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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.
Widrow, Lawrence M. "Galactic wave mechanics." Nature Physics 10, no. 7 (June 22, 2014): 477–78. http://dx.doi.org/10.1038/nphys3020.
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.
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.
Lima, Nathan, and Ricardo Karam. "Schrödinger’s equation from Snell’s law." European Journal of Physics 43, no. 3 (March 21, 2022): 035402. http://dx.doi.org/10.1088/1361-6404/ac5635.
Abstract A new derivation of Schrödinger’s equation is presented, based on Schrödinger’s original discussions on refraction and the optical-mechanical analogy, but adopting a much simpler formalism: Newtonian mechanics and some basic elements of classical wave theory (such as Snell’s law). We compare how particles and waves refract and show that the ‘law of particle refraction’ and the ‘law of wave refraction’ may become consistent if one assumes that a particle can be represented by a wave group. In this case, the differential equation whose solutions represent the waves forming such wave group is the Schrödinger equation. Due to the simplicity of the adopted mathematical formalism, we argue that this derivation can be used in quantum mechanics courses at introductory level to give students an idea of Schrödinger’s original path to his wave equation.
Nimtz, Guenter, and Paul Bruney. "On the Universal Scattering Time of Neutrons." Zeitschrift für Naturforschung A 73, no. 10 (October 25, 2018): 919–21. http://dx.doi.org/10.1515/zna-2018-0331.
AbstractTunnelling and barrier interaction times of neutrons were previously measured. Here we show that the neutron interaction time with barriers corresponds to the universal tunnelling time of wave mechanics which was formerly observed with elastic, electromagnetic and electron waves. The universal tunnelling time seems to hold for neutrons also. Such an adequate general wave mechanical behaviour was conjectured by Brillouin. Remarkably, wave mechanical effects, and even virtual particles, hold from the microcosm to the macrocosm.
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.
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.
Hayashi, Takahiro, Koichiro Kawashima, Zongqi Sun, and Joseph L. Rose. "Guided Wave Propagation Mechanics Across a Pipe Elbow." Journal of Pressure Vessel Technology 127, no. 3 (January 24, 2005): 322–27. http://dx.doi.org/10.1115/1.1990210.
Wave propagation across a pipe elbow region is complex. Subsequent reflected and transmitted waves are largely deformed due to mode conversions at the elbow. This prevents us to date from applying guided waves to the nondestructive evaluation of meandering pipeworks. Since theoretical development of guided wave propagation in a pipe is difficult, numerical modeling techniques are useful. We have introduced a semianalytical finite element method, a special modeling technique for guided wave propagation, because ordinary finite element methods require extremely long computational times and memory for such a long-range guided wave calculation. In this study, the semianalytical finite element method for curved pipes is developed. A curved cylindrical coordinate system is used for the curved pipe region, where a curved center axis of the pipe elbow region is an axis (z′ axis) of the coordinate system, instead of the straight axis (z axis) of the cylindrical coordinate system. Guided waves in the z′ direction are described as a superposition of orthogonal functions. The calculation region is divided only in the thickness and circumferential directions. Using this calculation technique, echoes from the back wall beyond up to four elbows are discussed.
Williamson, C. H. K., and A. Prasad. "A new mechanism for oblique wave resonance in the ‘natural’ far wake." Journal of Fluid Mechanics 256 (November 1993): 269–313. http://dx.doi.org/10.1017/s0022112093002794.
There has been some debate recently on whether the far-wake structure downstream of a cylinder is dependent on, or ‘connected’ with, the precise details of the near-wake structure. Indeed, it has previously been suggested that the far-wake scale and frequency are unconnected with those of the near wake. In the present paper, we demonstrate that both the far-wake scale and frequency are dependent on the near wake. Surprisingly, the characteristic that actually forges a ‘connection’ between the near and far wakes is the sensitivity to free-stream disturbances. It is these disturbances that are also responsible for the regular three-dimensional patterns that may be visualized. Observations of a regular ‘honeycomb’-like three-dimensional pattern in the far wake is found to be caused by an interaction between oblique shedding waves from upstream and large-scale two-dimensional waves, amplified from the free-stream disturbances. The symmetry and spanwise wavelength of Cimbala, Nagib & Roshko's (1988) three-dimensional pattern are precisely consistent with such wave interactions. In the presence of parallel shedding, the lack of a honeycomb pattern shows that such a three-dimensional pattern is clearly dependent on upstream oblique vortex shedding.With the deductions above as a starting point, we describe a new mechanism for the resonance of oblique waves, as follows. In the case of two-dimensional waves, corresponding to a very small spectral peak in the free stream (fT) interacting (quadratically) with the oblique shedding waves frequency (fK), it appears that the most amplified or resonant frequency in the far wake is a combination frequency fFW = (fK–fT), which corresponds physically with ‘oblique resonance waves’ at a large oblique angle. The large scatter in (fFW/fK) from previous studies is principally caused by the broad response of the far wake to a range of free-stream spectral peaks (fT). We present clear visualization of the oblique wave phenomenon, coupled with velocity measurements which demonstrate that the secondary oblique wave energy can far exceed the secondary two-dimensional wave energy by up to two orders of magnitude. Further experiments show that, in the absence of an influential free-stream spectral peak, the far wake does not resonate, but instead has a low-amplitude broad spectral response. The present phenomena are due to nonlinear instabilities in the far wake, and are not related to vortex pairing. There would appear to be distinct differences between this oblique wave resonance and the subharmonic resonances that have been previously studied in channel flow, boundary layers, mixing layers and airfoil wakes.
Engelbrecht, J. "Wave equations in mechanics." Estonian Journal of Engineering 19, no. 4 (2013): 273. http://dx.doi.org/10.3176/eng.2013.4.02.
This thesis investigates water particle kinematics and the wave forces exerted on a slender rigid vertical cylinder in regular bidirectional
wave fields. The instrumented portion of this cylinder is partitioned into nine independent segments enabling measurement of the vertical profile of hydrodynamic loading both in-line and transverse to the direction of wave propagation. Experiments conducted at the Hydraulics Laboratory of the National Research Council in Ottawa are described and some results are compared with the predictions of a wave force model based on the Morison equation and linear fluid kinematics. The influence of the crossing angle between the two wave components on the forces experienced by the column is determined.
These experiments consider short-crested wave behavior in intermediate
and deep water resulting from the interaction of two identical regular wave trains crossing at angles of 30, 60 and 90 degrees. The limit corresponding to unidirectional monochromatic waves is also investigated to provide a reference condition for comparison with the short-crested results. Conditions at the location of maximum short-crested wave height are of primary interest, however, forces at locations between the anti-node and node of the flow are also examined. In all, water surface elevations, flow velocities, and wave forces were measured in 24 short-crested and 8 different long-crested wave conditions
spanning the range of Keulegan-Carpenter number between 4 and 24.
The results of this study confirm the findings of previous researchers that short -crested waves with a certain period travel faster and rise higher before breaking than do their long-crested counterparts, but that in-line wave forces are not necessarily increased.
Lift force maxima equal to half the maximum in-line force were measured; these forces can contribute significantly to the magnitude and direction of the total force resultant. Applied Science, Faculty of Civil Engineering, Department of Graduate
Judd, Thomas Edward. "The wave mechanics of cold atoms." Thesis, University of Nottingham, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490985.
This thesis presents theoretical investigations on a range of topics in cold atom physics, primarily by means of wave mechanical simulations, implemented on High-Performance computers. Two particular concerns are the interaction of Bose-Einstein condensates with microfabricated surfaces, and the behaviour of strongly interacting Fermi atoms. In the course of this work. we have developed new theoretical models and computational techniques to handle problems which were beyond the scope of previous calculations.
Kil, Hyun-Gwon. "Propagation of elastic waves on thin-walled circular cylinders." Thesis, Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/15967.
Surfzone wave transformation under storm conditions is investigated through field and laboratory
measurements in this study. The observations have been used to examine currently available
models of wave energy dissipation.
Detailed field data has been collected by means of a novel method which was first introduced by
Nielsen (1988). This method has been utilised through a common program between Griffith
University and The University of Queensland at The Spit on the Gold Coast in Southeast
Queensland. The facility primarily consists of a manometer tube array with 12 different manometer
tube lengths varying from 60 m to 500 m offshore and a concrete manhole excavated into the dune
system to house the monitoring station. Accordingly, this system has enabled the monitoring of a
detailed wave height profile across the surfzone under any conditions from the safety of the
“bunker” on land.
The findings of new laboratory experiments on the frequency response of the semi-rigid
manometer tubes are also presented which extend and improve upon the previous work of Nielsen
et al. (1993). Testing was conducted over a range of frequencies (0.0067 Hz< f <2 Hz) and tube
lengths (10 m< L <900 m). New frequency response factors are determined by fitting the semiempirical
gain function of Nielsen et al. (1993) to the observed gain data. As a result, new
predictive formulas for the empirical coefficients as a function of tube parameters are provided in
Wave induced pore pressure in the surfzone seabed is investigated based on the recorded field data.
Two well-known models, i.e. Hsu and Jeng (1994) and Sleath (1970), are assessed against the
field measurements. The findings validate the accuracy of the models and indicate that the extent of
energy dissipation due to the overlying sand is less than 5% and depends on the incident wave
length. Thesis (PhD Doctorate) Doctor of Philosophy (PhD) Griffith School of Engineering Science, Environment, Engineering and Technology Full Text
Puckett, Anthony. "An Experimental and Theoretical Investigation fo Axially Symmetric Wave Propagation In Thick Cylindrical Waveguides." Fogler Library, University of Maine, 2004. http://www.library.umaine.edu/theses/pdf/PuckettA2004.pdf.
Mudge, Damien. "High power scalable diode-laser-pumped CW Nd:YAG laser using a stable-unstable resonator." Title page, contents and abstract only, 2000. http://web4.library.adelaide.edu.au/theses/09PH/09phm9438.pdf.
Bell, James Andrew, and andrew bell@anu edu au. "The Underwater Piano: A Resonance Theory of Cochlear Mechanics." The Australian National University. Research School of Biological Sciences, 2006. http://thesis.anu.edu.au./public/adt-ANU20080706.141018.
This thesis takes a fresh approach to cochlear mechanics. Over the last
quarter of a century, we have learnt that the cochlea is active and highly tuned,
observations suggesting that something may be resonating. Rather than accepting the standard traveling wave interpretation, here I investigate whether a resonance theory of some kind can be applied to this remarkable behaviour.¶
A historical survey of resonance theories is first conducted, and advantages
and drawbacks examined. A corresponding look at the traveling wave theory
includes a listing of its short-comings.¶
A new model of the cochlea is put forward that exhibits inherently high
tuning. The surface acoustic wave (SAW) model suggests that the three rows of outer hair cells (OHCs) interact in a similar way to the interdigital transducers of an
electronic SAW device. Analytic equations are developed to describe the conjectured interactions between rows of active OHCs in which each cell is treated as a point source of expanding wavefronts. Motion of a cell launches a wave that is sensed by the stereocilia of neighbouring cells, producing positive feedback. Numerical calculations confirm that this arrangement provides sharp tuning when the feedback gain is set just below oscillation threshold.¶
A major requirement of the SAW model is that the waves carrying the feedback have slow speed (5-200 mm/s) and high dispersion. A wave type with the
required properties is identified - a symmetric Lloyd-Redwood wave (or squirting wave) - and the physical properties of the organ of Corti are shown to well match those required by theory.¶
The squirting wave mechanism may provide a second filter for a primary
traveling wave stimulus, or stand-alone tuning in a pure resonance model. In both, cyclic activity of squirting waves leads to standing waves, and this provides a physical rendering of the cochlear amplifier.
In keeping with pure resonance, this thesis proposes that OHCs react to the
fast pressure wave rather than to bending of stereocilia induced by a traveling wave. Investigation of literature on OHC ultrastructure reveals anatomical features consistent with them being pressure detectors: they possess a cuticular pore (a small compliant spot in an otherwise rigid cell body) and a spherical body within (Hensens
body) that could be compressible. I conclude that OHCs are dual detectors, sensing displacement at high intensities and pressure at low. Thus, the conventional traveling wave could operate at high levels and resonance at levels dominated by the cochlear
The latter picture accords with the description due to Gold (1987) that the cochlea is an underwater piano - a bank of strings that are highly tuned despite immersion in liquid.¶
An autocorrelation analysis of the distinctive outer hair cell geometry shows
trends that support the SAW model. In particular, it explains why maximum
distortion occurs at a ratio of the two primaries of about 1.2. This ratio also produces near-integer ratios in certain hair-cell alignments, suggesting that music may have a cochlear basis.¶
The thesis concludes with an evaluation and proposals to experimentally test
Hosoglu, Selcuk. "Cellular automata an approach to wave propagation and fracture mechanics problems." Thesis, Monterey, Calif. : Naval Postgraduate School, 2006. http://bosun.nps.edu/uhtbin/hyperion.exe/06Dec%5FHosoglu.pdf.
Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, December 2006. Thesis Advisor(s): Young W. Kwon. "December 2006." Includes bibliographical references (p. 63-64). Also available in print.
Thomson, Edward Andrew. "Schrodinger wave-mechanics and large scale structure." Thesis, University of Glasgow, 2011. http://theses.gla.ac.uk/2976/.
In recent years various authors have developed a new numerical approach to cosmological simulations that formulates the equations describing large scale structure (LSS) formation within a quantum mechanical framework. This method couples the Schrodinger and Poisson equations. Previously, work has evolved mainly along two different strands of thought: (1) solving the full system of equations as Widrow & Kaiser attempted, (2) as an approximation to the full set of equations (the Free Particle Approximation developed by Coles, Spencer and Short). It has been suggested that this approach can be considered in two ways: (1) as a purely classical system that includes more physics than just gravity, or (2) as the representation of a dark matter field, perhaps an Axion field, where the de Broglie wavelength of the particles is large. In the quasi-linear regime, the Free Particle Approximation (FPA) is amenable to exact solution via standard techniques from the quantum mechanics literature. However, this method breaks down in the fully non-linear regime when shell crossing occurs (confer the Zel'dovich approximation). The first eighteen months of my PhD involved investigating the performance of illustrative 1-D and 3-D ``toy" models, as well as a test against the 3-D code Hydra. Much of this work is a reproduction of the work of Short, and I was able to verify and confirm his results. As an extension to his work I introduced a way of calculating the velocity via the probability current rather than using a phase unwrapping technique. Using the probability current deals directly with the wavefunction and provides a faster method of calculation in three dimensions. After working on the FPA I went on to develop a cosmological code that did not approximate the Schrodinger-Poisson system. The final code considered the full Schrodinger equation with the inclusion of a self-consistent gravitational potential via the Poisson equation. This method follows on from Widrow & Kaiser but extends their method from 2D to 3D, it includes periodic boundary conditions, and cosmological expansion. Widrow & Kaiser provided expansion via a change of variables in their Schrodinger equation; however, this was specific only to the Einstein-de Sitter model. In this thesis I provide a generalization of that approach which works for any flat universe that obeys the Robertson-Walker metric. In this thesis I aim to provide a comprehensive review of the FPA and of the Widrow-Kaiser method. I hope this work serves as an easy first point of contact to the wave-mechanical approach to LSS and that this work also serves as a solid reference point for all future research in this new field.
Coughtrie, David James. "Gaussian wave packets for quantum statistical mechanics." Thesis, University of Bristol, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682558.
Thermal (canonical) condensed-phase systems are of considerable interest in computational science, and include for example reactions in solution. Time-independent properties of these systems include free energies and thermally averaged geometries - time-dependent properties include correlation functions and thermal reaction rates. Accounting for quantum effects in such simulations remains a considerable challenge, especially for large systems, due to the quantum nature and high dimensionality of the phase space. Additionally time-dependent properties require treatment of quantum dynamics. Most current methods rely on semi-classical trajectories, path integrals or imaginary-time propagation of wave packets. Trajectory based approaches use continuous phase-space trajectories, similar to classical molecular dynamics, but lack a direct link to a wave packet and so the time-dependent schrodinger equation. Imaginary time propagation methods retain the wave packet, however the imaginary-time trajectory cannot be used as an approximation for real-time dynamics. We present a new approach that combines aspects of both. Using a generalisation of the coherent-state basis allows for mapping of the quantum canonical statistical average onto a phase-space average of the centre and width of thawed Gaussian wave packets. An approximate phase-space density that is exact in the low-temperature harmonic limit, and is a direct function of the phase space is proposed, defining the Gaussian statistical average. A novel Nose-Hoover looped chain thermostat is developed to generate the Gaussian statistical average via the ergodic principle, in conjunction with variational thawed Gaussian wave-packet dynamics. Numerical tests are performed on simple model systems, including quartic bond stretching modes and a double well potential. The Gaussian statistical average is found to be accurate to around 10% for geometric properties at room temperature, but gives energies two to three times too large. An approach to correct the Gaussian statistical average and ensure classical statistics is retrieved at high temperature is then derived, called the switched statistical average. This involves transitioning the potential surface upon which the Gaussian wave packet propagates, and the system property being averaged. Switching functions designed to perform these tasks are derived and tested on model systems. Bond lengths and their uncertainties calculated using the switched statistical average were found to be accurate to within 1% relative to exact results, and similarly for energies. The switched statistical average, calculated with Nose- Hoover looped chain thermostatted Gaussian dynamics, forms a new platform for evaluating statistical properties of quantum condensed-phase systems using an explicit real-time wave packet, whilst retaining appealing features of trajectory based approaches.
Тези доповідей конференцій з теми "Wave mechanics":
Smith, Brian J., and M. G. Raymer. "Photon wave mechanics." In 2006 Conference on Lasers and Electro-Optics and 2006 Quantum Electronics and Laser Science Conference. IEEE, 2006. http://dx.doi.org/10.1109/cleo.2006.4629000.
Aristodemo, Francesco, Giuseppe R. Tomasicchio, and Paolo Veltri. "Modelling of Periodic and Random Wave Forces on Submarine Pipelines." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92353.
A numerical model for the prediction of the time variation of the flow field and the hydrodynamic forces on bottom submarine pipelines is proposed. The model is an extension for periodic and random waves of the Wake II hydrodynamic forces model (Soedigdo et al., 1999), originally proposed for sinusoidal waves. An extensive laboratory investigation has been carried out in order to calibrate the model. The numerical model is based on an analysis of the time history of the velocity field at each wave semi-cycle. A modified relationship of the wake velocity is introduced and the time history of the drag and lift hydrodynamic coefficients are obtained using a Gauss integration of the start-up function. The laboratory investigation was performed at the large wave flume of the Centro Sperimentale per Modelli Idraulici at Voltabarozzo (Padua, Italy). The tests were carried out by measuring the pressure values at 8 transducers mounted on a cylinder subjected to different periodic and random waves. The experiments refer to the range 4 ÷ 12 of the Keulegan-Carpenter number for periodic waves and to the range 4 ÷ 9 for random waves. The empirical parameters involved in the extended Wake II and in the classical Morison models were calibrated using the results of the sampled velocities and force time histories under different wave conditions. The comparisons between the experimental and numerical results indicate that the extended Wake II model allows an accurate evaluation of the peaks and of the phase shifts of the horizontal and vertical forces and is more accurate than the Morison model.
Hayashi, Takahiro, Koichiro Kawashima, Zongqi Sun, and Joseph L. Rose. "Guided Wave Propagation Mechanics Across a Pipe Elbow." In ASME 2003 Pressure Vessels and Piping Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/pvp2003-1851.
Wave propagation across a pipe elbow region is complex. Subsequent reflected and transmitted waves are largely deformed due to mode conversions at the elbow. This prevents us to date from applying guided waves to the nondestructive evaluation of meandering pipeworks. Since theoretical development of guided wave propagation in a pipe is difficult, numerical modeling techniques are used. We have introduced a semi-analytical finite element method, a special modeling technique for guided wave propagation, because ordinary finite element methods require extremely long computational times and memory for such a long-range guided wave calculation. In this study, the semi-analytical finite element method for curved pipes is developed. A curved cylindrical coordinate system is used for the curved pipe region, where a curved center axis of the pipe elbow region is an axis (z′ axis) of the coordinate system, instead of the straight axis (z axis) of the cylindrical coordinate system. Guided waves in the z′ direction are described as a superposition of orthogonal functions. The calculation region is divided only in the thickness and circumferential directions. Using this calculation technique, echoes from the back wall beyond up to four elbows are discussed.
Hayashi, Takahiro, Koichiro Kawashima, Zongqi Sun, and Joseph L. Rose. "Guided Wave Focusing Mechanics in Pipe." In ASME 2003 Pressure Vessels and Piping Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/pvp2003-1850.
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 non-axisymmetric waveforms and subsequent time delayed superposition at a specific point in a pipe. A semi-analytical finite element method is used to present wave structure in the pipe. Focusing potential is also studied with various modes and frequencies.
Fedele, Francesco, and M. Aziz Tayfun. "Extreme Waves and Stochastic Wave Groups." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92527.
We introduce the concept of stochastic wave groups to explain the occurrence of extreme waves in nonlinear random seas, according to the dynamics imposed by the Zakharov equation (Zakharov, 1999). As a corollary, a new probability of exceedance of the crest-to-trough height which takes in to account the quasi-resonance interaction is derived. Furthermore, a generalization of the Tayfun distribution (Tayfun, 1986) for the wave crest height is also proposed. The new analytical distributions explain qualitatively well the experimental results of Onorato et al. (2004, 2005) and the numerical results of Juglard et al. (2005).
Schellin, Thomas E., and Ould El Moctar. "Numerical Prediction of Impact-Related Wave Loads on Ships." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92133.
We present a numerical procedure to predict impact-related wave-induced (slamming) loads on ships. The procedure was applied to predict slamming loads on two ships that feature a flared bow with a pronounced bulb, hull shapes typical of modern offshore supply vessels. The procedure used a chain of seakeeping codes. First, a linear Green function panel code computed ship responses in unit amplitude regular waves. Wave frequency and wave heading were systematically varied to cover all possible combinations likely to cause slamming. Regular design waves were selected on the basis of maximum magnitudes of relative normal velocity between ship critical areas and wave, averaged over the critical areas. Second, a nonlinear strip theory seakeeping code determined ship motions under design wave conditions, thereby accounting for the ship’s forward speed, the swell-up of water in finite amplitude waves, as well as the ship’s wake that influences the wave elevation around the ship. Third, these nonlinearly computed ship motions constituted part of the input for a Reynolds-averaged Navier-Stokes equations (RANSE) code that was used to obtain slamming loads. Favourable comparison with available model test data validated the procedure and demonstrated its capability to predict slamming loads suitable for design of ship structures.
Nascimento, Fa´bio, Carlos Levi, Antonio C. Fernandes, Paulo de Tarso Esperanc¸a, and Paulo Sergio Gomes. "A Wave Maker With Active Reflected Wave Compensation System." In ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/omae2002-28222.
Important aspects in the studies to assess the dynamic behavior of ocean vessels or structures, like ships or offshore oil platforms is the capability of generating gravity waves under strict laboratory control. Model test techniques are continuously improving and are very much dependent on the good quality waves that could be generated in a basin. Since ocean basins have finite dimensions, the waves reflected by the models, walls and even to some extent by the beaches, may become a critical issue if you need to guarantee accuracy and reliability for the tests. Besides the undesirable pattern of reflected waves within the test area of the basin, these waves come back onto the wave maker, affecting the correct properties of the wave to be generated. Modern wave generator apparatuses are now being equipped with real time control systems that enable them to generate an irregular wave pattern. At the same time they correct their flap motions to compensate re-reflection of waves from the wave-boards. The quality of such a system depends very much on the efficiency of the algorithm to be implemented in it. This paper discusses the development of an effective mathematical model of a control system used in an irregular wave maker–hinged flap type, featuring active wave reflection compensation. An efficient real time algorithm has been selected to run the control system device. The system is able to generate first order irregular waves and detect reflected waves that approach the wave maker by means of wave probes mounted on the face of the flap. The probe registers the input data to be used by the actuator to compensate the incoming wave by controlling the flap motion. Computer simulations obtained for a wave-maker in a flume are used to demonstrate the efficiency of each step of the theory and the overall accuracy of the compensation system.
Bunnik, Tim, and Rene´ Huijsmans. "Validation of Wave Propagation in Numerical Wave Tanks." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67221.
During the last few years there has been a strong growth in the availability and capabilities of numerical wave tanks. In order to assess the accuracy of such methods, a validation study was carried out. The study focuses on two types of numerical wave tanks: 1. A numerical wave tank based a non-linear potential flow algorithm. 2. A numerical wave tank based on a Volume of Fluid algorithm. The first algorithm uses a structured grid with triangular elements and a surface tracking technique. The second algorithm uses a structured, Cartesian grid and a surface capturing technique. Validation material is available by means of waves measured at multiple locations in two different model test basins. The first method is capable of generating waves up to the break limit. Wave absorption is therefore modeled by means of a numerical beach and not by mean of the parabolic beach that is used in the model basin. The second method is capable of modeling wave breaking. Therefore, the parabolic beach in the model test basin can be modeled and has also been included. Energy dissipation therefore takes place according to physics which are more related to the situation in the model test basin. Three types of waves are generated in the model test basin and in the numerical wave tanks. All these waves are generated on basin scale. The following waves are considered: 1. A scaled 100-year North-Sea wave (Hs = 0.24 meters, Tp = 2.0 seconds) in deep water (5 meters). 2. A scaled operational wave (Hs = 0.086 meters, Tp = 1.69 seconds) at intermediate water depth (0.86 meters) generated by a flap-type wave generator. 3. A scaled operational wave (Hs = 0.046 meters, Tp = 1.2 seconds) in shallow water (0.35 meters) generated by a piston-type wave generator. The waves are generated by means of a flap or piston-type wave generator. The motions of the wave generator in the simulations (either rotational or translational) are identical to the motions in the model test basin. Furthermore, in the simulations with intermediate water depth, the non-flat contour of the basin bottom (ramp) is accurately modeled. A comparison is made between the measured and computed wave elevation at several locations in the basin. The comparison focuses on: 1. Reflection characteristics of the model test basin and the numerical wave tanks. 2. The accuracy in the prediction of steep waves. 3. Second order effects like set-down in intermediate and shallow water depth. Furthermore, a convergence study is presented to check the grid independence of the wave tank predictions.
Bitner-Gregersen, Elzbieta M., and O̸istein Hagen. "Freak Wave Events Within the Second Order Wave Model." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51410.
Recently significant interest has been paid to abnormal waves, often called rogue waves or freak waves. These waves represent operational risks to ship and offshore structures, and are likely to be responsible for a number of accidents. As shown by several authors, in ‘the second order world’ the freak waves are pretty rare events. The present study focuses on statistical properties of freak waves. The analyses are based on second order time domain simulations, short term distributions for crest statistics obtained from the literature, and long term field data. Time series of wave elevations are generated using the Pierson-Moskowitz, JONSWAP and two-peak Torsethaugen frequency spectrum for long-crested seas and deep water. Effects of combined seas (swell and wind sea) on wave statistics are discussed. Assuming 2nd order wave theory, the short term and long term probability of occurrence of a freak wave is estimated. The difference between a “freak wave” and a “dangerous wave” is pointed out. Finally, 100 year and 10000 year crest events obtained by analysis procedures used in the offshore industry are discussed in relation to freak waves.
"Acoustic wave transmission on homogenized perforated plate." In Engineering Mechanics 2018. Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, 2018. http://dx.doi.org/10.21495/91-8-713.
Tellander, Felix B. A., and Karl-Fredrik Berggren. Non-Hermitian Wave Mechanics: An Unorthodox Way into Embedded Systems. Journal of Young Investigators, September 2017. http://dx.doi.org/10.22186/jyi.33.4.87-90.
Maudlin, P. J., J. C. Jr Foster, and S. E. Jones. On the Taylor test, Part 3: A continuum mechanics code analysis of steady plastic wave propagation. Office of Scientific and Technical Information (OSTI), November 1994. http://dx.doi.org/10.2172/10192108.
This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is oﬀered. Classical physics proceeds from the hypothesis that immediate values of all the physical quantities, characterizing system’s state, exist and can be accurately measured in principle. Non-relativistic quantum mechanics does not reject the existence of the immediate values of the classical physical quantities, nevertheless not each of them can be simultaneously measured (the uncertainty principle). Relativistic quantum mechanics rejects the existence of the immediate values of any physical quantity in principle, and consequently the notion of the system state, including the notion of the wave function, which becomes rigorously nondeﬁnable. The task of this work consists in econophysical analysis of the conceptual fundamentals and mathematical apparatus of the classical physics, relativity theory, non-relativistic and relativistic quantum mechanics, subject to the historical, psychological and philosophical aspects and modern state of the socio-economic modeling problem. We have shown that actually and, virtually, a long time ago, new paradigms of modeling were accepted in the quantum theory, within the bounds of which the notion of the physical quantity operator becomes the primary fundamental conception(operator is a mathematical image of the procedure, the action), description of the system dynamics becomes discrete and approximate in its essence, prediction of the future, even in the rough, is actually impossible when setting aside the aftereﬀect i.e. the memory. In consideration of the analysis conducted in the work we suggest new paradigms of the economical-mathematical modeling.
Liu, Tai-Ping. Nonlinear Waves in Mechanics and Gas Dynamics. Fort Belvoir, VA: Defense Technical Information Center, December 1990. http://dx.doi.org/10.21236/ada238340.
Dimits, A. M., and W. W. Lee. Nonlinear mechanisms for drift wave saturation and induced particle transport. Office of Scientific and Technical Information (OSTI), December 1989. http://dx.doi.org/10.2172/5215375.
Dalrymple, Robert A., John H. Trowbridge, Dick K. Yue, Samuel J. Bentley, Gail C. Kineke, Yuming Liu, Chiang C. Mei, Lian Shen, and Peter A. Traykovski. Mechanisms of Fluid-Mud Interactions Under Waves. Fort Belvoir, VA: Defense Technical Information Center, January 2011. http://dx.doi.org/10.21236/ada540757.
Dalrymple, Robert A., John H. Trowbridge, Dick K. Yue, Samuel J. Bentley, Gail C. Kineke, Yuming Liu, Chiang C. Mei, Lian Shen, and Peter A. Traykovski. Mechanisms of Fluid-Mud Interactions Under Waves. Fort Belvoir, VA: Defense Technical Information Center, January 2008. http://dx.doi.org/10.21236/ada514886.
Dalrymple, Robert A., John H. Trowbridge, Dick K. Yue, Samuel J. Bentley, Gail C. Kineke, Yuming Liu, Chiang C. Mei, Lian Shen, and Peter A. Traykovski. Mechanisms of Fluid-Mud Interactions Under Waves. Fort Belvoir, VA: Defense Technical Information Center, September 2011. http://dx.doi.org/10.21236/ada557227.
Daniel Szymanski. The Arabidopsis Wave Complex: Mechanisms Of Localized Actin Polymerization And Growth. Office of Scientific and Technical Information (OSTI), October 2012. http://dx.doi.org/10.2172/1053522.