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

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.

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

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.

Magnetic trajectories corresponding to Killing magnetic fields in a three-dimensional warped product

2020 ◽  
Vol 17 (14) ◽  
pp. 2050212
Author(s):  
Zafar Iqbal ◽  
Joydeep Sengupta ◽  
Subenoy Chakraborty
Keyword(s):  
Magnetic Fields ◽  
Warped Product ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Charged Particles ◽  
Open Interval ◽  
Product Formula ◽  
Warping Function ◽  
Killing Vector Fields

The aim of this paper is to investigate Killing magnetic trajectories of varying electrically charged particles in a three-dimensional warped product [Formula: see text] with positive warping function [Formula: see text], where [Formula: see text] is an open interval in [Formula: see text] equipped with an induced semi-Euclidean metric on [Formula: see text]. First, Killing vector fields on [Formula: see text] are characterized and it is observed that lifts to [Formula: see text] of Killing vector fields tangent to [Formula: see text] are also Killing on [Formula: see text]. Now, any Killing vector field on [Formula: see text] corresponds to a Killing magnetic field on [Formula: see text]. Magnetic trajectories (also known as magnetic curves) of charged particles which move under the influence of Lorentz force generated by Killing magnetic fields on [Formula: see text] are obtained in both Riemannian and Lorentzian cases. Moreover, some examples are exhibited with pictures determining Killing magnetic trajectories in hyperbolic [Formula: see text]-space [Formula: see text] modeled by the Riemannian warped product [Formula: see text]. Furthermore, some examples of spacelike, timelike and lightlike Killing magnetic trajectories are given with their possible graphs in the Lorentzian warped product [Formula: see text].

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