduction, we present a pedagogical discussion on linear internal waves and their different two-dimensional spatial forms. The general ideas concerning triadic resonance in internal waves are then introduced, before proceeding towards instability characteristics of plane waves, wave beams and modes. Results from various theoretical, experimental and numerical studies are summarized to provide an overall picture of the gaps in our understanding. An ocean perspective is then given, both in terms of the relevant outstanding questions and the various additional factors at play. While the applications in this review are focused on the ocean, several ideas are relevant to atmospheric and astrophysical systems too.</p></abstract>
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Elepfandt, Andreas, Silke Lebrecht, Kirsten Schroedter, Britta Brudermanns, Renate Hillig, Claire Schuberth, and Alexander Fliess. "Lateral Line Scene Analysis in the Purely Aquatic Frog Xenopus laevis Daudin (Pipidae)." Brain, Behavior and Evolution 87, no. 2 (2016): 117–27. http://dx.doi.org/10.1159/000445422.
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The ability to locate and discriminate water surface waves that impinge simultaneously from multiple directions was studied in the clawed frog, Xenopus laevis. Monofrequency waves of 5-30 Hz were presented from point sources at a distance of 10 cm from the frog, unless stated otherwise, and the animal's response turn towards the wave origin examined. Two-choice conditioning with two simultaneous frontal waves at a 90-degree inter-wave angle revealed discrimination thresholds lower than 1 Hz for 10- to 20-Hz source wave frequencies. Smaller inter-wave angles resulted in larger thresholds, and no discrimination was found below 40°. If a third wave was added from behind, the frequency discrimination of the two frontal waves deteriorated, with 18 Hz being discriminated from waves differing by at least 2.75 Hz. Subjects also discriminated between two simultaneous waves of equal frequency presented from differing distances. At a distance of 10 cm, the discrimination threshold was 0.95 cm. Thus, X. laevis is capable of discriminating source distances in an overlap on the basis of wave curvatures. The detection of source directions among four, six or eight waves of equal frequency and distance was investigated by measuring the angular distribution of the response turns. Turns were significantly more closely oriented towards sources than to intermediate directions. The orientation accuracy did not degrade with the number of waves.
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Song, N., W. Zhang, P. Wang, and Y. K. Xue. "Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation." Journal of Function Spaces 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/6910926.
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The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using the Darboux matrix, the generalized Darboux transformation is constructed and a recursive formula is derived. Based on the transformation, the first-order to the third-order rogue wave solutions are obtained. Then, the nonlinear dynamics of the first-order to the third-order rogue waves are studied on the basis of some free parameters. Several new structures of the rogue waves are found using numerical simulation. The conclusions will be a supportive tool to study the rogue waves better.
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Farhan, Muhammad, and Gunawan Handayani. "Shear Wave Velocity Analysis of 2-D Multichannel Analysis of Surface Wave (MASW) to investigate subsurface Fault of Alternative Bridge Construction in Kelok Sago Jambi." Jurnal Matematika dan Sains 25, no. 1 (September 2020): 18–20. http://dx.doi.org/10.5614/jms.2020.25.1.4.
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Every geotechnical measurement requires geophysical methods to classify soil types under the ground. S-wave velocity (Vs), P-wave velocity (Vp), and density (ρ), are the most important parameters in the classification of soils. There are various methods to determine Vs, one of them is P-S logging method. However, this method is less suitable to be applied in urban areas due to the difficulties of data acquisition and high expense in operational costs. In 1999, a seismic method uses surface waves to de-termine Vs profile with a higher signal to noise ratio which was known by the name of Multichannel Analysis of Surface Waves (MASW). A surface wave, especially Rayleigh wave, creeps slowly on the surface with a larger amplitude than a body wave. The wavelengths of the surface wave will disperse in the layers system i.e. the phase velocity of the surface waves is now func-tion of frequency. MASW 2-D method is used in this paper to determine subsoil properties and to identify the fault under the bridge abutments plan (abutment 1 and abutment 2) in Kelok Sago Jambi.
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Cho, Yong Jun. "Numerical Analysis of Stem Wave Control Effect of a Curved Slit Caisson Breakwater." Korea Society of Coastal Disaster Prevention 8, no. 3 (July 30, 2021): 181–92. http://dx.doi.org/10.20481/kscdp.2021.8.3.181.
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Curved slit caisson has been the preferred structural type of breakwater in South Korea, and effective control of stem waves is a crucial design factor significantly affecting the performance of a curved slit caisson breakwater. Most of the past studies on stem waves heavily relied on wave drivers like the cubic Schrödinger Eq. due to the intrinsic difficulties in analyzing stem waves. However, considering the perturbation method evoked in the derivation of cubic Schrödinger Eq., the wave driver mentioned above could give erroneous results in the rough sea due to the higher-order waves that appeared in the wave field by resonance wave-wave interaction. In this rationale, in this study, the numerical simulation was implemented to verify the stem wave control effect of curved slit caisson using the ihFoam, toolbox having its roots on OpenFoam. It was shown that curved slit caisson breakwater effectively alleviates the scope and height of stem waves.
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Faraci, Carla, Pietro Scandura, and Enrico Foti. "WAVE-CURRENT INTERACTION OVER SEABEDS WITH DIFFERENT ROUGHNESS: A STATISTICAL ANALYSIS." Coastal Engineering Proceedings, no. 35 (June 23, 2017): 16. http://dx.doi.org/10.9753/icce.v35.waves.16.
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Wave-current flow over seabeds covered with different roughness has been studied in order to deepen the knowledge on the statistical properties of the near-bed velocity. The results of three different experimental campaigns performed in the presence of a sandy bed, a gravel bed and a rippled bed, carried out superimposing a steady current onto an orthogonal wave, have been analysed. The statistics of the current velocity, including the wave effects on the steady current have been investigated. It has been observed that in the absence of waves, the fluctuations of the near-bed velocities closely follow a Gaussian distribution. When waves are also present, in order to obtain consistent near-bed velocity statistics, it is necessary to decouple the velocity events in the current direction by taking into account the sign of the wave velocities. In the latter case, the nature of the distribution functions is influenced by the mass conservation principle. A Gaussian distribution well describes the turbulent fluctuations obtained by removing the phase averaged velocity from the current velocity.
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Chávez-García, Francisco J., Jaime Ramos-Martínez, and Evangelina Romero-Jiménez. "Surface-wave dispersion analysis in Mexico City." Bulletin of the Seismological Society of America 85, no. 4 (August 1, 1995): 1116–26. http://dx.doi.org/10.1785/bssa0850041116.
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Abstract In this article, we present an observational investigation of ground motion at Mexico City focused on surface waves. Our purpose is 2-fold; first, to understand incident ground motion during the great Michoacán earthquake of 19 September 1985, and second, to characterize surface waves propagating in the lake-bed zone. To this end we analyze the strong-motion records obtained at Mexico City for the large (MS = 8.1) earthquake of 19 September 1985. It is shown that, in the low-frequency range, we observe the Rayleigh fundamental mode in both the vertical and the radial components, and the Love fundamental mode in the transverse component at all the strong-motion stations. The vertical component also shows the first higher mode of Rayleigh waves. We use a very broadband record obtained at station CU for the smaller (MS = 6.7) earthquake of 14 May 1993 to verify that the dispersion computed from the model of Campillo et al. (1989) represents well the average surface-wave propagation between the coast and Mexico City in the 7- to 10-sec period range. We use this result to assign absolute times to the strong-motion records of the Michoacán event. This allowed us to identify additional wave trains that propagate laterally in directions other than great circle in the 3- to 5-sec period range. These wave trains are identified as Love waves. In a second analysis, we study a set of refraction data obtained during a small-scale (250 m) experiment on the virgin clay of the lake-bed zone. Phase-velocity dispersion curves for several modes of Rayleigh waves are identified in the refraction data and inverted to obtain an S-wave velocity profile. This profile is used as the uppermost layering in a 2D model of Mexico City valley. The results of numerical simulation show that surface waves generated by lateral finiteness of the clay layer suffer large dispersion and attenuation. We conclude that surface waves generated by the lateral heterogeneity of the upper-most stratigraphy very significantly affect ground motion near the edge of the valley, but their importance is negligible for distances larger than 1.5 km from the edge. Thus, locally generated surface waves propagating through the clay layer cannot explain late arrivals observed for the 1985 event. We suggest that the long duration of strong motion is due to the interaction between lateral propagation of waves guided by deep layers (1 to 4 km) and the surficial clay layer. This interaction is possible by the coincidence of the dominant frequency of the uppermost layers and the frequency of the deeply guided waves.
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Powers, J. M., D. S. Stewart, and Herman Krier. "Analysis of Steady Compaction Waves in Porous Materials." Journal of Applied Mechanics 56, no. 1 (March 1, 1989): 15–24. http://dx.doi.org/10.1115/1.3176038.
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A two-phase continuum mixture model is used to analyze steady compaction waves in porous materials. It is shown that such a model admits both subsonic and supersonic steady compaction waves in response to a piston-driven boundary condition when a Tait equation is used to describe a solid matrix material and a generic static compaction relation is used to describe collapse of the matrix. Parameters for the Tait equation are chosen to match shock and compaction wave data. The model is able to predict compaction wave speed, final pressure, and final volume fraction in porous HMX. The structure of the compaction wave is also studied. A shock preceding the compaction wave structure is predicted for compaction waves travelling faster than the ambient sound speed of the solid. For subsonic compaction waves no leading shock is predicted. The compaction zone length is studied as a function of initial volume fraction, piston velocity, and compaction viscosity.
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Mankbadi, Reda R., Xuesong Wu, and Sang Soo Lee. "A critical-layer analysis of the resonant triad in boundary-layer transition: nonlinear interactions." Journal of Fluid Mechanics 256 (November 1993): 85–106. http://dx.doi.org/10.1017/s0022112093002721.
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A systematic theory is developed to study the nonlinear spatial evolution of the resonant triad in Blasius boundary layers. This triad consists of a plane wave at the fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low-frequency asymptotic scaling leads to a distinct critical layer wherein nonlinearity first becomes important, and the critical layer's nonlinear, viscous dynamics determine the development of the triad.The plane wave initially causes double-exponential growth of the oblique waves. The plane wave, however, continues to follow the linear theory, even when the oblique waves’ amplitude attains the same order of magnitude as that of the plane wave. However, when the amplitude of the oblique waves exceeds that of the plane wave by a certain level, a nonlinear stage comes into effect in which the self-interaction of the oblique waves becomes important. The self-interaction causes rapid growth of the phase of the oblique waves, which causes a change of the sign of the parametric-resonance term in the oblique-waves amplitude equation. Ultimately this effect causes the growth rate of the oblique waves to oscillate around their linear growth rate. Since the latter is usually small in the nonlinear regime, the net outcome is that the self-interaction of oblique waves causes the parametric resonance stage to be followed by an ‘oscillatory’ saturation stage.
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Mohtat, Ali, Casey Fagley, Kedar C. Chitale, and Stefan G. Siegel. "Efficiency analysis of the cycloidal wave energy convertor under real-time dynamic control using a 3D radiation model." International Marine Energy Journal 5, no. 1 (June 14, 2022): 45–56. http://dx.doi.org/10.36688/imej.5.45-56.
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Ocean waves provide a vast, uninterrupted resource of renewable energy collocated around large coastal population centers. Clean energy from ocean waves can contribute to the local electrical grid without the need for long-term electrical storage, yet due to the current high cost of energy extraction from ocean waves, there is no commercial ocean wave farm in operation. One of the wave energy converter (WEC) device classes that show the potential to enable economic energy generation from ocean waves is the class of wave terminators. This work investigates the Cycloidal Wave Energy Converter (CycWEC), which is a one-sided, lift-based wave terminator operating with coupled hydrofoils. The energy that the CycWEC extracted from ocean waves was estimated using a control volume analysis model of the 3D wave field in the presence of the CycWEC. The CycWEC was operated under feedback control to extract the maximum amount of energy possible from the incoming waves, and the interaction with different incoming regular, irregular, and short crested waves was examined.
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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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Barreto, Antônio Sá. "Interactions of conormal waves for fully semilinear wave equations." Journal of Functional Analysis 89, no. 2 (March 1990): 233–73. http://dx.doi.org/10.1016/0022-1236(90)90094-2.
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Ouyang, Zheng-yong, and Shan Zheng. "Travelling Wave Solutions of Nonlinear Dynamical Equations in a Double-Chain Model of DNA." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/317543.
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We consider the nonlinear dynamics in a double-chain model of DNA which consists of two long elastic homogeneous strands connected with each other by an elastic membrane. By using the method of dynamical systems, the bounded traveling wave solutions such as bell-shaped solitary waves and periodic waves for the coupled nonlinear dynamical equations of DNA model are obtained and simulated numerically. For the same wave speed, bell-shaped solitary waves of different heights are found to coexist.
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Veltcheva, Albena D., and C. Guedes Soares. "Analysis of Abnormal Wave Records by the Hilbert–Huang Transform Method." Journal of Atmospheric and Oceanic Technology 24, no. 9 (September 1, 2007): 1678–89. http://dx.doi.org/10.1175/jtech2067.1.
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Abstract The Hilbert–Huang transform method is used in this work to analyze wave records from the North Sea, which include abnormal waves. The analysis of the characteristics of abnormal waves is based on the local decomposition of wave data by using the intrinsic mode functions. The variations of amplitude of intrinsic mode functions around the time of the occurrence of abnormal waves are examined in order to investigate the contribution of different intrinsic mode functions on the abnormal waves’ profile, in an attempt to find relationships between them. The changes of local frequency of each intrinsic mode function in the vicinity of abnormal waves are examined. The essential nonlinearity of abnormal waves is considered as intrawave frequency modulation, a variation of the instantaneous frequency within one oscillation cycle. The Hilbert spectrum is used as a detector of abnormal waves.
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Harleman, Donald R. F., William C. Nolan, and Vernon C. Honsinger. "DYNAMIC ANALYSIS OF OFFSHORE STRUCTURES." Coastal Engineering Proceedings 1, no. 8 (January 29, 2011): 28. http://dx.doi.org/10.9753/icce.v8.28.
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Analytical procedures are presented for calculation of the dynamic displacements of fixed offshore structures in oscillatory waves. The structure considered has four legs in a square configuration with waves impinging normal to one side; however, the procedures are general and may be applied to other configurations and wave directions. The horizontal displacement of the deck is determined as a function of time by application of vibration theory for a damped, spring-mass system subject to a harmonic force. The instantaneous wave force on each leg is composed of a hydrodynamic drag component and an inertial component as in the usual "statical" wave force analysis. The wave force expression is approximated by a Fourier series which permits calculation of the platform displacement by superposition of solutions of the equation of motion for the platform. Depending on the ratio of the wave frequency to the natural frequency of the platform, the structural stresses may be considerably high* than those found by methods which neglect the elastic behavior of the structure. The highest wave to be expected in a given locality is not necessarily the critical design wave. Maximum displacements and structural stresses may occur for smaller waves having periods producing a resonant response of the platform. Displacement measurements in a wave tank using a platform constructed of plastic are presented to show the validity of the analytical method. Both small and finite amplitude waves are used over a wide range of frequency ratios. A digital computer program (7090 FORTRAN) is used for the displacement calculation.
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Lecacheux, S., R. Pedreros, G. Le Cozannet, J. Thiébot, Y. De La Torre, and T. Bulteau. "A method to characterize the different extreme waves for islands exposed to various wave regimes: a case study devoted to Reunion Island." Natural Hazards and Earth System Sciences 12, no. 7 (July 31, 2012): 2425–37. http://dx.doi.org/10.5194/nhess-12-2425-2012.
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Abstract. This paper outlines a new approach devoted to the analysis of extreme waves in presence of several wave regimes. It entails discriminating the different wave regimes from offshore wave data using classification algorithms, before conducting the extreme wave analysis for each regime separately. The concept is applied to the pilot site of Reunion Island which is affected by three main wave regimes: southern waves, trade-wind waves and cyclonic waves. Several extreme wave scenarios are determined for each regime, based on real historical cases (for cyclonic waves) and extreme value analysis (for non-cyclonic waves). For each scenario, the nearshore wave characteristics are modelled all around Reunion Island and the linear theory equations are used to back calculate the equivalent deep-water wave characteristics for each portion of the coast. The relative exposure of the coastline to the extreme waves of each regime is determined by comparing the equivalent deep-water wave characteristics. This method provides a practical framework to perform an analysis of extremes within a complex environment presenting several sources of extreme waves. First, at a particular coastal location, it allows for inter-comparison between various kinds of extreme waves that are generated by different processes and that may occur at different periods of the year. Then, it enables us to analyse the alongshore variability in wave exposition, which is a good indicator of potential runup extreme values. For the case of Reunion Island, cyclonic waves are dominant offshore around the island, with equivalent deep-water wave heights up to 18 m for the northern part. Nevertheless, due to nearshore wave refraction, southern waves may become as energetic as cyclonic waves on the western part of the island and induce similar impacts in terms of runup and submersion. This method can be easily transposed to other case studies and can be adapted, depending on the data availability.
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Teutsch, Ina, Ralf Weisse, Jens Moeller, and Oliver Krueger. "A statistical analysis of rogue waves in the southern North Sea." Natural Hazards and Earth System Sciences 20, no. 10 (October 9, 2020): 2665–80. http://dx.doi.org/10.5194/nhess-20-2665-2020.
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Abstract. A new wave data set from the southern North Sea covering the period 2011–2016 and composed of wave buoy and radar measurements sampling the sea surface height at frequencies between 1.28 and 4 Hz was quality controlled and scanned for the presence of rogue waves. Here, rogue waves refer to waves whose height exceeds twice the significant wave height. Rogue wave frequencies were analyzed and compared to Rayleigh and Forristall distributions, and spatial, seasonal, and long-term variability was assessed. Rogue wave frequency appeared to be relatively constant over the course of the year and uncorrelated among the different measurement sites. While data from buoys basically correspond with expectations from the Forristall distribution, radar measurement showed some deviations in the upper tail pointing towards higher rogue wave frequencies. The amount of data available in the upper tail is, however, still too limited to allow a robust assessment. Some indications were found that the distribution of waves in samples with and without rogue waves was different in a statistical sense. However, differences were small and deemed not to be relevant as attempts to use them as a criterion for rogue wave detection were not successful in Monte Carlo experiments based on the available data.
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Osborne, Alfred R. "Nonlinear Fourier Analysis: Rogue Waves in Numerical Modeling and Data Analysis." Journal of Marine Science and Engineering 8, no. 12 (December 9, 2020): 1005. http://dx.doi.org/10.3390/jmse8121005.
Full textAbstract:
Nonlinear Fourier Analysis (NLFA) as developed herein begins with the nonlinear Schrödinger equation in two-space and one-time dimensions (the 2+1 NLS equation). The integrability of the simpler nonlinear Schrödinger equation in one-space and one-time dimensions (1+1 NLS) is an important tool in this analysis. We demonstrate that small-time asymptotic spectral solutions of the 2+1 NLS equation can be constructed as the nonlinear superposition of many 1+1 NLS equations, each corresponding to a particular radial direction in the directional spectrum of the waves. The radial 1+1 NLS equations interact nonlinearly with one another. We determine practical asymptotic spectral solutions of the 2+1 NLS equation that are formed from the ratio of two phase-lagged Riemann theta functions: Surprisingly this construction can be written in terms of generalizations of periodic Fourier series called (1) quasiperiodic Fourier (QPF) series and (2) almost periodic Fourier (APF) series (with appropriate limits in space and time). To simplify the discourse with regard to QPF and APF Fourier series, we call them NLF series herein. The NLF series are the solutions or approximate solutions of the nonlinear dynamics of water waves. These series are indistinguishable in many ways from the linear superposition of sine waves introduced theoretically by Paley and Weiner, and exploited experimentally and theoretically by Barber and Longuet-Higgins assuming random phases. Generally speaking NLF series do not have random phases, but instead employ phase locking. We construct the asymptotic NLF series spectral solutions of 2+1 NLS as a linear superposition of sine waves, with particular amplitudes, frequencies and phases. Because of the phase locking the NLF basis functions consist not only of sine waves, but also of Stokes waves, breather trains, and superbreathers, all of which undergo complex pair-wise nonlinear interactions. Breather trains are known to be associated with rogue waves in solutions of nonlinear wave equations. It is remarkable that complex nonlinear dynamics can be represented as a generalized, linear superposition of sine waves. NLF series that solve nonlinear wave equations offer a significant advantage over traditional periodic Fourier series. We show how NLFA can be applied to numerically model nonlinear wave motions and to analyze experimentally measured wave data. Applications to the analysis of SINTEF wave tank data, measurements from Currituck Sound, North Carolina and to shipboard radar data taken by the U. S. Navy are discussed. The ubiquitous presence of coherent breather packets in many data sets, as analyzed by NLFA methods, has recently led to the discovery of breather turbulence in the ocean: In this case, nonlinear Fourier components occur as strongly interacting, phase locked, densely packed breather modes, in contrast to the previously held incorrect belief that ocean waves are weakly interacting sine waves.