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1
Akylas, T. R., and R. H. J. Grimshaw. "Solitary internal waves with oscillatory tails." Journal of Fluid Mechanics 242 (September 1992): 279–98. http://dx.doi.org/10.1017/s0022112092002374.
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Solitary internal waves in a density-stratified fluid of shallow depth are considered. According to the classical weakly nonlinear long-wave theory, the propagation of each long-wave mode is governed by the Korteweg–de Vries equation to leading order, and locally confined solitary waves with a ‘sech’ profile are possible. Using a singular-perturbation procedure, it is shown that, in general, solitary waves of mode n > 1 actually develop oscillatory tails of infinite extent, consisting of lower-mode short waves. The amplitude of these tails is exponentially small with respect to an amplitude parameter, and lies beyond all orders of the usual long-wave expansion. To illustrate the theory, two special cases of stratification are discussed in detail, and the amplitude of the oscillations at the solitary-wave tails is determined explicitly. The theoretical predictions are supported by experimental observations.
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Yuan, Jing, Ole Madsen, and Eng Soon Chan. "EXPERIMENTAL STUDY OF TURBULENT OSCILLATORY BOUNDARY LAYERS IN A NEW OSCILLATORY WATER TUNNEL." Coastal Engineering Proceedings 1, no. 33 (2012): 24. http://dx.doi.org/10.9753/icce.v33.waves.24.
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A new oscillatory water tunnel has been built in the Civil and Environmental Engineering Department’s Hydraulic Laboratory at the National University of Singapore. It can accurately produce oscillatory flows that correspond to full-scale sea waves. Tests including pure sinusoidal waves and combined wave-current flows over smooth and rough bottoms have been performed. High quality measurements of the boundary layer flow fields are obtained using a PIV system. The PIV measured flow field is phase and spatially averaged to give a mean vertical velocity profile. It is found that the logarithmic profile can accurately approximate the near-bottom first-harmonic amplitude of sinusoidal waves and give highly accurate determinations of the hydrodynamic roughness and the theoretical bottom location. The bottom shear stress obtained from momentum integral is in general agreement with results from log-profile fitting. The current profiles of combined wave-current flows indicate a two-log-profile structure as suggested by simple combined wave-current flow theory. The difference between the two current shear velocities obtained from combined wave-current flows, as well as a small but meaningful third harmonic embedded in a pure sinusoidal wave, suggest the existence of a time-varying turbulent eddy viscosity.
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Longuet-Higgins, M. S., and M. J. H. Fox. "Asymptotic theory for the almost-highest solitary wave." Journal of Fluid Mechanics 317 (June 25, 1996): 1–19. http://dx.doi.org/10.1017/s002211209600064x.
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The behaviour of the energy in a steep solitary wave as a function of the wave height has a direct bearing on the breaking of solitary waves on a gently shoaling beach. Here it is shown that the speed, energy and momentum of a steep solitary wave in water of finite depth all behave in an oscillatory manner as functions of the wave height and as the limiting height is approached. Asymptotic formulae for these and other wave parameters are derived by means of a theory for the ‘almost-highest wave’ similar to that formulated previously for periodic waves in deep water (Longuet-Higgins & Fox 1977, 1978). It is demonstrated that the theory fits very precisely some recent calculations of solitary waves by Tanaka (1995).
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Nicolaou, D., R. Liu, and T. N. Stevenson. "The evolution of thermocline waves from an oscillatory disturbance." Journal of Fluid Mechanics 254 (September 1993): 401–16. http://dx.doi.org/10.1017/s0022112093002198.
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The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier–Stokes equations.
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Sherratt, Jonathan A., and Matthew J. Smith. "Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models." Journal of The Royal Society Interface 5, no. 22 (2008): 483–505. http://dx.doi.org/10.1098/rsif.2007.1327.
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Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction–diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction–diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical.
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Schretlen, Jolanthe J. L. M., Jan S. Ribberink, and Tom O'Donoghue. "BOUNDARY LAYER FLOW AND SAND TRANSPORT UNDER FULL SCALE SURFACE WAVES." Coastal Engineering Proceedings 1, no. 32 (2011): 4. http://dx.doi.org/10.9753/icce.v32.sediment.4.
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Existing models for wave-related (cross-shore) sand transport are primarily based on data from oscillatory flow tunnel experiments. However, theory and former experiments indicate that flow differences between full scale surface waves and oscillatory flow tunnels may have a substantial effect on the net sand transport. In this paper, high resolution measurements of boundary layer flow characteristics, sheet-flow layer sediment concentrations and net sand transport rates under full scale surface waves are presented. These experiments were performed in a large wave flume (GWK) for different wave conditions with medium (D50 = 0.25 mm) and fine (D50 = 0.14 mm) sand. It is shown that, especially under sheet-flow conditions, small wave induced net currents are of large importance for the total sand transport rates under these conditions.
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SAJJADI, SHAHRDAD G. "Vorticity generated by pure capillary waves." Journal of Fluid Mechanics 459 (May 25, 2002): 277–88. http://dx.doi.org/10.1017/s0022112002008005.
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Capillary waves, like other surface waves on water, generate a rectified, or time-averaged, vorticity field extending beyond the oscillatory (Stokes) layer at the surface. This vorticity field ω is particularly interesting in relation to the parasitic capillary waves found on the forward slopes of steep gravity waves. Longuet-Higgins (1992) suggested that the rectified vorticity from the parasitic capillaries might contribute significantly to the vorticity observed beneath the crest of the gravity wave. The basic calculations by Longuet-Higgins (1992) were only of the horizontally averaged values of ω. Here we extend his theory by calculating, for pure capillary waves, the space variation of ω, to second order in the steepness of the capillary waves. Thus, the vorticity, and hence velocity, fields are calculated in the oscillatory Stokes layer and just beyond it, to the second order. Good agreement is found both with numerical simulations and with experimental measurements.
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Carmigniani, Remi A., Michel Benoit, Damien Violeau, and Morteza Gharib. "Resonance wave pumping with surface waves." Journal of Fluid Mechanics 811 (December 6, 2016): 1–36. http://dx.doi.org/10.1017/jfm.2016.720.
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In this paper, we present a novel extension of impedance (Liebau) wave pumping to a free-surface condition where resonance pumping could be used for hydraulic energy harvesting. Similar pumping behaviours are reported. Surface envelopes of the free surface are shown and outline two different dynamics: U-tube oscillator and wave/resonance pumping. The latter is particularly interesting, since, from an oscillatory motion, a unidirectional flow with small to moderate oscillations is generated. A linear theory is developed to evaluate pseudo-analytically the resonance frequencies of the pump using eigenfunction expansions, and a simplified model is proposed to understand the main pumping mechanism in this type of pump. It is found that the Stokes mass transport is driving the pump. The conversion of energy from paddle oscillation to mean flow is evaluated. Efficiency up to 22 % is reported.
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YOSHIKAWA, HARUNORI N., and JOSÉ EDUARDO WESFREID. "Oscillatory Kelvin–Helmholtz instability. Part 2. An experiment in fluids with a large viscosity contrast." Journal of Fluid Mechanics 675 (March 23, 2011): 249–67. http://dx.doi.org/10.1017/s0022112011000152.
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The stability of two-layer oscillatory flows was studied experimentally in a cylindrical container with a vertical axis. Two superposed immiscible liquids, differing greatly in viscosity, were set in relative oscillatory motion by alternating container rotation. Waves arising beyond a threshold were observed in detail for small oscillation frequencies ranging from 0.1 to 6 Hz. Measurements were performed on the growth rate and the wavenumber of these waves. The instability threshold was determined from the growth rate data. It was found that the threshold and the wavenumber varied with the frequency. In particular, significantly lower thresholds and longer waves were found than those predicted by the inviscid theory of the oscillatory Kelvin–Helmholtz instability. Favourable agreement with the predictions of an existing viscous theory for small oscillation amplitude flows indicates the important role of viscosity, even at the highest frequency, and suggests a similar mechanism behind the instability as that for the short wave instability in steady Couette flows. A semi-numerical stability determination for finite amplitude flows was also performed to improve the prediction in experiments with a frequency lower than 1 Hz.
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Mason, Martin A. "THE TRANSFORMATION OF WAVES IN SHALLOW WATER." Coastal Engineering Proceedings 1, no. 1 (2010): 3. http://dx.doi.org/10.9753/icce.v1.3.
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The purpose of this paper is to summarize existing knowledge of the processes involved in the movement of progressive oscillatory waves through shallow water and the fundamental principles controlling these processes. Variations in wave characteristics and their physical significance will be discussed as well as agreement between theory and observation. The application of available knowledge to engineering problems is treated in the following chapters.
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Song, Yang, Yan Lin, Ming Xia Zhang, and Pin Le Qin. "The Simulation of Ship Oscillatory Motions in Irregular Waves." Applied Mechanics and Materials 66-68 (July 2011): 1296–300. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.1296.
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Based on the theory of nonlinear random dynamic and ship oscillatory motions, by analyzing the spectrum of the random ocean wave and the force of the ship, the roll and pitch motion equations were erected respectively, then the irregular waves were created according to the superposition theory. Meanwhile, the coupling motion between rolling and heaving was studied, then the time-domain responses were the driving data of the motions simulation. Using VisualBasic, the interaction interface was established. Using MATLAB, the motions were solved. Using OpenGL the 3-D model of ship was described. We just need input the ship and environment parameters then the results will be displayed with the 2-D figures and the 3-D model quickly, then the visualization of ship motions simulation is achieved. The program developed can simulate 3-D ships and can be used for designers to analyze the properties of ship intuitively.
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HODYSS, DANIEL, and TERRENCE R. NATHAN. "The role of forcing in the local stability of stationary long waves. Part 1. Linear dynamics." Journal of Fluid Mechanics 576 (March 28, 2007): 349–76. http://dx.doi.org/10.1017/s0022112006004307.
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The local linear stability of forced, stationary long waves produced by topography or potential vorticity (PV) sources is examined using a quasi-geostrophic barotropic model. A multiple scale analysis yields coupled equations for the background stationary wave and low-frequency (LF) disturbance field. Forcing structures for which the LF dynamics are Hamiltonian are shown to yield conservation laws that provide necessary conditions for instability and a constraint on the LF structures that can develop. Explicit knowledge of the forcings that produce the stationary waves is shown to be crucial to predicting a unique LF field. Various topographies or external PV sources can be chosen to produce stationary waves that differ by asymptotically small amounts, yet the LF instabilities that develop can have fundamentally different structures and growth rates. If the stationary wave field is forced solely by topography, LF oscillatory modes always emerge. In contrast, if the stationary wave field is forced solely by PV, two LF structures are possible: oscillatory modes or non-oscillatory envelope modes. The development of the envelope modes within the context of a linear LF theory is novel.An analysis of the complex WKB branch points, which yields an analytical expres-sion for the leading-order eigenfrequency, shows that the streamwise distribution of absolute instability and convective growth is central to understanding and predicting the types of LF structures that develop on the forced stationary wave. The location of the absolute instability region with respect to the stationary wave determines whether oscillatory modes or envelope modes develop. In the absence of absolute instability, eastward propagating wavetrains generated in the far field can amplify via local convective growth in the stationary wave region. If the stationary wave region is streamwise symmetric (asymmetric), the local convective growth results in a local change in wave energy that is transient (permanent).
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Didenkulova, I., and E. Pelinovsky. "Nonlinear wave effects at the non-reflecting beach." Nonlinear Processes in Geophysics 19, no. 1 (2012): 1–8. http://dx.doi.org/10.5194/npg-19-1-2012.
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Abstract. Nonlinear effects at the bottom profile of convex shape (non-reflecting beach) are studied using asymptotic approach (nonlinear WKB approximation) and direct perturbation theory. In the asymptotic approach the nonlinearity leads to the generation of high-order harmonics in the propagating wave, which result in the wave breaking when the wave propagates shoreward, while within the perturbation theory besides wave deformation it leads to the variations in the mean sea level and wave reflection (waves do not reflect from "non-reflecting" beach in the linear theory). The nonlinear corrections (second harmonics) are calculated within both approaches and compared between each other. It is shown that for the wave propagating shoreward the nonlinear correction is smaller than the one predicted by the asymptotic approach, while for the offshore propagating wave they have a similar asymptotic. Nonlinear corrections for both waves propagating shoreward and seaward demonstrate the oscillatory character, caused by interference of the incident and reflected waves in the second-order perturbation theory, while there is no reflection in the linear approximation (first-order perturbation theory). Expressions for wave set-up and set-down along the non-reflecting beach are found and discussed.
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Grisouard, Nicolas, and Oliver Bühler. "Forcing of oceanic mean flows by dissipating internal tides." Journal of Fluid Mechanics 708 (August 8, 2012): 250–78. http://dx.doi.org/10.1017/jfm.2012.303.
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AbstractWe present a theoretical and numerical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by the oscillatory flow of a barotropic tide over undulating topography and are also subject to dissipation. This extends the classic lee-wave drag problem of atmospheric wave–mean interaction theory to a more complicated oceanographic setting, because now the steady lee waves are replaced by oscillatory internal tides and, most importantly, because now the three-dimensional oceanic mean flow is defined by time averaging over the fast tidal cycles rather than by the zonal averaging familiar from atmospheric theory. Although the details of our computation are quite different, we recover the main action-at-a-distance result from the atmospheric setting, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, we derive an explicit expression for the effective mean force at leading order using a perturbation series in small wave amplitude within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and then compute the effective mean force numerically in a number of idealized examples with simple topographies.
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Aranson, Igor S., Lorenz Kramer, and Andreas Weber. "Theory of interaction and bound states of spiral waves in oscillatory media." Physical Review E 47, no. 5 (1993): 3231–41. http://dx.doi.org/10.1103/physreve.47.3231.
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YANG, T. S., and T. R. AKYLAS. "On asymmetric gravity–capillary solitary waves." Journal of Fluid Mechanics 330 (January 10, 1997): 215–32. http://dx.doi.org/10.1017/s0022112096003643.
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Symme tric gravity–capillary solitary waves with decaying oscillatory tails are known to bifurcate from infinitesimal periodic waves at the minimum value of the phase speed where the group velocity is equal to the phase speed. In the small-amplitude limit, these solitary waves may be interpreted as envelope solitons with stationary crests and are described by the nonlinear Schrödinger (NLS) equation to leading order. In line with this interpretation, it would appear that one may also co nstruct asymmetric solitary waves by shifting the carrier oscillations relative to the envelope of a symmetric solitary wave. This possibility is examined here on the basis of the fifth-order Korteweg–de Vries (KdV) equation, a model for g ravity–capillary waves on water of finite depth when the Bond number is close to 1/3. Using techniques of exponential asymptotics beyond all orders of the NLS theory, it is shown that asymmetric solitary waves of the form suggested by the NLS theory in fact are not possible. On the other hand, an infinity of symmetric and asymmetric solitary-wave solution families comprising two or more NLS solitary wavepackets bifurcate at finite values of the amplitude parameter. The asymptotic results are consistent with numerical solutions of the fifth-order KdV equation. Moreover, the asymptotic theory suggests that such multi-packet gravity–capillary solitary waves also exist in the full water-wave problem near the minimum of t he phase speed.
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Zhang, Weiguo, Lanyun Bian, and Yan Zhao. "Qualitative analysis and solutions of bounded travelling waves for the fluidized-bed modelling equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 2 (2010): 241–57. http://dx.doi.org/10.1017/s030821050900064x.
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We apply the theory of planar dynamical systems to carry out a qualitative analysis for the planar dynamical system corresponding to the fluidized-bed modelling equation. We obtain the global phase portraits of this system under various parameter conditions and the existence conditions of bounded travelling-wave solutions of this equation. According to the discussion on relationships between the behaviours of bounded travelling-wave solutions and the dissipation coefficients ε and δ, we find a critical value λ0 for arbitrary travelling-wave velocity υ. This equation has a unique damped oscillatory solution as ∥ε + δυ∥ < λ0 and ∥ε + δυ∥ ≠ 0, while it has a unique monotone kink profile solitary-wave solution as ∥ε + δυ∥ > λ0. By means of the undetermined coefficients method, we obtain the exact bell profile solitary-wave solution and monotone kink profile solitary-wave solution. Meanwhile, we obtain the approximate damped oscillatory solution. We point out the positions of these solutions in the global phase portraits. Finally, based on integral equations that reflect the relationships between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate damped oscillatory solutions are presented.
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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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Bschorr, O. "Propulsive mechanisms in animal swimming and flying locomotion." Aeronautical Journal 92, no. 912 (1988): 84–90. http://dx.doi.org/10.1017/s0001924000021928.
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Summary The objective of this paper is a description of animal swimming and flying locomotion in terms of wave theory. In this context various oscillatory organs of locomotion, such as flagella, fins and wings, are interpreted as waveguides capable of transmitting mechanical transverse waves. Furthermore, the Poynting concept is used, according to which every type of wave transports not only energy but also momentum. Even with no detailed knowledge of the hydro- and aerodynamic flow fields it is possible to calculate the wave power, the propulsive force, and the propulsive efficiency with the means and methods of vibrational theory alone.
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Nachbin, André. "Kuramoto-Like Synchronization Mediated through Faraday Surface Waves." Fluids 5, no. 4 (2020): 226. http://dx.doi.org/10.3390/fluids5040226.
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A new class of problems in free surface hydrodynamics appeared after the groundbreaking discovery by Yves Couder and Emmanuel Fort. A bouncing droplet in association with Faraday surface waves gives rise to new nonlinear dynamics, in analogy with the pilot-wave proposed by de Broglie. The droplet and the underlying vibrating bath are of silicon oil. A weakly viscous potential theory model should be used. Numerical simulations are presented with one and two bouncing droplets oscillating while confined to their cavities. These oscillators are implicitly coupled by the underlying surface wave field. In certain regimes, the oscillators can spontaneously synchronize, even when placed at a distance. Cavity parameters are varied in order to highlight the sensitive wave-mediated coupling. The present nonlinear wave-mediated oscillator synchronization is more general than that displayed by the celebrated Kuramoto model and therefore of general interest.
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Meron, Ehud. "Phase fronts and synchronization patterns in forced oscillatory systems." Discrete Dynamics in Nature and Society 4, no. 3 (2000): 217–30. http://dx.doi.org/10.1155/s1026022600000212.
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This is a review of recent studies of extended oscillatory systems that are subjected to periodic temporal forcing. The periodic forcing breaks the continuous time translation symmetry and leaves a discrete set of stable uniform phase states. The multiplicity of phase states allows for front structures that shift the oscillation phase byπ/nwheren=1,2,…,hereafterπ/n-fronts. The main concern here is with front instabilities and their implications on pattern formation. Most theoretical studies have focused on the2:1resonance where the system oscillates at half the driving frequency. All front solutions in this case areπ-fronts. At high forcing strengths only stationary fronts exist. Upon decreasing the forcing strength the stationary fronts lose stability to pairs of counter-propagating fronts. The coexistence of counter-propagating fronts allows for traveling domains and spiral waves. In the4:1resonance stationaryπ-fronts coexist withπ/2-fronts. At high forcing strengths the stationaryπ-fronts are stable and standing two-phase waves, consisting of successive oscillatory domains whose phases differ byπ,, prevail. Upon decreasing the forcing strength the stationaryπ-fronts lose stability and decompose into pairs of propagatingπ/2-fronts. The instability designates a transition from standing two-phase waves to traveling four-phase waves. Analogous decomposition instabilities have been found numerically in higher2n:1resonances. The available theory is used to account for a few experimental observations made on the photosensitive Belousov–Zhabotinsky reaction subjected to periodic illumination. Observations not accounted for by the theory are pointed out.
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Smith, Matthew J., Jonathan A. Sherratt, and Nicola J. Armstrong. "The effects of obstacle size on periodic travelling waves in oscillatory reaction–diffusion equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2090 (2007): 365–90. http://dx.doi.org/10.1098/rspa.2007.0198.
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Many natural populations undergo multi-year cycles, and field studies have shown that these can be organized into periodic travelling waves (PTWs). Mathematical studies have shown that large-scale landscape obstacles represent a natural mechanism for wave generation. Here, we investigate how the amplitude and wavelength of the selected waves depend on the obstacle size. We firstly consider a large circular obstacle in an infinite domain for a reaction–diffusion system of ‘ λ – ω ’ type. We use perturbation theory to derive a leading order approximation to the wave generated by the obstacle. This shows the dependence of the wave properties on both parameter values and obstacle size. We find that the limiting values of the amplitude and wavelength are approached algebraically with distance from the obstacle edge, rather than exponentially in the case of a flat boundary. We use our results to predict the properties of waves generated by a large circular obstacle for an oscillatory predator–prey system, via a reduction of the predator–prey model to normal form close to Hopf bifurcation. Our predictions compare well with numerical simulations. We also discuss the implications of these results for wave stability and briefly investigate the effects of obstacles with elliptical geometries.
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Makomaski, A. H. "Numerical Simulation of Oscillations in a Continuous Optical Discharge." Transactions of the Canadian Society for Mechanical Engineering 11, no. 4 (1987): 201–14. http://dx.doi.org/10.1139/tcsme-1987-0023.
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A numerical method based on the assumptions of Forester and Emery is used to study the oscillatory behaviour of the plume and of the thermal wave associated with a point plasma, sustained by continuous optical discharge of a c.w. laser. Computations are carried out to simulate conditions in argon at 4 atm and initially at room temperature. The numerical results explain or confirm many experimental features and generally quantitative agreement with experiment is good. Application of Kimura’s stability theory to the plume suggests aerodynamic instability as the origin of the oscillations. As for flames, these oscillations are associated with waves analogous to the Tollmien-Schlichting waves in laminar boundary layers.
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Dong, G. H., L. Sun, Z. Zong, H. W. An, and Y. X. Wang. "Numerical Analysis of Ship-Generated Waves Action on a Vertical Cylinder." Journal of Ship Research 53, no. 02 (2009): 93–105. http://dx.doi.org/10.5957/jsr.2009.53.2.93.
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In this paper, the action of ship-generated waves on a nearby vertical cylinder is considered in pure theory. Intensive demands of modern sea transportation result in larger and larger ships. These ships generate high waves as they move in calm water. The ship-generated waves can travel long distances without much attenuation. They are so strong that they might cause damage to nearby marine structures (e.g., platforms, river banks, breakwaters, etc.). Therefore, it is necessary to evaluate the forces of ship-generated waves acting on nearby marine structures. The problem turns out to be composed of two problems: evaluation of waves generated by a moving ship (ship-wave problem) and evaluation of the action of ship waves on a cylinder (wave-action problem). Here the wave-action problem is computed in detail with a boundary element method in time domain. And the ship-wave problem is evaluated in the well-known Michell thin-ship theory. Thus, the problem posed in this paper is finally solved using numerical methods by combining the ship-wave and wave-action problems. The numerical analyses of the result are: The resultant forces and moments acting on the cylinder are surprisingly large, characterized by being highly oscillatory. The periods of the oscillations are proportional to ship speed. The actions of ship-generated waves on nearby structures are not negligible. This is a new factor necessary to be considered for design of both marine structures and ships. Meanwhile, the potential fatigue damage resulting from oscillations of the forces and moments should be considered, too.
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Parsons, Sean P., and Jan D. Huizinga. "Effects of gap junction inhibition on contraction waves in the murine small intestine in relation to coupled oscillator theory." American Journal of Physiology-Gastrointestinal and Liver Physiology 308, no. 4 (2015): G287—G297. http://dx.doi.org/10.1152/ajpgi.00338.2014.
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Waves of contraction in the small intestine correlate with slow waves generated by the myenteric network of interstitial cells of Cajal. Coupled oscillator theory has been used to explain steplike gradients in the frequency (frequency plateaux) of contraction waves along the length of the small intestine. Inhibition of gap junction coupling between oscillators should lead to predictable effects on these plateaux and the wave dislocation (wave drop) phenomena associated with their boundaries. It is these predictions that we wished to test. We used a novel multicamera diameter-mapping system to measure contraction along 25- to 30-cm lengths of murine small intestine. There were typically two to three plateaux per length of intestine. Dislocations could be limited to the wavefronts immediately about the terminated wave, giving the appearance of a three-pronged fork, i.e., a fork dislocation; additionally, localized decreases in velocity developed across a number of wavefronts, ending with the terminated wave, which could appear as a fork, i.e., slip dislocations. The gap junction inhibitor carbenoxolone increased the number of plateaux and dislocations and decreased contraction wave velocity. In some cases, the usual frequency gradient was reversed, with a plateau at a higher frequency than its proximal neighbor; thus fork dislocations were inverted, and the direction of propagation was reversed. Heptanol had no effect on the frequency or velocity of contractions but did reduce their amplitude. To understand intestinal motor patterns, the pacemaker network of the interstitial cells of Cajal is best evaluated as a system of coupled oscillators.
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Publicover, N. G., and K. M. Sanders. "Are relaxation oscillators an appropriate model of gastrointestinal electrical activity?" American Journal of Physiology-Gastrointestinal and Liver Physiology 256, no. 2 (1989): G265—G274. http://dx.doi.org/10.1152/ajpgi.1989.256.2.g265.
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Mathematical models based on relaxation oscillators have heavily influenced the terminology and experimental designs of investigations in gastrointestinal motility for nearly two decades. Relaxation oscillator equations have been used to stimulate the electrical activities of the esophagus, stomach, small intestine, colon, and rectosigmoid region. It has been suggested that many attributes of gastrointestinal electrical activity cannot be adequately explained by classic "core-conductor" or "cable" models of excitation and conduction. This article critically reviews the relaxation oscillator model and provides an explanation for each of the putative inadequacies of core-conductor theory. Furthermore, we question whether relaxation oscillator equations are able to simulate the waveforms of gastrointestinal slow waves, alterations in waveform in response to drugs or electrical stimulation, patterns of slow-wave activity when stimulated at physiological frequencies, prolonged periods of constant resting membrane potential between gastric slow waves and electrotonic spread into inactive regions. We conclude that the relaxation oscillator equations do not fully describe gastrointestinal electrical activity; excitation and propagation can be modeled by a theory that provides for morphological features, ionic conductances, and other elements included in the cable equations.
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Mok, Y., and G. Einaudi. "Resistive decay of Alfvén waves in a non-uniform plasma." Journal of Plasma Physics 33, no. 2 (1985): 199–208. http://dx.doi.org/10.1017/s0022377800002440.
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The effect of resistive dissipation on the propagation of an MHD disturbance in a non-uniform plasma is examined. The present analysis, based on a boundarylayer technique, shows the existence of resistive normal modes with complex eigenfrequencies. The real part of the eigenfrequency is associated with an oscillatory behaviour and defines the location in space of the layer where resistivity is important. The dissipation mechanism is responsible for the damping of the wave, in contrast with previous works in which the ideal MHD theory was used.
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Felsen, L. B. "Progressing and Oscillatory Waves for Hybrid Synthesis of Source-Excited Propagation and Diffraction." Journal of Applied Mechanics 52, no. 1 (1985): 27–32. http://dx.doi.org/10.1115/1.3169022.
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Time-harmonic and transient propagation and diffraction phenomena can be described alternatively by progressing and oscillatory waves that express the wave motion in terms of direct and multiple wavefronts or rays, and in terms of resonances or modes, respectively. Each description is convenient and physically appealing when it requires few contributing elements. It is inconvenient and physically less transparent when it requires many elements, and it would then be desirable to combine many inconvenient elements into fewer convenient ones. For a variety of propagation environments, including layered or other guiding regions, this can be done by expressing a group of rays collectively in terms of modes, or a group of modes collectively in terms of rays. When this ray-mode equivalence is invoked selectively, there emerges a hybrid representation that combines ray fields and modal fields in uniquely defined proportions. The theory is based on Poisson summation and on alternative treatments of wave spectra. It has been applied to electromagnetics, underwater acoustics, and SH elastic motion, and is now being extended to general propagation in elastic media.
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Sammarco, Paolo, Chiang C. Mei, and Karsten Trulsen. "Nonlinear resonance of free surface waves in a current over a sinusoidal bottom: a numerical study." Journal of Fluid Mechanics 279 (November 25, 1994): 377–405. http://dx.doi.org/10.1017/s0022112094003940.
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We examine the free surface flow over a fixed bed covered by rigid sinusoidal dunes. The mean current velocity is near the critical value at which the linearized theory predicts unbounded response. By allowing transients we examine the instability of the steady and nonlinear solution of Mei (1969) and the possibility of chaos when the current has a small oscillatory component.
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Hassoul, Sara, Salah Menouar, Jeong Ryeol Choi, and Ramazan Sever. "Quantum dynamics of a general time-dependent coupled oscillator." Modern Physics Letters B 35, no. 14 (2021): 2150230. http://dx.doi.org/10.1142/s0217984921502304.
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Quantum dynamical properties of a general time-dependent coupled oscillator are investigated based on the theory of two-dimensional (2D) dynamical invariants. The quantum dynamical invariant of the system satisfies the Liouville–von Neumann equation and it coincides with its classical counterpart. The mathematical formula of this invariant involves a cross term which couples the two oscillators mutually. However, we show that, by introducing two pairs of annihilation and creation operators, it is possible to uncouple the original invariant operator so that it becomes the one that describes two independent subsystems. The eigenvalue problem of this decoupled quantum invariant can be solved by using a unitary transformation approach. Through this procedure, we eventually obtain the eigenfunctions of the invariant operator and the wave functions of the system in the Fock state. The wave functions that we have developed are necessary in studying the basic quantum characteristics of the system. In order to show the validity of our theory, we apply our consequences to the derivation of the fluctuations of canonical variables and the uncertainty products for a particular 2D oscillatory system whose masses are exponentially increasing.
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VLACHOMITROU, M., and N. PELEKASIS. "Short- to long-wave resonance and soliton formation in boundary-layer interaction with a liquid film." Journal of Fluid Mechanics 660 (July 12, 2010): 162–96. http://dx.doi.org/10.1017/s0022112010002612.
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Dynamic interaction between a boundary layer of air and a liquid film is investigated in this paper. The low air-to-film-viscosity ratio is considered in which case the boundary layer is quasi-steady on the time scale within which interfacial waves develop. The base flow consists of a boundary layer that drags a film of constant shear. Linear analysis, in the context of triple-deck theory, predicts the formation of a wavepacket of capillary waves that advances and spreads with time. The Froude number of de-/anti-icing fluids or water interacting with air falls well within the supercritical regime, i.e. Fr > FrCr. Numerical simulations of such flow systems were performed in the context of triple-deck theory, and they do not exhibit wave saturation or formation of uniform wavetrains. The long-term interaction is mainly dependent on film inertia as this is characterized by parameter = (μ/μf)2(ρf/ρ), which involves film and air viscosity and density ratios, and the dimensionless film thickness, H0, and shear, λ, provided by the base flow. Weakly nonlinear analysis taking into consideration mean drift, i.e. generation of long waves, due to self-interaction of the linear wave to O(ϵ2) in amplitude of the initial disturbance, reveals resonance between the wavepacket predicted by linear theory and long waves when the group velocity of the former happens to coincide with the phase velocity, H0λ, of long interfacial waves. Numerical simulations with anti-icing fluids and water verify this pattern. In both cases, long waves eventually dominate the dynamics and, as they are modulated with time, they lead to soliton-type structures. Anti-icing fluids eventually exhibit oscillatory spikes whose mean value never exceeds 2H0, roughly. Water films exhibit a single spike that keeps growing, thus generating a large separation bubble.
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El-Labany, S. K. "Weakly relativistic effect on the modulation of nonlinear ion-acoustic waves in a warm plasma." Journal of Plasma Physics 54, no. 3 (1995): 295–308. http://dx.doi.org/10.1017/s0022377800018523.
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The derivative expansion perturbation method is applied to investigate the modulation of nonlinear ion-acoustic waves in a weakly relativistic warm plasma. At the second order of perturbation theory, a nonlinear Schrödingertype equation for the complex amplitude of the perturbed ion density is obtained. The coefficients in this equation show that the condition of modulational stability is modified by the relativistic effect as well as by the finite ion temperature. The association between the small-wavenumber limit of the nonlinear Schrödinger-type equation and the oscillatory solution of the Korteweg-de Vries equation obtained by reductive perturbation theory is considered. Different limits are considered in order to compare with previous work.
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SANCHEZ, NORMA G. "CLASSICAL AND QUANTUM STRINGS IN PLANE WAVES, SHOCK WAVES AND SPACE–TIME SINGULARITIES: SYNTHESIS AND NEW RESULTS." International Journal of Modern Physics A 18, no. 26 (2003): 4797–809. http://dx.doi.org/10.1142/s0217751x03015787.
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Key issues and essential features of classical and quantum strings in gravitational plane waves, shock waves and space–time singularities are synthetically understood. This includes the string mass and mode number excitations, energy–momentum tensor, scattering amplitudes, vacuum polarization and wave-string polarization effect. The role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) and that of the space–time singularities is clearly exhibited. This throws light on the issue of singularities in string theory which can be thus classified and fully physically characterized in two different sets: strong singularities (poles of order ≥ 2, and black holes) where the string motion is collective and nonoscillating in time, outgoing states and scattering sector do not appear, the string does not cross the singularities; and weak singularities (poles of order < 2, (Dirac δ belongs to this class) and conic/orbifold singularities) where the whole string motion is oscillatory in time, outgoing and scattering states exist, and the string crosses the singularities. Common features of strings in singular wave backgrounds and in inflationary backgrounds are explicitly exhibited. The string dynamics and the scattering/excitation through the singularities (whatever their kind: strong or weak) is fully physically consistent and meaningful.
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Sun, S. M., and M. C. Shen. "Exact Theory of Solitary Waves in a Stratified Fluid with Surface Tension. Part II. Oscillatory Case." Journal of Differential Equations 105, no. 1 (1993): 117–66. http://dx.doi.org/10.1006/jdeq.1993.1085.
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Hussain, Manzoor, and Sirajul Haq. "A computational study of solitary wave solutions of Kawahara-type equations by meshless spectral interpolation method." International Journal of Modern Physics C 30, no. 12 (2019): 1950102. http://dx.doi.org/10.1142/s012918311950102x.
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In this paper, a meshless spectral radial point interpolation (MSRPI) method using weighted [Formula: see text]-scheme is formulated for the numerical solutions of a class of nonlinear Kawahara-type evolutionary equations. The formulated method is applied for simulation of single and double solitary waves motion, wave generation and oscillatory shock waves propagation. Quality of approximation is measured via discrete [Formula: see text], [Formula: see text] and [Formula: see text] error norms. Three invariant quantities corresponding to mass, momentum and energy are also computed for the method validation. Stability analysis of the proposed method is briefly discussed and verified computationally. Comparison of the obtained results are made with other existing results in the literature revealing the method superiority.
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VANNESTE, JACQUES. "A nonlinear critical layer generated by the interaction of free Rossby waves." Journal of Fluid Mechanics 371 (September 25, 1998): 319–44. http://dx.doi.org/10.1017/s0022112098002237.
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Two free waves propagating in a parallel shear flow generate a critical layer when their nonlinear interaction induces a perturbation whose phase velocity matches the basic-state velocity somewhere in the flow domain. The condition necessary for this to occur may be interpreted as a resonance condition for a triad formed by the two waves and a (singular) mode of the continuous spectrum associated with the shear. The formation of the critical layer is investigated in the case of freely propagating Rossby waves in a two-dimensional inviscid flow in a β-channel.A weakly nonlinear analysis based on a normal-mode expansion in terms of Rossby waves and modes of the continuous spectrum is developed; it leads to a system of amplitude equations describing the evolution of the two Rossby waves and of the modes of the continuous spectrum excited during the interaction. The assumption of weak nonlinearity is not however self-consistent: it breaks down because nonlinearity always becomes strong within the critical layer, however small the initial amplitudes of the Rossby waves. This demonstrates the relevance of nonlinear critical layers to monotonic, stable, unforced shear flows which sustain wave propagation.A nonlinear critical-layer theory is developed that is analogous to the well-known theory for forced critical layers. Differences arise because of the presence of the Rossby waves: the vorticity in the critical layer is advected in the cross-stream direction by the oscillatory velocity field due to the Rossby waves. An equation is derived which governs the modification of the Rossby waves that results from their interaction; it indicates that the two Rossby waves are undisturbed at leading order. An analogue of the Stewartson–Warn–Warn analytical solution is also considered.
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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 (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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Gordillo, Leonardo, and Nicolás Mujica. "Measurement of the velocity field in parametrically excited solitary waves." Journal of Fluid Mechanics 754 (August 14, 2014): 590–604. http://dx.doi.org/10.1017/jfm.2014.416.
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AbstractParametrically excited solitary waves emerge as localized structures in high-aspect-ratio free surfaces subject to vertical vibrations. Herein, we provide the first experimental characterization of the hydrodynamics of these waves using particle image velocimetry. We show that the underlying velocity field of parametrically excited solitary waves is primarily composed of a subharmonic oscillatory component. Our results confirm the accuracy of Hamiltonian models with added dissipation in describing this field. Remarkably, our measurements also uncover the onset of a streaming velocity field which we show to be as important as other crucial nonlinear terms in the current theory. Using vorticity equations, we show that the streaming pattern arises from the coupling of the potential bulk flow with the oscillating boundary layers on the vertical walls. Numerical simulations provide good agreement between this model and experiments.
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Zhao, Yan, and Weiguo Zhang. "A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results." Journal of Applied Mathematics 2014 (2014): 1–19. http://dx.doi.org/10.1155/2014/935915.
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This paper is focused on studying approximate damped oscillatory solutions of the compound KdV-Burgers-type equation with nonlinear terms of any order. By the theory and method of planar dynamical systems, existence conditions and number of bounded traveling wave solutions including damped oscillatory solutions are obtained. Utilizing the undetermined coefficients method, the approximate solutions of damped oscillatory solutions traveling to the left are presented. Error estimates of these approximate solutions are given by the thought of homogeneous principle. The results indicate that errors between implicit exact damped oscillatory solutions and approximate damped oscillatory solutions are infinitesimal decreasing in the exponential form.
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Trowbridge, John, Malcolm Scully, and Christopher R. Sherwood. "The Cospectrum of Stress-Carrying Turbulence in the Presence of Surface Gravity Waves." Journal of Physical Oceanography 48, no. 1 (2018): 29–44. http://dx.doi.org/10.1175/jpo-d-17-0016.1.
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AbstractThe cospectrum of the horizontal and vertical turbulent velocity fluctuations, an essential tool for understanding measurements of the turbulent Reynolds shear stress, often departs in the ocean from the shape that has been established in the atmospheric surface layer. Here, we test the hypothesis that this departure is caused by advection of standard boundary layer turbulence by the random oscillatory velocities produced by surface gravity waves. The test is based on a model with two elements. The first is a representation of the spatial structure of the turbulence, guided by rapid distortion theory, and consistent with the one-dimensional cospectra that have been measured in the atmosphere. The second model element is a map of the spatial structure of the turbulence to the temporal fluctuations measured at fixed sensors, assuming advection of frozen turbulence by the velocities associated with surface waves. The model is adapted to removal of the wave velocities from the turbulent fluctuations using spatial filtering. The model is tested against previously published laboratory measurements under wave-free conditions and two new sets of measurements near the seafloor in the coastal ocean in the presence of waves. Although quantitative discrepancies exist, the model captures the dominant features of the laboratory and field measurements, suggesting that the underlying model physics are sound.
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Pfirsch, D. "Nonlinear Instabilities, Negative Energy Modes and Generalized Cherry Oscillators." Zeitschrift für Naturforschung A 45, no. 7 (1990): 839–46. http://dx.doi.org/10.1515/zna-1990-0701.
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AbstractIn 1925 Cherry [1] discussed two oscillators of positive and negative energy that are nonlinearly coupled in a special way, and presented a class of exact solutions of the nonlinear equations showing explosive instability independent of the strength of the nonlinearity and the initial amplitudes. In this paper Cherry's Hamiltonian is transformed into a form which allows a simple physical interpretation. The new Hamiltonian is generalized to three nonlinearly coupled oscillators; it corresponds to three-wave interaction in a continuum theory, like the Vlasov-Maxwell theory, if there exist linear negative energy waves [2-4, 5, 6], Cherry was able to present a two-parameter solution set for his example which would, however, allow a four-parameter solution set, and, as a first result, an analogous three-parameter solution set for the resonant three-oscillator case is obtained here which, however, would allow a six-parameter solution set. Nonlinear instability is therefore proven so far only for a very small part of the phase space of the oscillators. This paper gives in addition the complete solution for the three-oscillator case and shows that, except for a singular case, all initial conditions, especially those with arbitrarily small amplitudes, lead to explosive behaviour. This is true of the resonant case. The non-resonant oscillators can sometimes also become explosively unstable, but the initial amplitudes must not be infinitesimally small. A few examples are presented for illustration.
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Xu, Jian-Jun. "Interfacial wave theory for oscillatory finger formation in a Hele–Shaw cell: a comparison with experiments." European Journal of Applied Mathematics 7, no. 2 (1996): 169–99. http://dx.doi.org/10.1017/s095679250000228x.
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This paper is devoted to an analysis of the formation of oscillatory viscous fingers in a Hele-Shaw cell on the basis of the interfacial wave theory, previously established for the pattern formation dynamics in dendrite growth, as well as in the classic Saffman–Taylor flow. In particular, we study the problem of selection and persistence of oscillatory fingers with a tiny bubble at the finger tip. We obtain uniformly valid asymptotic solutions for this problem, and derive the linear, global wave instability mechanism for this more complicated system. The global, neutrally stable modes are computed in a large region of parameters, which select the form of oscillatory fingers in the later stage of evolution. We have compared the theoretical predictions with the experimental data by Couder et al. (1986) and by Kopf-Sill & Homsy (1987), and found excellent quantitative agreement.
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Padmanabhan, B., and R. C. Ertekin. "On the Interaction of Waves With Intake/Discharge Flows Originating From a Freely-Floating Body." Journal of Offshore Mechanics and Arctic Engineering 125, no. 1 (2003): 41–47. http://dx.doi.org/10.1115/1.1537724.
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A linear theory is developed to obtain the motions of a two-dimensional, freely floating body (from which steady intake/discharge flows originate) that encounters incoming waves. The boundary-value problem is formulated within the assumptions of linear potential theory by decomposing the total potential into its oscillatory and steady components. The steady potential is further decomposed into the double-model and perturbation potentials. The time-harmonic potential is coupled with the steady potential through the free-surface condition. The potentials are obtained by use of the quadratic boundary-element method based on the Rankine source. The effect of the steady intake/discharge flows on the diffraction loads, hydrodynamic force coefficients, as well as the motions of a two-dimensional prismatic body floating on the free surface are presented. It is shown that the exciting wave forces and the hydrodynamic coefficients other than the damping coefficients are not appreciably affected in the case of low intake/discharge Froude numbers that are estimated, for example, for a 100 MW floating OTEC plant.
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TRIBECHE, MOULOUD, and ABDERREZAK BERBRI. "Weakly nonlinear dust ion-acoustic waves in a charge varying dusty plasma with non-thermal electrons." Journal of Plasma Physics 74, no. 2 (2008): 245–59. http://dx.doi.org/10.1017/s0022377807006812.
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AbstractThe weakly nonlinear dynamics of dust ion-acoustic waves (DIAWs) are investigated in a dusty plasma consisting of hot ion fluid, variable charge stationary dust grains and non-thermally distributed electrons. The Korteweg–de Vries equation, as well as the Korteweg–de Vries–Burgers equation, are derived on the basis of the well-known reductive perturbation theory. It is shown that, due to electron non-thermality and finite ion temperature, the present dusty plasma model can support compressive as well as rarefactive DIA solitary waves. Furthermore, there may exist collisionless DIA shock-like waves which have either monotonic or oscillatory behavior, the properties of which depend sensitively on the number of fast non-thermal electrons. The results complement and provide new insights into previously published results on this problem (Mamun, A. A. and Shukla, P. K. 2002 IEEE Trans. Plasma Sci. 30, 720).
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Šimko, Milan, Miroslav Gutten, Milan Chupáč, and Daniel Korenčiak. "The Application of the Theory of Synthesis of a Delay Line with a Surface Acoustic Wave for a Single-Mode Oscillator of Electric Signals in Some Sensors of Non-Electrical Quantities." Metrology and Measurement Systems 24, no. 3 (2017): 563–76. http://dx.doi.org/10.1515/mms-2017-0040.
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AbstractThe paper deals with the issue of constructing delay lines on the basis of surface acoustic waves and their application to single-mode oscillators. As a result of a theoretical analysis concrete delay lines are proposed.In the contribution, there is presented a theory of designing a symmetrical mismatched and matched delay line for a single-mode oscillator of electrical signals on the basis of which there were designed and fabricated acoustic-electronic components for sensors of non-electrical quantities.From the experimental results it can be stated that all of six designed and fabricated delay lines can be effectively used in the construction of single-mode oscillators.
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Mann, Brian P., and Keith A. Young. "An empirical approach for delayed oscillator stability and parametric identification." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2071 (2006): 2145–60. http://dx.doi.org/10.1098/rspa.2006.1677.
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This paper investigates a semi-empirical approach for determining the stability of systems that can be modelled by ordinary differential equations with a time delay. This type of model is relevant to biological oscillators, machining processes, feedback control systems and models for wave propagation and reflection, where the motion of the waves themselves is considered to be outside the system model. A primary aim is to investigate the extension of empirical Floquet theory to experimental or numerical data obtained from time-delayed oscillators. More specifically, the reconstructed time series from a numerical example and an experimental milling system are examined to obtain a finite number of characteristic multipliers from the reduced order dynamics. A secondary goal of this work is to demonstrate a benefit of empirical characteristic multiplier estimation by performing system identification on a delayed oscillator. The principal results from this study are the accurate estimation of delayed oscillator characteristic multipliers and the utilization the empirical results for parametric identification of model parameters. Combining these results with previous research on an experimental milling system provides a particularly relevant result—the first approach for identifying all model parameters for stability prediction directly from the cutting process vibration history.
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GAO, PENG, and XI-YUN LU. "Instability of an oscillatory fluid layer with insoluble surfactants." Journal of Fluid Mechanics 595 (January 8, 2008): 461–90. http://dx.doi.org/10.1017/s0022112007009512.
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The linear stability of an infinite fluid layer with a deformable free surface covered by an insoluble surfactant and bounded below by a horizontal rigid plate oscillating in its own plane is studied based on the Floquet theory. The differential system governing the stability problem for perturbations of arbitrary wavenumbers is solved numerically by a Chebyshev collocation method. Stability boundaries are obtained in a wide range of amplitude and frequency of the modulation as well as surfactant elasticity. Results show that the presence of the surfactant may significantly stabilize (destabilize) the flow by raising (lowering) the critical Reynolds number associated with the onset of instability. The effect of the surfactant plays a stabilizing role for small surfactant elasticity and a destabilizing one for relatively large surfactant elasticity. The destabilizing effect of the surfactant on the stability of flows with a zero-shear surface is found for the first time. The disturbance modes in the form of travelling waves may be induced by the surfactant and dominate the instability of the flow.
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Liu, Philip L. F., Matthew H. Davis, and Sean Downing. "Wave-induced boundary layer flows above and in a permeable bed." Journal of Fluid Mechanics 325 (October 25, 1996): 195–218. http://dx.doi.org/10.1017/s0022112096008087.
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In this paper, the oscillatory and steady streaming velocities over a permeable bed are studied both theoretically and experimentally. Three different sizes of glass beads are used to construct permeable beds in laboratory experiments: the diameters of the glass beads are 0.5 mm, 1.5 mm, and 3.0 mm, respectively. Several experiments are performed using different wave parameters. A one-component laser-doppler velocimeter (LDV) is used to measure the horizontal velocity component inside the Stokes boundary layer above the solid and permeable surfaces. It is observed that neither oscillatory nor steady velocity components vanish on the permeable surface. The ‘slip velocities’ increase with increasing permeability. Based on the laminar flow assumption and the order of magnitude of the parameters used in the experiments, a perturbation theory is developed for the oscillatory velocity and the steady wave-induced streaming in the boundary layers above and inside the permeable bed. The theory confirms many experimental observations. The theory also provides the damping rate and the phase changes caused by the permeable bed.
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MARSHALL, J. S. "Particle clustering in periodically forced straining flows." Journal of Fluid Mechanics 624 (April 10, 2009): 69–100. http://dx.doi.org/10.1017/s0022112008005326.
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Numerous biomedical and industrial applications require separation or sorting of particles in systems in which it is undesirable to allow particle adhesion to a surface, such as a centrifuge wall and a filter fibre. Such systems typically involve either adhesive particles which could easily foul such surfaces or very delicate particles as is the case with suspensions of biological cells. The current study explores an approach for particle separation based on exposure to an oscillating straining flow, which would be typical for peristaltic and other types of contractive wall motions in a channel or tube. We find that particles immersed in an oscillating straining flow are attracted to the nodal points of the straining field, a phenomenon which we refer to as ‘oscillatory clustering’. A simplified theory of this process is developed for cases with isolated particles immersed in an unbounded uniform straining flow, in which the particle motion is found to be governed by a damped Mathieu equation. Moreover, the drift velocity imposed on particles through oscillatory clustering is sufficient to suspend them against a downward gravitational force in a limit-cycle oscillatory path. Theoretical approximations for the average suspension height and oscillation amplitude are obtained. A discrete-element method (DEM) for colliding and adhesive particles is then employed to examine oscillatory clustering for more realistic systems in which particles collide with each other and with container walls. The DEM is used to examine oscillatory clustering of a particle suspension in an oscillating box and for standing peristaltic waves in a channel, both with and without particle adhesion forces and gravitational forces.
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Webber, Joseph J., and Herbert E. Huppert. "Stokes drift in coral reefs with depth-varying permeability." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2179 (2020): 20190531. http://dx.doi.org/10.1098/rsta.2019.0531.
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In his famous paper of 1847 (Stokes GG. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8 , 441–455), Stokes introduced the drift effect of particles in a fluid that is undergoing wave motion. This effect, now known as Stokes drift, is the result of differences between the Lagrangian and Eulerian velocities of the fluid element and has been well-studied, both in the laboratory and as a mechanism of mass transport in the oceans. On a smaller scale, it is of vital importance to the hydrodynamics of coral reefs to understand drift effects arising from waves on the ocean surface, transporting nutrients and oxygen to the complex ecosystems within. A new model is proposed for a class of coral reefs in shallow seas, which have a permeable layer of depth-varying permeability. We then note that the behaviour of the waves above the reef is only affected by the permeability at the top of the porous layer, and not its properties within, which only affect flow inside the porous layer. This model is then used to describe two situations found in coral reefs; namely, algal layers overlying the reef itself and reef layers whose permeability decreases with depth. This article is part of the theme issue ‘Stokes at 200 (part 2)’.