Three-dimensional standing waves on an obliquely flowing film

1988 ◽  
Vol 28 (4) ◽  
pp. 618-624
Author(s):  
S. V. Alekseenko ◽  
S. I. Shtork
Keyword(s):  
Three Dimensional ◽  
Standing Waves

The two-sided lid-driven cavity: experiments on stationary and time-dependent flows

2002 ◽  
Vol 450 ◽  
pp. 67-95 ◽  
Author(s):  
CH. BLOHM ◽  
H. C. KUHLMANN
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Flow State ◽  
Incompressible Fluid Flow ◽  
Velocity Measurements ◽  
Driven Cavity ◽  
Rectangular Container ◽  
Hot Film

The incompressible fluid flow in a rectangular container driven by two facing sidewalls which move steadily in anti-parallel directions is investigated experimentally for Reynolds numbers up to 1200. The moving sidewalls are realized by two rotating cylinders of large radii tightly closing the cavity. The distance between the moving walls relative to the height of the cavity (aspect ratio) is Γ = 1.96. Laser-Doppler and hot-film techniques are employed to measure steady and time-dependent vortex flows. Beyond a first threshold robust, steady, three-dimensional cells bifurcate supercritically out of the basic flow state. Through a further instability the cellular flow becomes unstable to oscillations in the form of standing waves with the same wavelength as the underlying cellular flow. If both sidewalls move with the same velocity (symmetrical driving), the oscillatory instability is found to be tricritical. The dependence on two sidewall Reynolds numbers of the ranges of existence of steady and oscillatory cellular flows is explored. Flow symmetries and quantitative velocity measurements are presented for representative cases.

scholarly journals Two-Layer Tidal Circulation in a Frictional, Rotating Basin

2010 ◽  
Vol 40 (6) ◽  
pp. 1390-1404 ◽  
Author(s):  
Clinton D. Winant
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Internal Tides ◽  
Surface Pattern ◽  
Layer Model ◽  
Interface Deformation ◽  
Tidal Circulation ◽  
Density Anomaly ◽  
Two Layer Model

Abstract The three-dimensional tidal circulation in an elongated basin of arbitrary depth is described with a coupled barotropic and baroclinic two-layer model on the f plane. As long as friction is not dominant, near-standing waves are present on the interface as well as on the surface. The surface pattern is principally determined by the product of the tidal barotropic wavenumber by the basin length. The interface deformation is determined by a baroclinic equivalent, usually a much larger number. As a result, the shape of the interface is characterized by horizontally smaller features than the surface. If the product of the tidal baroclinic wavenumber by the basin width is greater than one, both lateral and axial modes can be excited at the interface. If these modes are near resonant, large internal tides can be forced directly by the co-oscillating surface tide at the basin entrance. The amplitude and phase of the baroclinic component are sensitive functions of the density anomaly and the interface depth. As a result, the phase and amplitude of the interface vary by large amounts with comparatively small changes in those parameters. The model behavior is qualitatively consistent with observations in fjords and straits.

Three-Dimensional Containment of Charged Particles by Orthogonal Standing Waves

1963 ◽  
Vol 131 (2) ◽  
pp. 495-500 ◽  
Author(s):  
A. R. Shapiro ◽  
W. K. R. Watson
Keyword(s):  
Three Dimensional ◽  
Charged Particles ◽  
Standing Waves

Two- and three-dimensional standing waves in a reaction-diffusion system

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
Tamás Bánsági ◽  
Vladimir K. Vanag ◽  
Irving R. Epstein
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System

Parameters for polarization gradients in three-dimensional electromagnetic standing waves

1997 ◽  
Vol 56 (5) ◽  
pp. 4012-4022 ◽  
Author(s):  
S. A. Hopkins ◽  
A. V. Durrant
Keyword(s):  
Three Dimensional ◽  
Standing Waves

Separation of Traveling and Standing Waves in a Rigid-Walled Circular Duct Containing an Intermediate Impedance Discontinuity

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Yongxiong Xiao ◽  
Antoine Blanchard ◽  
Yao Zhang ◽  
Huancai Lu ◽  
D. Michael McFarland ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Standing Waves ◽  
Side Branch ◽  
Element Analysis ◽  
Circular Duct ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Impedance Discontinuity

In this paper, we study the phenomenon of separation of traveling and standing waves in a one-dimensional rigid-walled circular duct. The underlying mechanism for separation, mode complexity, is linear and introduced here by a damped side branch representing an impedance discontinuity. The left end of the duct is driven at a single frequency by a harmonic acoustic source, and the right end is a rigid termination. The position and impedance of the side branch are independent parameters in the analysis. Sufficient conditions for acoustic wave separation in the duct are derived analytically and employed in a three-dimensional finite element analysis to verify the theoretical result. A physical experiment, consisting of a circular duct with a damped side branch, was constructed based on analytical predictions, the physical parameters were measured or identified, and its performance was documented. These experimental parameters were employed in a second three-dimensional finite element analysis to obtain a direct comparison with experimental results. The comparison reveals the extent to which higher-order (unmodeled) effects degrade the separation phenomenon. It is demonstrated that an intermediate damped side branch used as a nonresonant device can be predictively designed to achieve nearly ideal separation of traveling and standing waves in a rigid-walled circular duct in order to direct and control acoustic energy transmission through the duct system.

An experimental study of standing waves

1953 ◽  
Vol 218 (1132) ◽  
pp. 44-59 ◽  
Keyword(s):  
Small Amplitude ◽  
Wave Length ◽  
Three Dimensional ◽  
Standing Waves ◽  
Close Approximation ◽  
Frequency Curve ◽  
Free Standing ◽  
Experimental Conditions ◽  
The Moment ◽  
Good Agreement

The experiments here described were designed to test experimentally some conclusions about free standing waves recently reached analytically by Penney & Price. A close approximation to free oscillations was produced in a tank by wave makers operating with small amplitude and at frequencies where great amplification occurred, owing to resonance. The amplitude-frequency curve proved to consist of two non-intersecting branches, a result which can be explained theoretically. A striking prediction made by Penney & Price was that when the height of the crests of standing waves reaches about 0·15 wave-length they will become pointed, in the form of a 90° ridge. Higher waves were expected to be unstable because the downward acceleration of the free surface near the crest would exceed that of gravity. The experimental conditions necessary for producing a crest in the form of an angled ridge were found and the wave photographed in this condition. Good agreement was found with the calculated form of the profile of the highest wave, which had an angle very near to 90°. The predicted instability for two-dimensional waves was found to begin at the moment the crest became a sharp ridge. It rapidly assumed a three-dimensional character which was revealed by two photographic techniques. Even when the amplitude of oscillation of the wave makers was only 0·85°, violent types of instability developed which produced effects that are here recorded.

The Conservation of Energy and Momentum in the Positron-Electron Annihilation According to Complete Relativity

2014 ◽  
Vol 5 (3) ◽  
pp. 854-858
Author(s):  
Giuseppe Bellotti
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Energy Conditions ◽  
Conservation Of Energy ◽  
Electron Positron ◽  
Pair Annihilation ◽  
Conservation Of Momentum ◽  
Energy And Momentum ◽  
The Right ◽  
Electron Positron Pair

According to Complete Relativity (an improvement of Special Relativity where a new postulate was introduced: an electron cannot move at average speeds less than  u0 = αc / π  where  α  is the constant of fine structure and  c  is the speed of light), and with the hypothesis that the electron and positron are two three-dimensional electromagnetic spherical standing waves, the electromagnetic standing waves of an electron-positron pair can overlap in the low energy conditions and generate a single  γ ray  of  E = 1.022  MeV.  Instead the actual physical theories consider a model of positron-electron pair annihilation, where conservation of momentum requires the creation of two 511 keV photons moving toward opposite directions. But in the paper we do not consider any photons: there is only a progressive electromagnetic wave compound by two electromagnetic standing waves. Only a thorough test will be able to decide the right model.

scholarly journals Existence and Stability of Standing Waves For Schrödinger-Poisson-Slater Equation

2007 ◽  
Vol 7 (3) ◽  
Author(s):  
Hiroaki Kikuchi
Keyword(s):  
Variational Methods ◽  
Standing Wave ◽  
Nonlinear Term ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Standing Waves ◽  
Existence And Stability ◽  
Three Dimensional Space

AbstractWe study the existence and stability of standing wave for the Schrödinger-Poisson-Slater equation in three dimensional space. Let p be the exponent of the nonlinear term. Then we first show that standing wave exists for 1 < p < 5. Next, we show that when 1 < p < 7/3 and p ≠ 2, standing wave is stable for some ω > 0. We also show that when 7/3 < p < 5, standing wave is unstable for some ω > 0. Furthermore, we investigate the case of p = 2. We prove these results by using variational methods.

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